diff --git a/dev/404.html b/dev/404.html index e513378..e9a6239 100644 --- a/dev/404.html +++ b/dev/404.html @@ -8,14 +8,14 @@ - +
- + \ No newline at end of file diff --git a/dev/api/00_public.html b/dev/api/00_public.html index 2268de9..fa95900 100644 --- a/dev/api/00_public.html +++ b/dev/api/00_public.html @@ -8,9 +8,9 @@ - + - + @@ -40,7 +40,7 @@ nvars, dom_size, param=nothing, icn=ICN(nvars, dom_size, param), X, X_sols, global_iter=100, local_iter=100, metric=hamming, popSize=200 )

Create an ICN, optimize it, and return its composition.

source

CompositionalNetworks.manhattan Method
julia
manhattan(x, X)

source

CompositionalNetworks.minkowski Method
julia
minkowski(x, X, p)

source

CompositionalNetworks.nbits Method
julia
nbits(icn)

Return the expected number of bits of a viable weight of an ICN.

source

CompositionalNetworks.regularization Method
julia
regularization(icn)

Return the regularization value of an ICN weights, which is proportional to the normalized number of operations selected in the icn layers.

source

CompositionalNetworks.show_layers Method
julia
show_layers(icn)

Return a formatted string with each layers in the icn.

source

CompositionalNetworks.symbols Method
julia
symbols(c::Composition)

Output the composition as a layered collection of Symbols.

source

CompositionalNetworks.transformation_layer Function
julia
transformation_layer(param = Vector{Symbol}())

Generate the layer of transformations functions of the ICN. Iff param value is non empty, also includes all the related parametric transformations.

source

CompositionalNetworks.weights! Method
julia
weights!(icn, weights)

Set the weights of an ICN with a BitVector.

source

CompositionalNetworks.weights Method
julia
weights(icn)

Access the current set of weights of an ICN.

source

CompositionalNetworks.weights_bias Method
julia
weights_bias(x)

A metric that bias x towards operations with a lower bit. Do not affect the main metric.

source

QUBOConstraints.QUBO_linear_sum Method
julia
QUBO_linear_sum(n, σ)

One valid QUBO matrix given n variables and parameter σ for the linear sum constraint.

source

QUBOConstraints.binarize Method
julia
binarize(x[, domain]; binarization = :one_hot)

Binarize x following the binarization encoding. If x is a vector (instead of a number per say), domain is optional.

source

QUBOConstraints.debinarize Method
julia
debinarize(x[, domain]; binarization = :one_hot)

Transform a binary vector into a number or a set of number. If domain is not given, it will compute a default value based on binarization and x.

source

QUBOConstraints.is_valid Function
julia
is_valid(x, encoding::Symbol = :none)

Check if x has a valid format for encoding.

For instance, if encoding == :one_hot, at most one bit of x can be set to 1.

source

QUBOConstraints.train Method
julia
train(args...)

Default train method for any AbstractOptimizer.

source

ConstraintsTranslator.GoogleLLM Type
julia
Google LLM

Structure encapsulating the parameters for accessing the Google LLM API.

source

ConstraintsTranslator.GroqLLM Type
julia
GroqLLM

Structure encapsulating the parameters for accessing the Groq LLM API.

source

ConstraintsTranslator.LlamaCppLLM Type
julia
LlamaCppLLM

Structure encapsulating the parameters for accessing the llama.cpp server API.

NOTE: we do not apply the appropriate chat templates to the prompt. This must be handled either in an external code path or by the server.

source

ConstraintsTranslator.Prompt Type
julia
Prompt

Simple data structure encapsulating a system prompt and a user prompt for LLM generation.

Fields

source

ConstraintsTranslator.PromptTemplate Type
julia
PromptTemplate

Represents a complete prompt template, comprising metadata, system, and user messages.

Fields

source

ConstraintsTranslator.format_template Method
julia
format_template(template::PromptTemplate; kwargs...)::Prompt

Formats a PromptTemplate by substituting all variables in the system and user messages with user-provided values.

Arguments

Returns

Raises

source

ConstraintsTranslator.get_completion Method
julia
get_completion(llm::AbstractLLM, prompt::AbstractPrompt)

Returns a completion for a prompt using the llm model API.

source

ConstraintsTranslator.get_completion Method
julia
get_completion(llm::OpenAILLM, prompt::Prompt)

Returns a completion for the given prompt using an OpenAI API compatible LLM

source

ConstraintsTranslator.get_completion Method
julia
get_completion(llm::GoogleLLM, prompt::Prompt)

Returns a completion for the given prompt using the Google Gemini LLM API.

source

ConstraintsTranslator.parse_code Method
julia
parse_code(s::String)

Parse the code blocks in the input string s delimited by triple backticks and an optional language annotation. Returns a dictionary keyed by language. Code blocks from the same language are concatenated.

source

ConstraintsTranslator.read_template Method
julia
read_template(data_path::String)

Reads a prompt template from a JSON file specified by data_path. The function parses the JSON data and constructs a PromptTemplate object containing metadata, system, and user messages. TODO: validate the JSON data against a schema to ensure it is valid before parsing.

Arguments

Returns

Raises

source

ConstraintsTranslator.stream_completion Method
julia
stream_completion(llm::AbstractLLM, prompt::AbstractPrompt)

Returns a completion for a prompt using the llm model API. The completion is streamed to the terminal as it is generated.

source

ConstraintsTranslator.stream_completion Method
julia
stream_completion(llm::OpenAILLM, prompt::Prompt)

Returns a completion for the given prompt using an OpenAI API compatible model. The completion is streamed to the terminal as it is generated.

source

ConstraintsTranslator.stream_completion Method
julia
stream_completion(llm::GoogleLLM, prompt::Prompt)

Returns a completion for the given prompt using the Google Gemini LLM API. The completion is streamed to the terminal as it is generated.

source

ConstraintsTranslator.translate Method
julia
translate(model::AbstractLLM, description::AbstractString; interactive::Bool = false)

Translate the natural-language description of an optimization problem into a Constraint Programming model by querying the Large Language Model model. If interactive, the user will be prompted via the command line to inspect the intermediate outputs of the LLM, and possibly modify them.

source

- + \ No newline at end of file diff --git a/dev/api/10_full.html b/dev/api/10_full.html index 8441c08..382c504 100644 --- a/dev/api/10_full.html +++ b/dev/api/10_full.html @@ -8,9 +8,9 @@ - + - + @@ -280,7 +280,7 @@ tr_val_minus_var(x, X::AbstractVector; val)

Return the difference val - x[i] if positive, 0.0 otherwise. Extended method to vector with sig (x, val) are generated. When X is provided, the result is computed without allocations.

source

CompositionalNetworks.tr_var_minus_val Method
julia
tr_var_minus_val(i, x; val)
 tr_var_minus_val(x; val)
 tr_var_minus_val(x, X::AbstractVector; val)

Return the difference x[i] - val if positive, 0.0 otherwise. Extended method to vector with sig (x, val) are generated. When X is provided, the result is computed without allocations.

source

CompositionalNetworks.transformation_layer Function
julia
transformation_layer(param = Vector{Symbol}())

Generate the layer of transformations functions of the ICN. Iff param value is non empty, also includes all the related parametric transformations.

source

CompositionalNetworks.weights! Method
julia
weights!(icn, weights)

Set the weights of an ICN with a BitVector.

source

CompositionalNetworks.weights Method
julia
weights(icn)

Access the current set of weights of an ICN.

source

CompositionalNetworks.weights_bias Method
julia
weights_bias(x)

A metric that bias x towards operations with a lower bit. Do not affect the main metric.

source

QUBOConstraints.AbstractOptimizer Type
julia
AbstractOptimizer

An abstract type (interface) used to learn QUBO matrices from constraints. Only a train method is required.

source

QUBOConstraints.QUBO_base Function
julia
QUBO_base(n, weight = 1)

A basic QUBO matrix to ensure that binarized variables keep a valid encoding.

source

QUBOConstraints.QUBO_linear_sum Method
julia
QUBO_linear_sum(n, σ)

One valid QUBO matrix given n variables and parameter σ for the linear sum constraint.

source

QUBOConstraints.binarize Method
julia
binarize(x[, domain]; binarization = :one_hot)

Binarize x following the binarization encoding. If x is a vector (instead of a number per say), domain is optional.

source

QUBOConstraints.debinarize Method
julia
debinarize(x[, domain]; binarization = :one_hot)

Transform a binary vector into a number or a set of number. If domain is not given, it will compute a default value based on binarization and x.

source

QUBOConstraints.is_valid Function
julia
is_valid(x, encoding::Symbol = :none)

Check if x has a valid format for encoding.

For instance, if encoding == :one_hot, at most one bit of x can be set to 1.

source

QUBOConstraints.train Method
julia
train(args...)

Default train method for any AbstractOptimizer.

source

ConstraintsTranslator.GoogleLLM Type
julia
Google LLM

Structure encapsulating the parameters for accessing the Google LLM API.

source

ConstraintsTranslator.GroqLLM Type
julia
GroqLLM

Structure encapsulating the parameters for accessing the Groq LLM API.

source

ConstraintsTranslator.LlamaCppLLM Type
julia
LlamaCppLLM

Structure encapsulating the parameters for accessing the llama.cpp server API.

NOTE: we do not apply the appropriate chat templates to the prompt. This must be handled either in an external code path or by the server.

source

ConstraintsTranslator.MetadataMessage Type
julia
MetadataMessage

Represents the metadata information of a prompt template. The templates follow the specifications of PromptingTools.jl.

Fields

source

ConstraintsTranslator.Prompt Type
julia
Prompt

Simple data structure encapsulating a system prompt and a user prompt for LLM generation.

Fields

source

ConstraintsTranslator.PromptTemplate Type
julia
PromptTemplate

Represents a complete prompt template, comprising metadata, system, and user messages.

Fields

source

ConstraintsTranslator.SystemMessage Type
julia
SystemMessage

Represents the prompt template of a system message. The template can optionally contain string placeholders enclosed in double curly braces, e.g., . Placeholders must be replaced with actual values when generating prompts.

Fields

source

ConstraintsTranslator.UserMessage Type
julia
UserMessage

Represents the prompt template of a user message. The template can optionally contain string placeholders enclosed in double curly braces, e.g., . Placeholders must be replaced with actual values when generating prompts.

Fields

source

ConstraintsTranslator.check_syntax_errors Method
julia
check_syntax_errors(s::String)

Parses the string s as Julia code. In the case of syntax errors, it returns the error message of the parser as a string. Otherwise, it returns an empty string.

source

ConstraintsTranslator.edit_in_editor Method
julia
edit_in_vim(s::String)

Edits the input string s in a temporary file using the Vim editor. Returns the modified string after the editor is closed.

source

ConstraintsTranslator.extract_structure Method
julia
extract_structure(model <: AbstractLLM, description <: AbstractString)

Extracts the parameters, decision variables and constraints of an optimization problem given a natural-language description. Returns a Markdown-formatted text containing the above information.

source

ConstraintsTranslator.fix_syntax_errors Method
julia
fix_syntax_errors(model::AbstractLLM, code::AbstractString, error::AbstractString)

Fixes syntax errors in the code by querying the Large Language Model model, based on an error produced by the Julia parser. Returns Markdown-formatted text containing the corrected code in a Julia code block.

source

ConstraintsTranslator.format_template Method
julia
format_template(template::PromptTemplate; kwargs...)::Prompt

Formats a PromptTemplate by substituting all variables in the system and user messages with user-provided values.

Arguments

Returns

Raises

source

ConstraintsTranslator.get_completion Method
julia
get_completion(llm::AbstractLLM, prompt::AbstractPrompt)

Returns a completion for a prompt using the llm model API.

source

ConstraintsTranslator.get_completion Method
julia
get_completion(llm::OpenAILLM, prompt::Prompt)

Returns a completion for the given prompt using an OpenAI API compatible LLM

source

ConstraintsTranslator.get_completion Method
julia
get_completion(llm::GoogleLLM, prompt::Prompt)

Returns a completion for the given prompt using the Google Gemini LLM API.

source

ConstraintsTranslator.get_package_path Method
julia
get_package_path()

Returns the absolute path of the root directory of ConstraintsTranslator.jl.

source

ConstraintsTranslator.jumpify_model Method
julia
jumpify_model(model::AbstractLLM, description::AbstractString, examples::AbstractString)

Translates the natural language description of an optimization problem into a JuMP constraints programming model to be solved with CBL by querying the Large Language Model model. The examples are snippets from ConstraintModels.jl used as in-context examples to the LLM. To work optimally, the model expects the description to be a structured Markdown-formatted description as the ones generated by extract_structure. Returns a Markdown-formatted text containing Julia code in a code block.

source

ConstraintsTranslator.parse_code Method
julia
parse_code(s::String)

Parse the code blocks in the input string s delimited by triple backticks and an optional language annotation. Returns a dictionary keyed by language. Code blocks from the same language are concatenated.

source

ConstraintsTranslator.read_template Method
julia
read_template(data_path::String)

Reads a prompt template from a JSON file specified by data_path. The function parses the JSON data and constructs a PromptTemplate object containing metadata, system, and user messages. TODO: validate the JSON data against a schema to ensure it is valid before parsing.

Arguments

Returns

Raises

source

ConstraintsTranslator.stream_completion Method
julia
stream_completion(llm::AbstractLLM, prompt::AbstractPrompt)

Returns a completion for a prompt using the llm model API. The completion is streamed to the terminal as it is generated.

source

ConstraintsTranslator.stream_completion Method
julia
stream_completion(llm::OpenAILLM, prompt::Prompt)

Returns a completion for the given prompt using an OpenAI API compatible model. The completion is streamed to the terminal as it is generated.

source

ConstraintsTranslator.stream_completion Method
julia
stream_completion(llm::GoogleLLM, prompt::Prompt)

Returns a completion for the given prompt using the Google Gemini LLM API. The completion is streamed to the terminal as it is generated.

source

ConstraintsTranslator.translate Method
julia
translate(model::AbstractLLM, description::AbstractString; interactive::Bool = false)

Translate the natural-language description of an optimization problem into a Constraint Programming model by querying the Large Language Model model. If interactive, the user will be prompted via the command line to inspect the intermediate outputs of the LLM, and possibly modify them.

source

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nt(Pe.Layout,null,{})},enhanceApp({app:o,router:e,siteData:t}){Ya(o)}};export{Qa as R,bo as c,L as u}; diff --git a/dev/assets/constraints_10_variables_and_domains.md.2DoRmBqU.js b/dev/assets/constraints_10_variables_and_domains.md.BmMtN-L8.js similarity index 96% rename from dev/assets/constraints_10_variables_and_domains.md.2DoRmBqU.js rename to dev/assets/constraints_10_variables_and_domains.md.BmMtN-L8.js index 72266df..e12b088 100644 --- a/dev/assets/constraints_10_variables_and_domains.md.2DoRmBqU.js +++ b/dev/assets/constraints_10_variables_and_domains.md.BmMtN-L8.js @@ -1,4 +1,4 @@ -import{_ as p,c as t,a5 as n,j as i,a,G as h,B as k,o as e}from"./chunks/framework.CJakPlgM.js";const b=JSON.parse('{"title":"Defining Variables and Exploring Domains","description":"","frontmatter":{},"headers":[],"relativePath":"constraints/10_variables_and_domains.md","filePath":"constraints/10_variables_and_domains.md","lastUpdated":null}'),d={name:"constraints/10_variables_and_domains.md"},r={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},o={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.09ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.509ex",height:"1.312ex",role:"img",focusable:"false",viewBox:"0 -540 667 580","aria-hidden":"true"},E={class:"jldocstring custom-block",open:""};function g(y,s,c,m,C,F){const l=k("Badge");return e(),t("div",null,[s[17]||(s[17]=n('

Defining Variables and Exploring Domains ​

ConstraintDomains.jl stands as the standard way to define variables and explore domains within the Julia Constraints ecosystem. This package provides the infrastructure necessary for specifying both discrete and continuous domains. Explorations features are mainly related to the learning about constraints aspect and will be detailed in that chapter.

Variables and their domains can also be defined through MOI and JuMP syntaxes in their respective models.

Implementing the AbstractDomain Interface ​

',4)),i("p",null,[s[2]||(s[2]=a("At the foundation of ")),s[3]||(s[3]=i("em",null,"ConstraintDomains.jl",-1)),s[4]||(s[4]=a(" is the ")),s[5]||(s[5]=i("code",null,"AbstractDomain",-1)),s[6]||(s[6]=a(" type, an abstract supertype for all domain types. Implementations of ")),s[7]||(s[7]=i("code",null,"AbstractDomain",-1)),s[8]||(s[8]=a(" must provide methods for checking membership (")),i("mjx-container",r,[(e(),t("svg",o,s[0]||(s[0]=[i("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[i("g",{"data-mml-node":"math"},[i("g",{"data-mml-node":"mo"},[i("path",{"data-c":"2208",d:"M84 250Q84 372 166 450T360 539Q361 539 377 539T419 540T469 540H568Q583 532 583 520Q583 511 570 501L466 500Q355 499 329 494Q280 482 242 458T183 409T147 354T129 306T124 272V270H568Q583 262 583 250T568 230H124V228Q124 207 134 177T167 112T231 48T328 7Q355 1 466 0H570Q583 -10 583 -20Q583 -32 568 -40H471Q464 -40 446 -40T417 -41Q262 -41 172 45Q84 127 84 250Z",style:{"stroke-width":"3"}})])])],-1)]))),s[1]||(s[1]=i("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[i("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[i("mo",null,"∈")])],-1))]),s[9]||(s[9]=a("), generating random elements (")),s[10]||(s[10]=i("code",null,"rand",-1)),s[11]||(s[11]=a("), and determining the domain's size or range (")),s[12]||(s[12]=i("code",null,"length",-1)),s[13]||(s[13]=a("). These functionalities are essential for defining the behavior and properties of variable domains within constraint models."))]),i("details",E,[i("summary",null,[s[14]||(s[14]=i("a",{id:"ConstraintDomains.AbstractDomain-constraints-10_variables_and_domains",href:"#ConstraintDomains.AbstractDomain-constraints-10_variables_and_domains"},[i("span",{class:"jlbinding"},"ConstraintDomains.AbstractDomain")],-1)),s[15]||(s[15]=a()),h(l,{type:"info",class:"jlObjectType jlType",text:"Type"})]),s[16]||(s[16]=n('
julia
AbstractDomain

An abstract super type for any domain type. A domain type D <: AbstractDomain must implement the following methods to properly interface AbstractDomain.

  • Base.∈(val, ::D)

  • Base.rand(::D)

  • Base.length(::D) that is the number of elements in a discrete domain, and the distance between bounds or similar for a continuous domain

Additionally, if the domain is used in a dynamic context, it can extend

  • add!(::D, args)

  • delete!(::D, args)

where args depends on D's structure

source

',7))]),s[18]||(s[18]=n(`

Discrete Domains ​

Optimization in discrete spaces has been the core of Constraint Programming since its inception. We provide three kinds of discrete domains.

SetDomain ​

A SetDomain is simply a Set of unordered numerical values.

julia
using ConstraintDomains
+import{_ as p,c as t,a5 as n,j as i,a,G as h,B as k,o as e}from"./chunks/framework.CJakPlgM.js";const b=JSON.parse('{"title":"Defining Variables and Exploring Domains","description":"","frontmatter":{},"headers":[],"relativePath":"constraints/10_variables_and_domains.md","filePath":"constraints/10_variables_and_domains.md","lastUpdated":null}'),r={name:"constraints/10_variables_and_domains.md"},d={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},o={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.09ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.509ex",height:"1.312ex",role:"img",focusable:"false",viewBox:"0 -540 667 580","aria-hidden":"true"},E={class:"jldocstring custom-block",open:""};function g(y,s,c,m,C,F){const l=k("Badge");return e(),t("div",null,[s[17]||(s[17]=n('
Defining Variables and Exploring Domains ​
ConstraintDomains.jl stands as the standard way to define variables and explore domains within the Julia Constraints ecosystem. This package provides the infrastructure necessary for specifying both discrete and continuous domains. Explorations features are mainly related to the learning about constraints aspect and will be detailed in that chapter.
Variables and their domains can also be defined through MOI and JuMP syntaxes in their respective models.
Implementing the AbstractDomain Interface ​
',4)),i("p",null,[s[2]||(s[2]=a("At the foundation of ")),s[3]||(s[3]=i("em",null,"ConstraintDomains.jl",-1)),s[4]||(s[4]=a(" is the ")),s[5]||(s[5]=i("code",null,"AbstractDomain",-1)),s[6]||(s[6]=a(" type, an abstract supertype for all domain types. Implementations of ")),s[7]||(s[7]=i("code",null,"AbstractDomain",-1)),s[8]||(s[8]=a(" must provide methods for checking membership (")),i("mjx-container",d,[(e(),t("svg",o,s[0]||(s[0]=[i("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[i("g",{"data-mml-node":"math"},[i("g",{"data-mml-node":"mo"},[i("path",{"data-c":"2208",d:"M84 250Q84 372 166 450T360 539Q361 539 377 539T419 540T469 540H568Q583 532 583 520Q583 511 570 501L466 500Q355 499 329 494Q280 482 242 458T183 409T147 354T129 306T124 272V270H568Q583 262 583 250T568 230H124V228Q124 207 134 177T167 112T231 48T328 7Q355 1 466 0H570Q583 -10 583 -20Q583 -32 568 -40H471Q464 -40 446 -40T417 -41Q262 -41 172 45Q84 127 84 250Z",style:{"stroke-width":"3"}})])])],-1)]))),s[1]||(s[1]=i("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[i("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[i("mo",null,"∈")])],-1))]),s[9]||(s[9]=a("), generating random elements (")),s[10]||(s[10]=i("code",null,"rand",-1)),s[11]||(s[11]=a("), and determining the domain's size or range (")),s[12]||(s[12]=i("code",null,"length",-1)),s[13]||(s[13]=a("). These functionalities are essential for defining the behavior and properties of variable domains within constraint models."))]),i("details",E,[i("summary",null,[s[14]||(s[14]=i("a",{id:"ConstraintDomains.AbstractDomain-constraints-10_variables_and_domains",href:"#ConstraintDomains.AbstractDomain-constraints-10_variables_and_domains"},[i("span",{class:"jlbinding"},"ConstraintDomains.AbstractDomain")],-1)),s[15]||(s[15]=a()),h(l,{type:"info",class:"jlObjectType jlType",text:"Type"})]),s[16]||(s[16]=n('
julia
AbstractDomain
An abstract super type for any domain type. A domain type D <: AbstractDomain must implement the following methods to properly interface AbstractDomain.
  • Base.∈(val, ::D)
  • Base.rand(::D)
  • Base.length(::D) that is the number of elements in a discrete domain, and the distance between bounds or similar for a continuous domain
Additionally, if the domain is used in a dynamic context, it can extend
  • add!(::D, args)
  • delete!(::D, args)
where args depends on D's structure
source
',7))]),s[18]||(s[18]=n(`
Discrete Domains ​
Optimization in discrete spaces has been the core of Constraint Programming since its inception. We provide three kinds of discrete domains.
SetDomain ​
A SetDomain is simply a Set of unordered numerical values.
julia
using ConstraintDomains
 
 d1 = domain([53.69, 89.2, 0.12])
 d2 = domain([2//3, 89//123])
@@ -25,7 +25,7 @@ import{_ as p,c as t,a5 as n,j as i,a,G as h,B as k,o as e}from"./chunks/framewo
 MOI.add_constraint(optimizer, v3, CBLS.DiscreteSet(4.3))
 
 v4 = MOI.add_variable(optimizer)
-MOI.add_constraint(optimizer, v4, CBLS.DiscreteSet([1, 42, 3.14]))
RangeDomain ​
A range domain allows for minimal storage and more efficient operation on discrete sets defined as Range in Julia. It is not recommended for dynamic domains (it will be replaced with SetDomain as soon as a non-extremal element is removed).
julia
using ConstraintDomains
+MOI.add_constraint(optimizer, v4, CBLS.DiscreteSet([1, 42, 3.14]))
RangeDomain ​
A range domain allows for minimal storage and more efficient operation on discrete sets defined as Range in Julia. It is not recommended for dynamic domains (it will be replaced with SetDomain as soon as a non-extremal element is removed).
julia
using ConstraintDomains
 
 d1 = domain(1:5)
 d2 = domain(0.4:0.1:1.3)
julia
## To be implemented
@@ -45,8 +45,8 @@ import{_ as p,c as t,a5 as n,j as i,a,G as h,B as k,o as e}from"./chunks/framewo
 
 # v2 = MOI.add_variable(optimizer)
 
-# MOI.add_constraint(optimizer, v1, MOI.RangeSet(0.4:0.1:1.3))
Arbitrary Domains ​
As odd as it may sound, we provide a constructor for sets of elements making up arbitrary, possibly non-numerical, domains.
Until some practical examples are implemented, this structure will mainly be a placeholder with default behavior.
Continuous Domains ​
Numerous problems cannot be challenged without expressing at least part of their domains as continuous variables. In Julia Constraints we provide such domains as (set of) intervals.
julia
using ConstraintDomains, Intervals
+# MOI.add_constraint(optimizer, v1, MOI.RangeSet(0.4:0.1:1.3))
Arbitrary Domains ​
As odd as it may sound, we provide a constructor for sets of elements making up arbitrary, possibly non-numerical, domains.
Until some practical examples are implemented, this structure will mainly be a placeholder with default behavior.
Continuous Domains ​
Numerous problems cannot be challenged without expressing at least part of their domains as continuous variables. In Julia Constraints we provide such domains as (set of) intervals.
julia
using ConstraintDomains, Intervals
 
 d1 = domain(Interval{Open,Closed}(3.2, true), (42, false))
 d2 = domain(3.2..42)
-d3 = domain([3.2..42, 63.2..324.1])
julia
## see MOI.Interval
julia
## see MOI.Interval
`,14))])}const D=p(d,[["render",g]]);export{b as __pageData,D as default};
+d3 = domain([3.2..42, 63.2..324.1])
julia
## see MOI.Interval
julia
## see MOI.Interval
`,14))])}const D=p(r,[["render",g]]);export{b as __pageData,D as default}; diff --git a/dev/assets/constraints_10_variables_and_domains.md.2DoRmBqU.lean.js b/dev/assets/constraints_10_variables_and_domains.md.BmMtN-L8.lean.js similarity index 96% rename from dev/assets/constraints_10_variables_and_domains.md.2DoRmBqU.lean.js rename to dev/assets/constraints_10_variables_and_domains.md.BmMtN-L8.lean.js index 72266df..e12b088 100644 --- a/dev/assets/constraints_10_variables_and_domains.md.2DoRmBqU.lean.js +++ b/dev/assets/constraints_10_variables_and_domains.md.BmMtN-L8.lean.js @@ -1,4 +1,4 @@ -import{_ as p,c as t,a5 as n,j as i,a,G as h,B as k,o as e}from"./chunks/framework.CJakPlgM.js";const b=JSON.parse('{"title":"Defining Variables and Exploring Domains","description":"","frontmatter":{},"headers":[],"relativePath":"constraints/10_variables_and_domains.md","filePath":"constraints/10_variables_and_domains.md","lastUpdated":null}'),d={name:"constraints/10_variables_and_domains.md"},r={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},o={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.09ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.509ex",height:"1.312ex",role:"img",focusable:"false",viewBox:"0 -540 667 580","aria-hidden":"true"},E={class:"jldocstring custom-block",open:""};function g(y,s,c,m,C,F){const l=k("Badge");return e(),t("div",null,[s[17]||(s[17]=n('

Defining Variables and Exploring Domains ​

ConstraintDomains.jl stands as the standard way to define variables and explore domains within the Julia Constraints ecosystem. This package provides the infrastructure necessary for specifying both discrete and continuous domains. Explorations features are mainly related to the learning about constraints aspect and will be detailed in that chapter.

Variables and their domains can also be defined through MOI and JuMP syntaxes in their respective models.

Implementing the AbstractDomain Interface ​

',4)),i("p",null,[s[2]||(s[2]=a("At the foundation of ")),s[3]||(s[3]=i("em",null,"ConstraintDomains.jl",-1)),s[4]||(s[4]=a(" is the ")),s[5]||(s[5]=i("code",null,"AbstractDomain",-1)),s[6]||(s[6]=a(" type, an abstract supertype for all domain types. Implementations of ")),s[7]||(s[7]=i("code",null,"AbstractDomain",-1)),s[8]||(s[8]=a(" must provide methods for checking membership (")),i("mjx-container",r,[(e(),t("svg",o,s[0]||(s[0]=[i("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[i("g",{"data-mml-node":"math"},[i("g",{"data-mml-node":"mo"},[i("path",{"data-c":"2208",d:"M84 250Q84 372 166 450T360 539Q361 539 377 539T419 540T469 540H568Q583 532 583 520Q583 511 570 501L466 500Q355 499 329 494Q280 482 242 458T183 409T147 354T129 306T124 272V270H568Q583 262 583 250T568 230H124V228Q124 207 134 177T167 112T231 48T328 7Q355 1 466 0H570Q583 -10 583 -20Q583 -32 568 -40H471Q464 -40 446 -40T417 -41Q262 -41 172 45Q84 127 84 250Z",style:{"stroke-width":"3"}})])])],-1)]))),s[1]||(s[1]=i("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[i("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[i("mo",null,"∈")])],-1))]),s[9]||(s[9]=a("), generating random elements (")),s[10]||(s[10]=i("code",null,"rand",-1)),s[11]||(s[11]=a("), and determining the domain's size or range (")),s[12]||(s[12]=i("code",null,"length",-1)),s[13]||(s[13]=a("). These functionalities are essential for defining the behavior and properties of variable domains within constraint models."))]),i("details",E,[i("summary",null,[s[14]||(s[14]=i("a",{id:"ConstraintDomains.AbstractDomain-constraints-10_variables_and_domains",href:"#ConstraintDomains.AbstractDomain-constraints-10_variables_and_domains"},[i("span",{class:"jlbinding"},"ConstraintDomains.AbstractDomain")],-1)),s[15]||(s[15]=a()),h(l,{type:"info",class:"jlObjectType jlType",text:"Type"})]),s[16]||(s[16]=n('
julia
AbstractDomain

An abstract super type for any domain type. A domain type D <: AbstractDomain must implement the following methods to properly interface AbstractDomain.

  • Base.∈(val, ::D)

  • Base.rand(::D)

  • Base.length(::D) that is the number of elements in a discrete domain, and the distance between bounds or similar for a continuous domain

Additionally, if the domain is used in a dynamic context, it can extend

  • add!(::D, args)

  • delete!(::D, args)

where args depends on D's structure

source

',7))]),s[18]||(s[18]=n(`

Discrete Domains ​

Optimization in discrete spaces has been the core of Constraint Programming since its inception. We provide three kinds of discrete domains.

SetDomain ​

A SetDomain is simply a Set of unordered numerical values.

julia
using ConstraintDomains
+import{_ as p,c as t,a5 as n,j as i,a,G as h,B as k,o as e}from"./chunks/framework.CJakPlgM.js";const b=JSON.parse('{"title":"Defining Variables and Exploring Domains","description":"","frontmatter":{},"headers":[],"relativePath":"constraints/10_variables_and_domains.md","filePath":"constraints/10_variables_and_domains.md","lastUpdated":null}'),r={name:"constraints/10_variables_and_domains.md"},d={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},o={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.09ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.509ex",height:"1.312ex",role:"img",focusable:"false",viewBox:"0 -540 667 580","aria-hidden":"true"},E={class:"jldocstring custom-block",open:""};function g(y,s,c,m,C,F){const l=k("Badge");return e(),t("div",null,[s[17]||(s[17]=n('
Defining Variables and Exploring Domains ​
ConstraintDomains.jl stands as the standard way to define variables and explore domains within the Julia Constraints ecosystem. This package provides the infrastructure necessary for specifying both discrete and continuous domains. Explorations features are mainly related to the learning about constraints aspect and will be detailed in that chapter.
Variables and their domains can also be defined through MOI and JuMP syntaxes in their respective models.
Implementing the AbstractDomain Interface ​
',4)),i("p",null,[s[2]||(s[2]=a("At the foundation of ")),s[3]||(s[3]=i("em",null,"ConstraintDomains.jl",-1)),s[4]||(s[4]=a(" is the ")),s[5]||(s[5]=i("code",null,"AbstractDomain",-1)),s[6]||(s[6]=a(" type, an abstract supertype for all domain types. Implementations of ")),s[7]||(s[7]=i("code",null,"AbstractDomain",-1)),s[8]||(s[8]=a(" must provide methods for checking membership (")),i("mjx-container",d,[(e(),t("svg",o,s[0]||(s[0]=[i("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[i("g",{"data-mml-node":"math"},[i("g",{"data-mml-node":"mo"},[i("path",{"data-c":"2208",d:"M84 250Q84 372 166 450T360 539Q361 539 377 539T419 540T469 540H568Q583 532 583 520Q583 511 570 501L466 500Q355 499 329 494Q280 482 242 458T183 409T147 354T129 306T124 272V270H568Q583 262 583 250T568 230H124V228Q124 207 134 177T167 112T231 48T328 7Q355 1 466 0H570Q583 -10 583 -20Q583 -32 568 -40H471Q464 -40 446 -40T417 -41Q262 -41 172 45Q84 127 84 250Z",style:{"stroke-width":"3"}})])])],-1)]))),s[1]||(s[1]=i("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[i("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[i("mo",null,"∈")])],-1))]),s[9]||(s[9]=a("), generating random elements (")),s[10]||(s[10]=i("code",null,"rand",-1)),s[11]||(s[11]=a("), and determining the domain's size or range (")),s[12]||(s[12]=i("code",null,"length",-1)),s[13]||(s[13]=a("). These functionalities are essential for defining the behavior and properties of variable domains within constraint models."))]),i("details",E,[i("summary",null,[s[14]||(s[14]=i("a",{id:"ConstraintDomains.AbstractDomain-constraints-10_variables_and_domains",href:"#ConstraintDomains.AbstractDomain-constraints-10_variables_and_domains"},[i("span",{class:"jlbinding"},"ConstraintDomains.AbstractDomain")],-1)),s[15]||(s[15]=a()),h(l,{type:"info",class:"jlObjectType jlType",text:"Type"})]),s[16]||(s[16]=n('
julia
AbstractDomain
An abstract super type for any domain type. A domain type D <: AbstractDomain must implement the following methods to properly interface AbstractDomain.
  • Base.∈(val, ::D)
  • Base.rand(::D)
  • Base.length(::D) that is the number of elements in a discrete domain, and the distance between bounds or similar for a continuous domain
Additionally, if the domain is used in a dynamic context, it can extend
  • add!(::D, args)
  • delete!(::D, args)
where args depends on D's structure
source
',7))]),s[18]||(s[18]=n(`
Discrete Domains ​
Optimization in discrete spaces has been the core of Constraint Programming since its inception. We provide three kinds of discrete domains.
SetDomain ​
A SetDomain is simply a Set of unordered numerical values.
julia
using ConstraintDomains
 
 d1 = domain([53.69, 89.2, 0.12])
 d2 = domain([2//3, 89//123])
@@ -25,7 +25,7 @@ import{_ as p,c as t,a5 as n,j as i,a,G as h,B as k,o as e}from"./chunks/framewo
 MOI.add_constraint(optimizer, v3, CBLS.DiscreteSet(4.3))
 
 v4 = MOI.add_variable(optimizer)
-MOI.add_constraint(optimizer, v4, CBLS.DiscreteSet([1, 42, 3.14]))
RangeDomain ​
A range domain allows for minimal storage and more efficient operation on discrete sets defined as Range in Julia. It is not recommended for dynamic domains (it will be replaced with SetDomain as soon as a non-extremal element is removed).
julia
using ConstraintDomains
+MOI.add_constraint(optimizer, v4, CBLS.DiscreteSet([1, 42, 3.14]))
RangeDomain ​
A range domain allows for minimal storage and more efficient operation on discrete sets defined as Range in Julia. It is not recommended for dynamic domains (it will be replaced with SetDomain as soon as a non-extremal element is removed).
julia
using ConstraintDomains
 
 d1 = domain(1:5)
 d2 = domain(0.4:0.1:1.3)
julia
## To be implemented
@@ -45,8 +45,8 @@ import{_ as p,c as t,a5 as n,j as i,a,G as h,B as k,o as e}from"./chunks/framewo
 
 # v2 = MOI.add_variable(optimizer)
 
-# MOI.add_constraint(optimizer, v1, MOI.RangeSet(0.4:0.1:1.3))
Arbitrary Domains ​
As odd as it may sound, we provide a constructor for sets of elements making up arbitrary, possibly non-numerical, domains.
Until some practical examples are implemented, this structure will mainly be a placeholder with default behavior.
Continuous Domains ​
Numerous problems cannot be challenged without expressing at least part of their domains as continuous variables. In Julia Constraints we provide such domains as (set of) intervals.
julia
using ConstraintDomains, Intervals
+# MOI.add_constraint(optimizer, v1, MOI.RangeSet(0.4:0.1:1.3))
Arbitrary Domains ​
As odd as it may sound, we provide a constructor for sets of elements making up arbitrary, possibly non-numerical, domains.
Until some practical examples are implemented, this structure will mainly be a placeholder with default behavior.
Continuous Domains ​
Numerous problems cannot be challenged without expressing at least part of their domains as continuous variables. In Julia Constraints we provide such domains as (set of) intervals.
julia
using ConstraintDomains, Intervals
 
 d1 = domain(Interval{Open,Closed}(3.2, true), (42, false))
 d2 = domain(3.2..42)
-d3 = domain([3.2..42, 63.2..324.1])
julia
## see MOI.Interval
julia
## see MOI.Interval
`,14))])}const D=p(d,[["render",g]]);export{b as __pageData,D as default};
+d3 = domain([3.2..42, 63.2..324.1])
julia
## see MOI.Interval
julia
## see MOI.Interval
`,14))])}const D=p(r,[["render",g]]);export{b as __pageData,D as default}; diff --git a/dev/assets/constraints_21_generic_constraints.md.Cq_hAjZf.js b/dev/assets/constraints_21_generic_constraints.md.DIVWDhM8.js similarity index 97% rename from dev/assets/constraints_21_generic_constraints.md.Cq_hAjZf.js rename to dev/assets/constraints_21_generic_constraints.md.DIVWDhM8.js index 3992c3c..35bb1d7 100644 --- a/dev/assets/constraints_21_generic_constraints.md.Cq_hAjZf.js +++ b/dev/assets/constraints_21_generic_constraints.md.DIVWDhM8.js @@ -1,4 +1,4 @@ -import{_ as l,c as t,a5 as e,j as s,a,o as n}from"./chunks/framework.CJakPlgM.js";const z=JSON.parse('{"title":"Generic Constraints","description":"","frontmatter":{},"headers":[],"relativePath":"constraints/21_generic_constraints.md","filePath":"constraints/21_generic_constraints.md","lastUpdated":null}'),h={name:"constraints/21_generic_constraints.md"},p={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},k={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.294ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 572 453","aria-hidden":"true"},r={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},d={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.464ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.109ex",height:"1.464ex",role:"img",focusable:"false",viewBox:"0 -442 490 647","aria-hidden":"true"},o={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},g={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.464ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.42ex",height:"1.686ex",role:"img",focusable:"false",viewBox:"0 -540 2395.6 745","aria-hidden":"true"},E={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},T={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.294ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 572 453","aria-hidden":"true"},Q={class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},y={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"25.797ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 11402.4 1000","aria-hidden":"true"},m={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},c={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"0"},xmlns:"http://www.w3.org/2000/svg",width:"1.928ex",height:"1.545ex",role:"img",focusable:"false",viewBox:"0 -683 852 683","aria-hidden":"true"},u={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},F={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"0"},xmlns:"http://www.w3.org/2000/svg",width:"1.131ex",height:"1.507ex",role:"img",focusable:"false",viewBox:"0 -666 500 666","aria-hidden":"true"},C={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},x={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"0"},xmlns:"http://www.w3.org/2000/svg",width:"1.131ex",height:"1.507ex",role:"img",focusable:"false",viewBox:"0 -666 500 666","aria-hidden":"true"},w={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},f={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"0"},xmlns:"http://www.w3.org/2000/svg",width:"1.726ex",height:"1.545ex",role:"img",focusable:"false",viewBox:"0 -683 763 683","aria-hidden":"true"},b={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},v={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.05ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.131ex",height:"1.554ex",role:"img",focusable:"false",viewBox:"0 -665 500 687","aria-hidden":"true"},H={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},B={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"0"},xmlns:"http://www.w3.org/2000/svg",width:"1.131ex",height:"1.532ex",role:"img",focusable:"false",viewBox:"0 -677 500 677","aria-hidden":"true"},D={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},A={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"23.762ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 10502.7 1000","aria-hidden":"true"};function V(M,i,L,Z,j,I){return n(),t("div",null,[i[43]||(i[43]=e('

Generic Constraints ​

In the XCSP³-core standard, generic constraints are categorized into two main types: intention and extension constraints.

Intention Constraints ​

',3)),s("p",null,[i[6]||(i[6]=a("These are constraints that are defined by a logical expression or a function. They are called intentional because they are defined by the property they satisfy. For example, a constraint that specifies that a variable ")),s("mjx-container",p,[(n(),t("svg",k,i[0]||(i[0]=[s("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[s("g",{"data-mml-node":"math"},[s("g",{"data-mml-node":"mi"},[s("path",{"data-c":"1D465",d:"M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z",style:{"stroke-width":"3"}})])])],-1)]))),i[1]||(i[1]=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"x")])],-1))]),i[7]||(i[7]=a(" must be less than a variable ")),s("mjx-container",r,[(n(),t("svg",d,i[2]||(i[2]=[s("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[s("g",{"data-mml-node":"math"},[s("g",{"data-mml-node":"mi"},[s("path",{"data-c":"1D466",d:"M21 287Q21 301 36 335T84 406T158 442Q199 442 224 419T250 355Q248 336 247 334Q247 331 231 288T198 191T182 105Q182 62 196 45T238 27Q261 27 281 38T312 61T339 94Q339 95 344 114T358 173T377 247Q415 397 419 404Q432 431 462 431Q475 431 483 424T494 412T496 403Q496 390 447 193T391 -23Q363 -106 294 -155T156 -205Q111 -205 77 -183T43 -117Q43 -95 50 -80T69 -58T89 -48T106 -45Q150 -45 150 -87Q150 -107 138 -122T115 -142T102 -147L99 -148Q101 -153 118 -160T152 -167H160Q177 -167 186 -165Q219 -156 247 -127T290 -65T313 -9T321 21L315 17Q309 13 296 6T270 -6Q250 -11 231 -11Q185 -11 150 11T104 82Q103 89 103 113Q103 170 138 262T173 379Q173 380 173 381Q173 390 173 393T169 400T158 404H154Q131 404 112 385T82 344T65 302T57 280Q55 278 41 278H27Q21 284 21 287Z",style:{"stroke-width":"3"}})])])],-1)]))),i[3]||(i[3]=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"y")])],-1))]),i[8]||(i[8]=a(" could be defined intentionally as ")),s("mjx-container",o,[(n(),t("svg",g,i[4]||(i[4]=[e('',1)]))),i[5]||(i[5]=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"x"),s("mo",null,"<"),s("mi",null,"y")])],-1))]),i[9]||(i[9]=a("."))]),i[44]||(i[44]=e('

Note that the intention constraint is not directly available through the JC-API in Constraints.jl. It is designed as such since defining a constraint through a predicate is the natural way.

We provide a straightforward example through the :dist_different constraint on how to define and add such a constraint in the USUAL_CONSTRAINTS collection.

Higher level modeling languages such as JuMP should provide a Intention interface.

Defining an intention constraint in JC-API ​

',4)),s("p",null,[i[12]||(i[12]=a("We use the ")),i[13]||(i[13]=s("code",null,"dist_different",-1)),i[14]||(i[14]=a(" constraint to illustrate how to define an intention constraint in ")),i[15]||(i[15]=s("em",null,"Constraints.jl",-1)),i[16]||(i[16]=a(". The ")),i[17]||(i[17]=s("code",null,"dist_different",-1)),i[18]||(i[18]=a(" constraint ensures that the distances between marks ")),s("mjx-container",E,[(n(),t("svg",T,i[10]||(i[10]=[s("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[s("g",{"data-mml-node":"math"},[s("g",{"data-mml-node":"mi"},[s("path",{"data-c":"1D465",d:"M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z",style:{"stroke-width":"3"}})])])],-1)]))),i[11]||(i[11]=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"x")])],-1))]),i[19]||(i[19]=a(" on a ruler are unique."))]),s("mjx-container",Q,[(n(),t("svg",y,i[20]||(i[20]=[e('',1)]))),i[21]||(i[21]=s("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mi",null,"x"),s("mo",{stretchy:"false"},"["),s("mn",null,"1"),s("mo",{stretchy:"false"},"]"),s("mo",null,"−"),s("mi",null,"x"),s("mo",{stretchy:"false"},"["),s("mn",null,"2"),s("mo",{stretchy:"false"},"]"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mo",null,"≠"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mi",null,"x"),s("mo",{stretchy:"false"},"["),s("mn",null,"3"),s("mo",{stretchy:"false"},"]"),s("mo",null,"−"),s("mi",null,"x"),s("mo",{stretchy:"false"},"["),s("mn",null,"4"),s("mo",{stretchy:"false"},"]"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|")])],-1))]),i[45]||(i[45]=e(`

The constraint is then added to the usual constraints collection.

julia
const description_dist_different = """
+import{_ as e,c as t,a5 as l,j as s,a,o as n}from"./chunks/framework.CJakPlgM.js";const J=JSON.parse('{"title":"Generic Constraints","description":"","frontmatter":{},"headers":[],"relativePath":"constraints/21_generic_constraints.md","filePath":"constraints/21_generic_constraints.md","lastUpdated":null}'),h={name:"constraints/21_generic_constraints.md"},p={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},k={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.294ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 572 453","aria-hidden":"true"},r={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},d={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.464ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.109ex",height:"1.464ex",role:"img",focusable:"false",viewBox:"0 -442 490 647","aria-hidden":"true"},o={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},g={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.464ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.42ex",height:"1.686ex",role:"img",focusable:"false",viewBox:"0 -540 2395.6 745","aria-hidden":"true"},E={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},T={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.294ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 572 453","aria-hidden":"true"},Q={class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},y={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"25.797ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 11402.4 1000","aria-hidden":"true"},m={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},c={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"0"},xmlns:"http://www.w3.org/2000/svg",width:"1.928ex",height:"1.545ex",role:"img",focusable:"false",viewBox:"0 -683 852 683","aria-hidden":"true"},u={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},C={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"0"},xmlns:"http://www.w3.org/2000/svg",width:"1.131ex",height:"1.507ex",role:"img",focusable:"false",viewBox:"0 -666 500 666","aria-hidden":"true"},F={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},x={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"0"},xmlns:"http://www.w3.org/2000/svg",width:"1.131ex",height:"1.507ex",role:"img",focusable:"false",viewBox:"0 -666 500 666","aria-hidden":"true"},w={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},f={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"0"},xmlns:"http://www.w3.org/2000/svg",width:"1.726ex",height:"1.545ex",role:"img",focusable:"false",viewBox:"0 -683 763 683","aria-hidden":"true"},b={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},v={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.05ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.131ex",height:"1.554ex",role:"img",focusable:"false",viewBox:"0 -665 500 687","aria-hidden":"true"},H={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},B={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"0"},xmlns:"http://www.w3.org/2000/svg",width:"1.131ex",height:"1.532ex",role:"img",focusable:"false",viewBox:"0 -677 500 677","aria-hidden":"true"},D={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},A={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"23.762ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 10502.7 1000","aria-hidden":"true"};function V(M,i,L,j,Z,I){return n(),t("div",null,[i[43]||(i[43]=l('
Generic Constraints ​
In the XCSP³-core standard, generic constraints are categorized into two main types: intention and extension constraints.
Intention Constraints ​
',3)),s("p",null,[i[6]||(i[6]=a("These are constraints that are defined by a logical expression or a function. They are called intentional because they are defined by the property they satisfy. For example, a constraint that specifies that a variable ")),s("mjx-container",p,[(n(),t("svg",k,i[0]||(i[0]=[s("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[s("g",{"data-mml-node":"math"},[s("g",{"data-mml-node":"mi"},[s("path",{"data-c":"1D465",d:"M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z",style:{"stroke-width":"3"}})])])],-1)]))),i[1]||(i[1]=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"x")])],-1))]),i[7]||(i[7]=a(" must be less than a variable ")),s("mjx-container",r,[(n(),t("svg",d,i[2]||(i[2]=[s("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[s("g",{"data-mml-node":"math"},[s("g",{"data-mml-node":"mi"},[s("path",{"data-c":"1D466",d:"M21 287Q21 301 36 335T84 406T158 442Q199 442 224 419T250 355Q248 336 247 334Q247 331 231 288T198 191T182 105Q182 62 196 45T238 27Q261 27 281 38T312 61T339 94Q339 95 344 114T358 173T377 247Q415 397 419 404Q432 431 462 431Q475 431 483 424T494 412T496 403Q496 390 447 193T391 -23Q363 -106 294 -155T156 -205Q111 -205 77 -183T43 -117Q43 -95 50 -80T69 -58T89 -48T106 -45Q150 -45 150 -87Q150 -107 138 -122T115 -142T102 -147L99 -148Q101 -153 118 -160T152 -167H160Q177 -167 186 -165Q219 -156 247 -127T290 -65T313 -9T321 21L315 17Q309 13 296 6T270 -6Q250 -11 231 -11Q185 -11 150 11T104 82Q103 89 103 113Q103 170 138 262T173 379Q173 380 173 381Q173 390 173 393T169 400T158 404H154Q131 404 112 385T82 344T65 302T57 280Q55 278 41 278H27Q21 284 21 287Z",style:{"stroke-width":"3"}})])])],-1)]))),i[3]||(i[3]=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"y")])],-1))]),i[8]||(i[8]=a(" could be defined intentionally as ")),s("mjx-container",o,[(n(),t("svg",g,i[4]||(i[4]=[l('',1)]))),i[5]||(i[5]=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"x"),s("mo",null,"<"),s("mi",null,"y")])],-1))]),i[9]||(i[9]=a("."))]),i[44]||(i[44]=l('
Note that the intention constraint is not directly available through the JC-API in Constraints.jl. It is designed as such since defining a constraint through a predicate is the natural way.
We provide a straightforward example through the :dist_different constraint on how to define and add such a constraint in the USUAL_CONSTRAINTS collection.
Higher level modeling languages such as JuMP should provide a Intention interface.
Defining an intention constraint in JC-API ​
',4)),s("p",null,[i[12]||(i[12]=a("We use the ")),i[13]||(i[13]=s("code",null,"dist_different",-1)),i[14]||(i[14]=a(" constraint to illustrate how to define an intention constraint in ")),i[15]||(i[15]=s("em",null,"Constraints.jl",-1)),i[16]||(i[16]=a(". The ")),i[17]||(i[17]=s("code",null,"dist_different",-1)),i[18]||(i[18]=a(" constraint ensures that the distances between marks ")),s("mjx-container",E,[(n(),t("svg",T,i[10]||(i[10]=[s("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[s("g",{"data-mml-node":"math"},[s("g",{"data-mml-node":"mi"},[s("path",{"data-c":"1D465",d:"M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z",style:{"stroke-width":"3"}})])])],-1)]))),i[11]||(i[11]=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"x")])],-1))]),i[19]||(i[19]=a(" on a ruler are unique."))]),s("mjx-container",Q,[(n(),t("svg",y,i[20]||(i[20]=[l('',1)]))),i[21]||(i[21]=s("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mi",null,"x"),s("mo",{stretchy:"false"},"["),s("mn",null,"1"),s("mo",{stretchy:"false"},"]"),s("mo",null,"−"),s("mi",null,"x"),s("mo",{stretchy:"false"},"["),s("mn",null,"2"),s("mo",{stretchy:"false"},"]"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mo",null,"≠"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mi",null,"x"),s("mo",{stretchy:"false"},"["),s("mn",null,"3"),s("mo",{stretchy:"false"},"]"),s("mo",null,"−"),s("mi",null,"x"),s("mo",{stretchy:"false"},"["),s("mn",null,"4"),s("mo",{stretchy:"false"},"]"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|")])],-1))]),i[45]||(i[45]=l(`
The constraint is then added to the usual constraints collection.
julia
const description_dist_different = """
 Ensures that the distances between marks on the ruler are unique.
 """
 
@@ -9,7 +9,7 @@ import{_ as l,c as t,a5 as e,j as s,a,o as n}from"./chunks/framework.CJakPlgM.js
 @usual concept_dist_different(x) = xcsp_intention(
     list = x,
     predicate = predicate_dist_different
-)
Please check the section dedicated to the Golomb Ruler problem to see a use for this constraint. <!– TODO: Golomb Ruler –>
APIs ​
Note that the intention constraint is not directly available through the JC-API in Constraints.jl. It is designed as such since defining a constraint through a predicate is the natural way.
We provide here a usage example for the :dist_different constraint, previously added to the USUAL_CONSTRAINTS collection.
Higher level modeling language such as JuMP should provide an Intention interface.
julia
using Constraints
+)
Please check the section dedicated to the Golomb Ruler problem to see a use for this constraint. <!– TODO: Golomb Ruler –>
APIs ​
Note that the intention constraint is not directly available through the JC-API in Constraints.jl. It is designed as such since defining a constraint through a predicate is the natural way.
We provide here a usage example for the :dist_different constraint, previously added to the USUAL_CONSTRAINTS collection.
Higher level modeling language such as JuMP should provide an Intention interface.
julia
using Constraints
 
 concept(:dist_different, x)
 concept(:dist_different)(x)
julia
# Defines the DistDifferent constraint
@@ -48,7 +48,7 @@ import{_ as l,c as t,a5 as e,j as s,a,o as n}from"./chunks/framework.CJakPlgM.js
 end
 MOI.add_constraint(optimizer, x, CBLS.Intention(y -> abs(y[1] - y[2]) ≠ abs(y[3] - y[4])))
 
-MOI.optimize!(optimizer)
Extension Constraints ​
`,9)),s("p",null,[i[36]||(i[36]=a("These are constraints that are defined by explicitly listing all the tuples of values that satisfy the constraint. They are called extensional because they are defined by the set of values they allow. 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0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"Y")])],-1))]),i[40]||(i[40]=a(" must be either ")),s("mjx-container",b,[(n(),t("svg",v,i[30]||(i[30]=[s("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[s("g",{"data-mml-node":"math"},[s("g",{"data-mml-node":"mn"},[s("path",{"data-c":"33",d:"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 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677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z",style:{"stroke-width":"3"}})])])],-1)]))),i[33]||(i[33]=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mn",null,"4")])],-1))]),i[42]||(i[42]=a(" could be defined extensionally by the set of tuples ")),s("mjx-container",D,[(n(),t("svg",A,i[34]||(i[34]=[e('',1)]))),i[35]||(i[35]=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mrow",{"data-mjx-texclass":"ORD"},[s("mo",{stretchy:"false"},"("),s("mn",null,"1"),s("mo",null,","),s("mn",null,"3"),s("mo",{stretchy:"false"},")"),s("mo",null,","),s("mo",{stretchy:"false"},"("),s("mn",null,"1"),s("mo",null,","),s("mn",null,"4"),s("mo",{stretchy:"false"},")"),s("mo",null,","),s("mo",{stretchy:"false"},"("),s("mn",null,"2"),s("mo",null,","),s("mn",null,"3"),s("mo",{stretchy:"false"},")"),s("mo",null,","),s("mo",{stretchy:"false"},"("),s("mn",null,"2"),s("mo",null,","),s("mn",null,"4"),s("mo",{stretchy:"false"},")")]),s("mo",null,".")])],-1))])]),i[46]||(i[46]=e(`
These two types of constraints provide a flexible way to define complex relationships between variables in constraint programming.
julia
using Constraints
+MOI.optimize!(optimizer)
Extension Constraints ​
`,9)),s("p",null,[i[36]||(i[36]=a("These are constraints that are defined by explicitly listing all the tuples of values that satisfy the constraint. They are called extensional because they are defined by the set of values they allow. For example, a binary constraint that specifies that a variable ")),s("mjx-container",m,[(n(),t("svg",c,i[22]||(i[22]=[s("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[s("g",{"data-mml-node":"math"},[s("g",{"data-mml-node":"mi"},[s("path",{"data-c":"1D44B",d:"M42 0H40Q26 0 26 11Q26 15 29 27Q33 41 36 43T55 46Q141 49 190 98Q200 108 306 224T411 342Q302 620 297 625Q288 636 234 637H206Q200 643 200 645T202 664Q206 677 212 683H226Q260 681 347 681Q380 681 408 681T453 682T473 682Q490 682 490 671Q490 670 488 658Q484 643 481 640T465 637Q434 634 411 620L488 426L541 485Q646 598 646 610Q646 628 622 635Q617 635 609 637Q594 637 594 648Q594 650 596 664Q600 677 606 683H618Q619 683 643 683T697 681T738 680Q828 680 837 683H845Q852 676 852 672Q850 647 840 637H824Q790 636 763 628T722 611T698 593L687 584Q687 585 592 480L505 384Q505 383 536 304T601 142T638 56Q648 47 699 46Q734 46 734 37Q734 35 732 23Q728 7 725 4T711 1Q708 1 678 1T589 2Q528 2 496 2T461 1Q444 1 444 10Q444 11 446 25Q448 35 450 39T455 44T464 46T480 47T506 54Q523 62 523 64Q522 64 476 181L429 299Q241 95 236 84Q232 76 232 72Q232 53 261 47Q262 47 267 47T273 46Q276 46 277 46T280 45T283 42T284 35Q284 26 282 19Q279 6 276 4T261 1Q258 1 243 1T201 2T142 2Q64 2 42 0Z",style:{"stroke-width":"3"}})])])],-1)]))),i[23]||(i[23]=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"X")])],-1))]),i[37]||(i[37]=a(" must be either ")),s("mjx-container",u,[(n(),t("svg",C,i[24]||(i[24]=[s("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[s("g",{"data-mml-node":"math"},[s("g",{"data-mml-node":"mn"},[s("path",{"data-c":"31",d:"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z",style:{"stroke-width":"3"}})])])],-1)]))),i[25]||(i[25]=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mn",null,"1")])],-1))]),i[38]||(i[38]=a(" or ")),s("mjx-container",F,[(n(),t("svg",x,i[26]||(i[26]=[s("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[s("g",{"data-mml-node":"math"},[s("g",{"data-mml-node":"mn"},[s("path",{"data-c":"32",d:"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z",style:{"stroke-width":"3"}})])])],-1)]))),i[27]||(i[27]=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mn",null,"2")])],-1))]),i[39]||(i[39]=a(" and a variable ")),s("mjx-container",w,[(n(),t("svg",f,i[28]||(i[28]=[s("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[s("g",{"data-mml-node":"math"},[s("g",{"data-mml-node":"mi"},[s("path",{"data-c":"1D44C",d:"M66 637Q54 637 49 637T39 638T32 641T30 647T33 664T42 682Q44 683 56 683Q104 680 165 680Q288 680 306 683H316Q322 677 322 674T320 656Q316 643 310 637H298Q242 637 242 624Q242 619 292 477T343 333L346 336Q350 340 358 349T379 373T411 410T454 461Q546 568 561 587T577 618Q577 634 545 637Q528 637 528 647Q528 649 530 661Q533 676 535 679T549 683Q551 683 578 682T657 680Q684 680 713 681T746 682Q763 682 763 673Q763 669 760 657T755 643Q753 637 734 637Q662 632 617 587Q608 578 477 424L348 273L322 169Q295 62 295 57Q295 46 363 46Q379 46 384 45T390 35Q390 33 388 23Q384 6 382 4T366 1Q361 1 324 1T232 2Q170 2 138 2T102 1Q84 1 84 9Q84 14 87 24Q88 27 89 30T90 35T91 39T93 42T96 44T101 45T107 45T116 46T129 46Q168 47 180 50T198 63Q201 68 227 171L252 274L129 623Q128 624 127 625T125 627T122 629T118 631T113 633T105 634T96 635T83 636T66 637Z",style:{"stroke-width":"3"}})])])],-1)]))),i[29]||(i[29]=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"Y")])],-1))]),i[40]||(i[40]=a(" must be either ")),s("mjx-container",b,[(n(),t("svg",v,i[30]||(i[30]=[s("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[s("g",{"data-mml-node":"math"},[s("g",{"data-mml-node":"mn"},[s("path",{"data-c":"33",d:"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z",style:{"stroke-width":"3"}})])])],-1)]))),i[31]||(i[31]=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mn",null,"3")])],-1))]),i[41]||(i[41]=a(" or ")),s("mjx-container",H,[(n(),t("svg",B,i[32]||(i[32]=[s("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[s("g",{"data-mml-node":"math"},[s("g",{"data-mml-node":"mn"},[s("path",{"data-c":"34",d:"M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z",style:{"stroke-width":"3"}})])])],-1)]))),i[33]||(i[33]=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mn",null,"4")])],-1))]),i[42]||(i[42]=a(" could be defined extensionally by the set of tuples ")),s("mjx-container",D,[(n(),t("svg",A,i[34]||(i[34]=[l('',1)]))),i[35]||(i[35]=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mrow",{"data-mjx-texclass":"ORD"},[s("mo",{stretchy:"false"},"("),s("mn",null,"1"),s("mo",null,","),s("mn",null,"3"),s("mo",{stretchy:"false"},")"),s("mo",null,","),s("mo",{stretchy:"false"},"("),s("mn",null,"1"),s("mo",null,","),s("mn",null,"4"),s("mo",{stretchy:"false"},")"),s("mo",null,","),s("mo",{stretchy:"false"},"("),s("mn",null,"2"),s("mo",null,","),s("mn",null,"3"),s("mo",{stretchy:"false"},")"),s("mo",null,","),s("mo",{stretchy:"false"},"("),s("mn",null,"2"),s("mo",null,","),s("mn",null,"4"),s("mo",{stretchy:"false"},")")]),s("mo",null,".")])],-1))])]),i[46]||(i[46]=l(`
These two types of constraints provide a flexible way to define complex relationships between variables in constraint programming.
julia
using Constraints
 
 concept(:dist_different, x)
 concept(:dist_different)(x)
julia
# Defines the DistDifferent constraint
@@ -87,4 +87,4 @@ import{_ as l,c as t,a5 as e,j as s,a,o as n}from"./chunks/framework.CJakPlgM.js
 end
 MOI.add_constraint(optimizer, x, CBLS.Intention(y -> abs(y[1] - y[2]) ≠ abs(y[3] - y[4])))
 
-MOI.optimize!(optimizer)
`,2))])}const O=l(h,[["render",V]]);export{z as __pageData,O as default};
+MOI.optimize!(optimizer)
`,2))])}const z=e(h,[["render",V]]);export{J as __pageData,z as default}; diff --git a/dev/assets/constraints_21_generic_constraints.md.Cq_hAjZf.lean.js b/dev/assets/constraints_21_generic_constraints.md.DIVWDhM8.lean.js similarity index 97% rename from dev/assets/constraints_21_generic_constraints.md.Cq_hAjZf.lean.js rename to dev/assets/constraints_21_generic_constraints.md.DIVWDhM8.lean.js index 3992c3c..35bb1d7 100644 --- a/dev/assets/constraints_21_generic_constraints.md.Cq_hAjZf.lean.js +++ b/dev/assets/constraints_21_generic_constraints.md.DIVWDhM8.lean.js @@ -1,4 +1,4 @@ -import{_ as l,c as t,a5 as e,j as s,a,o as n}from"./chunks/framework.CJakPlgM.js";const z=JSON.parse('{"title":"Generic Constraints","description":"","frontmatter":{},"headers":[],"relativePath":"constraints/21_generic_constraints.md","filePath":"constraints/21_generic_constraints.md","lastUpdated":null}'),h={name:"constraints/21_generic_constraints.md"},p={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},k={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.294ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 572 453","aria-hidden":"true"},r={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},d={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.464ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.109ex",height:"1.464ex",role:"img",focusable:"false",viewBox:"0 -442 490 647","aria-hidden":"true"},o={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},g={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.464ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.42ex",height:"1.686ex",role:"img",focusable:"false",viewBox:"0 -540 2395.6 745","aria-hidden":"true"},E={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},T={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.294ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 572 453","aria-hidden":"true"},Q={class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},y={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"25.797ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 11402.4 1000","aria-hidden":"true"},m={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},c={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"0"},xmlns:"http://www.w3.org/2000/svg",width:"1.928ex",height:"1.545ex",role:"img",focusable:"false",viewBox:"0 -683 852 683","aria-hidden":"true"},u={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},F={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"0"},xmlns:"http://www.w3.org/2000/svg",width:"1.131ex",height:"1.507ex",role:"img",focusable:"false",viewBox:"0 -666 500 666","aria-hidden":"true"},C={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},x={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"0"},xmlns:"http://www.w3.org/2000/svg",width:"1.131ex",height:"1.507ex",role:"img",focusable:"false",viewBox:"0 -666 500 666","aria-hidden":"true"},w={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},f={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"0"},xmlns:"http://www.w3.org/2000/svg",width:"1.726ex",height:"1.545ex",role:"img",focusable:"false",viewBox:"0 -683 763 683","aria-hidden":"true"},b={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},v={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.05ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.131ex",height:"1.554ex",role:"img",focusable:"false",viewBox:"0 -665 500 687","aria-hidden":"true"},H={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},B={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"0"},xmlns:"http://www.w3.org/2000/svg",width:"1.131ex",height:"1.532ex",role:"img",focusable:"false",viewBox:"0 -677 500 677","aria-hidden":"true"},D={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},A={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"23.762ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 10502.7 1000","aria-hidden":"true"};function V(M,i,L,Z,j,I){return n(),t("div",null,[i[43]||(i[43]=e('

Generic Constraints ​

In the XCSP³-core standard, generic constraints are categorized into two main types: intention and extension constraints.

Intention Constraints ​

',3)),s("p",null,[i[6]||(i[6]=a("These are constraints that are defined by a logical expression or a function. They are called intentional because they are defined by the property they satisfy. For example, a constraint that specifies that a variable ")),s("mjx-container",p,[(n(),t("svg",k,i[0]||(i[0]=[s("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[s("g",{"data-mml-node":"math"},[s("g",{"data-mml-node":"mi"},[s("path",{"data-c":"1D465",d:"M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z",style:{"stroke-width":"3"}})])])],-1)]))),i[1]||(i[1]=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"x")])],-1))]),i[7]||(i[7]=a(" must be less than a variable ")),s("mjx-container",r,[(n(),t("svg",d,i[2]||(i[2]=[s("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[s("g",{"data-mml-node":"math"},[s("g",{"data-mml-node":"mi"},[s("path",{"data-c":"1D466",d:"M21 287Q21 301 36 335T84 406T158 442Q199 442 224 419T250 355Q248 336 247 334Q247 331 231 288T198 191T182 105Q182 62 196 45T238 27Q261 27 281 38T312 61T339 94Q339 95 344 114T358 173T377 247Q415 397 419 404Q432 431 462 431Q475 431 483 424T494 412T496 403Q496 390 447 193T391 -23Q363 -106 294 -155T156 -205Q111 -205 77 -183T43 -117Q43 -95 50 -80T69 -58T89 -48T106 -45Q150 -45 150 -87Q150 -107 138 -122T115 -142T102 -147L99 -148Q101 -153 118 -160T152 -167H160Q177 -167 186 -165Q219 -156 247 -127T290 -65T313 -9T321 21L315 17Q309 13 296 6T270 -6Q250 -11 231 -11Q185 -11 150 11T104 82Q103 89 103 113Q103 170 138 262T173 379Q173 380 173 381Q173 390 173 393T169 400T158 404H154Q131 404 112 385T82 344T65 302T57 280Q55 278 41 278H27Q21 284 21 287Z",style:{"stroke-width":"3"}})])])],-1)]))),i[3]||(i[3]=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"y")])],-1))]),i[8]||(i[8]=a(" could be defined intentionally as ")),s("mjx-container",o,[(n(),t("svg",g,i[4]||(i[4]=[e('',1)]))),i[5]||(i[5]=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"x"),s("mo",null,"<"),s("mi",null,"y")])],-1))]),i[9]||(i[9]=a("."))]),i[44]||(i[44]=e('

Note that the intention constraint is not directly available through the JC-API in Constraints.jl. It is designed as such since defining a constraint through a predicate is the natural way.

We provide a straightforward example through the :dist_different constraint on how to define and add such a constraint in the USUAL_CONSTRAINTS collection.

Higher level modeling languages such as JuMP should provide a Intention interface.

Defining an intention constraint in JC-API ​

',4)),s("p",null,[i[12]||(i[12]=a("We use the ")),i[13]||(i[13]=s("code",null,"dist_different",-1)),i[14]||(i[14]=a(" constraint to illustrate how to define an intention constraint in ")),i[15]||(i[15]=s("em",null,"Constraints.jl",-1)),i[16]||(i[16]=a(". The ")),i[17]||(i[17]=s("code",null,"dist_different",-1)),i[18]||(i[18]=a(" constraint ensures that the distances between marks ")),s("mjx-container",E,[(n(),t("svg",T,i[10]||(i[10]=[s("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[s("g",{"data-mml-node":"math"},[s("g",{"data-mml-node":"mi"},[s("path",{"data-c":"1D465",d:"M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z",style:{"stroke-width":"3"}})])])],-1)]))),i[11]||(i[11]=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"x")])],-1))]),i[19]||(i[19]=a(" on a ruler are unique."))]),s("mjx-container",Q,[(n(),t("svg",y,i[20]||(i[20]=[e('',1)]))),i[21]||(i[21]=s("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mi",null,"x"),s("mo",{stretchy:"false"},"["),s("mn",null,"1"),s("mo",{stretchy:"false"},"]"),s("mo",null,"−"),s("mi",null,"x"),s("mo",{stretchy:"false"},"["),s("mn",null,"2"),s("mo",{stretchy:"false"},"]"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mo",null,"≠"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mi",null,"x"),s("mo",{stretchy:"false"},"["),s("mn",null,"3"),s("mo",{stretchy:"false"},"]"),s("mo",null,"−"),s("mi",null,"x"),s("mo",{stretchy:"false"},"["),s("mn",null,"4"),s("mo",{stretchy:"false"},"]"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|")])],-1))]),i[45]||(i[45]=e(`

The constraint is then added to the usual constraints collection.

julia
const description_dist_different = """
+import{_ as e,c as t,a5 as l,j as s,a,o as n}from"./chunks/framework.CJakPlgM.js";const J=JSON.parse('{"title":"Generic Constraints","description":"","frontmatter":{},"headers":[],"relativePath":"constraints/21_generic_constraints.md","filePath":"constraints/21_generic_constraints.md","lastUpdated":null}'),h={name:"constraints/21_generic_constraints.md"},p={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},k={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.294ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 572 453","aria-hidden":"true"},r={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},d={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.464ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.109ex",height:"1.464ex",role:"img",focusable:"false",viewBox:"0 -442 490 647","aria-hidden":"true"},o={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},g={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.464ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.42ex",height:"1.686ex",role:"img",focusable:"false",viewBox:"0 -540 2395.6 745","aria-hidden":"true"},E={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},T={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.294ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 572 453","aria-hidden":"true"},Q={class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},y={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"25.797ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 11402.4 1000","aria-hidden":"true"},m={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},c={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"0"},xmlns:"http://www.w3.org/2000/svg",width:"1.928ex",height:"1.545ex",role:"img",focusable:"false",viewBox:"0 -683 852 683","aria-hidden":"true"},u={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},C={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"0"},xmlns:"http://www.w3.org/2000/svg",width:"1.131ex",height:"1.507ex",role:"img",focusable:"false",viewBox:"0 -666 500 666","aria-hidden":"true"},F={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},x={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"0"},xmlns:"http://www.w3.org/2000/svg",width:"1.131ex",height:"1.507ex",role:"img",focusable:"false",viewBox:"0 -666 500 666","aria-hidden":"true"},w={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},f={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"0"},xmlns:"http://www.w3.org/2000/svg",width:"1.726ex",height:"1.545ex",role:"img",focusable:"false",viewBox:"0 -683 763 683","aria-hidden":"true"},b={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},v={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.05ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.131ex",height:"1.554ex",role:"img",focusable:"false",viewBox:"0 -665 500 687","aria-hidden":"true"},H={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},B={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"0"},xmlns:"http://www.w3.org/2000/svg",width:"1.131ex",height:"1.532ex",role:"img",focusable:"false",viewBox:"0 -677 500 677","aria-hidden":"true"},D={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},A={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"23.762ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 10502.7 1000","aria-hidden":"true"};function V(M,i,L,j,Z,I){return n(),t("div",null,[i[43]||(i[43]=l('
Generic Constraints ​
In the XCSP³-core standard, generic constraints are categorized into two main types: intention and extension constraints.
Intention Constraints ​
',3)),s("p",null,[i[6]||(i[6]=a("These are constraints that are defined by a logical expression or a function. They are called intentional because they are defined by the property they satisfy. For example, a constraint that specifies that a variable ")),s("mjx-container",p,[(n(),t("svg",k,i[0]||(i[0]=[s("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[s("g",{"data-mml-node":"math"},[s("g",{"data-mml-node":"mi"},[s("path",{"data-c":"1D465",d:"M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z",style:{"stroke-width":"3"}})])])],-1)]))),i[1]||(i[1]=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"x")])],-1))]),i[7]||(i[7]=a(" must be less than a variable ")),s("mjx-container",r,[(n(),t("svg",d,i[2]||(i[2]=[s("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[s("g",{"data-mml-node":"math"},[s("g",{"data-mml-node":"mi"},[s("path",{"data-c":"1D466",d:"M21 287Q21 301 36 335T84 406T158 442Q199 442 224 419T250 355Q248 336 247 334Q247 331 231 288T198 191T182 105Q182 62 196 45T238 27Q261 27 281 38T312 61T339 94Q339 95 344 114T358 173T377 247Q415 397 419 404Q432 431 462 431Q475 431 483 424T494 412T496 403Q496 390 447 193T391 -23Q363 -106 294 -155T156 -205Q111 -205 77 -183T43 -117Q43 -95 50 -80T69 -58T89 -48T106 -45Q150 -45 150 -87Q150 -107 138 -122T115 -142T102 -147L99 -148Q101 -153 118 -160T152 -167H160Q177 -167 186 -165Q219 -156 247 -127T290 -65T313 -9T321 21L315 17Q309 13 296 6T270 -6Q250 -11 231 -11Q185 -11 150 11T104 82Q103 89 103 113Q103 170 138 262T173 379Q173 380 173 381Q173 390 173 393T169 400T158 404H154Q131 404 112 385T82 344T65 302T57 280Q55 278 41 278H27Q21 284 21 287Z",style:{"stroke-width":"3"}})])])],-1)]))),i[3]||(i[3]=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"y")])],-1))]),i[8]||(i[8]=a(" could be defined intentionally as ")),s("mjx-container",o,[(n(),t("svg",g,i[4]||(i[4]=[l('',1)]))),i[5]||(i[5]=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"x"),s("mo",null,"<"),s("mi",null,"y")])],-1))]),i[9]||(i[9]=a("."))]),i[44]||(i[44]=l('
Note that the intention constraint is not directly available through the JC-API in Constraints.jl. It is designed as such since defining a constraint through a predicate is the natural way.
We provide a straightforward example through the :dist_different constraint on how to define and add such a constraint in the USUAL_CONSTRAINTS collection.
Higher level modeling languages such as JuMP should provide a Intention interface.
Defining an intention constraint in JC-API ​
',4)),s("p",null,[i[12]||(i[12]=a("We use the ")),i[13]||(i[13]=s("code",null,"dist_different",-1)),i[14]||(i[14]=a(" constraint to illustrate how to define an intention constraint in ")),i[15]||(i[15]=s("em",null,"Constraints.jl",-1)),i[16]||(i[16]=a(". The ")),i[17]||(i[17]=s("code",null,"dist_different",-1)),i[18]||(i[18]=a(" constraint ensures that the distances between marks ")),s("mjx-container",E,[(n(),t("svg",T,i[10]||(i[10]=[s("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[s("g",{"data-mml-node":"math"},[s("g",{"data-mml-node":"mi"},[s("path",{"data-c":"1D465",d:"M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z",style:{"stroke-width":"3"}})])])],-1)]))),i[11]||(i[11]=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"x")])],-1))]),i[19]||(i[19]=a(" on a ruler are unique."))]),s("mjx-container",Q,[(n(),t("svg",y,i[20]||(i[20]=[l('',1)]))),i[21]||(i[21]=s("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mi",null,"x"),s("mo",{stretchy:"false"},"["),s("mn",null,"1"),s("mo",{stretchy:"false"},"]"),s("mo",null,"−"),s("mi",null,"x"),s("mo",{stretchy:"false"},"["),s("mn",null,"2"),s("mo",{stretchy:"false"},"]"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mo",null,"≠"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mi",null,"x"),s("mo",{stretchy:"false"},"["),s("mn",null,"3"),s("mo",{stretchy:"false"},"]"),s("mo",null,"−"),s("mi",null,"x"),s("mo",{stretchy:"false"},"["),s("mn",null,"4"),s("mo",{stretchy:"false"},"]"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|")])],-1))]),i[45]||(i[45]=l(`
The constraint is then added to the usual constraints collection.
julia
const description_dist_different = """
 Ensures that the distances between marks on the ruler are unique.
 """
 
@@ -9,7 +9,7 @@ import{_ as l,c as t,a5 as e,j as s,a,o as n}from"./chunks/framework.CJakPlgM.js
 @usual concept_dist_different(x) = xcsp_intention(
     list = x,
     predicate = predicate_dist_different
-)
Please check the section dedicated to the Golomb Ruler problem to see a use for this constraint. <!– TODO: Golomb Ruler –>
APIs ​
Note that the intention constraint is not directly available through the JC-API in Constraints.jl. It is designed as such since defining a constraint through a predicate is the natural way.
We provide here a usage example for the :dist_different constraint, previously added to the USUAL_CONSTRAINTS collection.
Higher level modeling language such as JuMP should provide an Intention interface.
julia
using Constraints
+)
Please check the section dedicated to the Golomb Ruler problem to see a use for this constraint. <!– TODO: Golomb Ruler –>
APIs ​
Note that the intention constraint is not directly available through the JC-API in Constraints.jl. It is designed as such since defining a constraint through a predicate is the natural way.
We provide here a usage example for the :dist_different constraint, previously added to the USUAL_CONSTRAINTS collection.
Higher level modeling language such as JuMP should provide an Intention interface.
julia
using Constraints
 
 concept(:dist_different, x)
 concept(:dist_different)(x)
julia
# Defines the DistDifferent constraint
@@ -48,7 +48,7 @@ import{_ as l,c as t,a5 as e,j as s,a,o as n}from"./chunks/framework.CJakPlgM.js
 end
 MOI.add_constraint(optimizer, x, CBLS.Intention(y -> abs(y[1] - y[2]) ≠ abs(y[3] - y[4])))
 
-MOI.optimize!(optimizer)
Extension Constraints ​
`,9)),s("p",null,[i[36]||(i[36]=a("These are constraints that are defined by explicitly listing all the tuples of values that satisfy the constraint. They are called extensional because they are defined by the set of values they allow. For example, a binary constraint that specifies that a variable ")),s("mjx-container",m,[(n(),t("svg",c,i[22]||(i[22]=[s("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[s("g",{"data-mml-node":"math"},[s("g",{"data-mml-node":"mi"},[s("path",{"data-c":"1D44B",d:"M42 0H40Q26 0 26 11Q26 15 29 27Q33 41 36 43T55 46Q141 49 190 98Q200 108 306 224T411 342Q302 620 297 625Q288 636 234 637H206Q200 643 200 645T202 664Q206 677 212 683H226Q260 681 347 681Q380 681 408 681T453 682T473 682Q490 682 490 671Q490 670 488 658Q484 643 481 640T465 637Q434 634 411 620L488 426L541 485Q646 598 646 610Q646 628 622 635Q617 635 609 637Q594 637 594 648Q594 650 596 664Q600 677 606 683H618Q619 683 643 683T697 681T738 680Q828 680 837 683H845Q852 676 852 672Q850 647 840 637H824Q790 636 763 628T722 611T698 593L687 584Q687 585 592 480L505 384Q505 383 536 304T601 142T638 56Q648 47 699 46Q734 46 734 37Q734 35 732 23Q728 7 725 4T711 1Q708 1 678 1T589 2Q528 2 496 2T461 1Q444 1 444 10Q444 11 446 25Q448 35 450 39T455 44T464 46T480 47T506 54Q523 62 523 64Q522 64 476 181L429 299Q241 95 236 84Q232 76 232 72Q232 53 261 47Q262 47 267 47T273 46Q276 46 277 46T280 45T283 42T284 35Q284 26 282 19Q279 6 276 4T261 1Q258 1 243 1T201 2T142 2Q64 2 42 0Z",style:{"stroke-width":"3"}})])])],-1)]))),i[23]||(i[23]=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"X")])],-1))]),i[37]||(i[37]=a(" must be either ")),s("mjx-container",u,[(n(),t("svg",F,i[24]||(i[24]=[s("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[s("g",{"data-mml-node":"math"},[s("g",{"data-mml-node":"mn"},[s("path",{"data-c":"31",d:"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z",style:{"stroke-width":"3"}})])])],-1)]))),i[25]||(i[25]=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mn",null,"1")])],-1))]),i[38]||(i[38]=a(" or ")),s("mjx-container",C,[(n(),t("svg",x,i[26]||(i[26]=[s("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[s("g",{"data-mml-node":"math"},[s("g",{"data-mml-node":"mn"},[s("path",{"data-c":"32",d:"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z",style:{"stroke-width":"3"}})])])],-1)]))),i[27]||(i[27]=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mn",null,"2")])],-1))]),i[39]||(i[39]=a(" and a variable ")),s("mjx-container",w,[(n(),t("svg",f,i[28]||(i[28]=[s("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[s("g",{"data-mml-node":"math"},[s("g",{"data-mml-node":"mi"},[s("path",{"data-c":"1D44C",d:"M66 637Q54 637 49 637T39 638T32 641T30 647T33 664T42 682Q44 683 56 683Q104 680 165 680Q288 680 306 683H316Q322 677 322 674T320 656Q316 643 310 637H298Q242 637 242 624Q242 619 292 477T343 333L346 336Q350 340 358 349T379 373T411 410T454 461Q546 568 561 587T577 618Q577 634 545 637Q528 637 528 647Q528 649 530 661Q533 676 535 679T549 683Q551 683 578 682T657 680Q684 680 713 681T746 682Q763 682 763 673Q763 669 760 657T755 643Q753 637 734 637Q662 632 617 587Q608 578 477 424L348 273L322 169Q295 62 295 57Q295 46 363 46Q379 46 384 45T390 35Q390 33 388 23Q384 6 382 4T366 1Q361 1 324 1T232 2Q170 2 138 2T102 1Q84 1 84 9Q84 14 87 24Q88 27 89 30T90 35T91 39T93 42T96 44T101 45T107 45T116 46T129 46Q168 47 180 50T198 63Q201 68 227 171L252 274L129 623Q128 624 127 625T125 627T122 629T118 631T113 633T105 634T96 635T83 636T66 637Z",style:{"stroke-width":"3"}})])])],-1)]))),i[29]||(i[29]=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"Y")])],-1))]),i[40]||(i[40]=a(" must be either ")),s("mjx-container",b,[(n(),t("svg",v,i[30]||(i[30]=[s("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[s("g",{"data-mml-node":"math"},[s("g",{"data-mml-node":"mn"},[s("path",{"data-c":"33",d:"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z",style:{"stroke-width":"3"}})])])],-1)]))),i[31]||(i[31]=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mn",null,"3")])],-1))]),i[41]||(i[41]=a(" or ")),s("mjx-container",H,[(n(),t("svg",B,i[32]||(i[32]=[s("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[s("g",{"data-mml-node":"math"},[s("g",{"data-mml-node":"mn"},[s("path",{"data-c":"34",d:"M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z",style:{"stroke-width":"3"}})])])],-1)]))),i[33]||(i[33]=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mn",null,"4")])],-1))]),i[42]||(i[42]=a(" could be defined extensionally by the set of tuples ")),s("mjx-container",D,[(n(),t("svg",A,i[34]||(i[34]=[e('',1)]))),i[35]||(i[35]=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mrow",{"data-mjx-texclass":"ORD"},[s("mo",{stretchy:"false"},"("),s("mn",null,"1"),s("mo",null,","),s("mn",null,"3"),s("mo",{stretchy:"false"},")"),s("mo",null,","),s("mo",{stretchy:"false"},"("),s("mn",null,"1"),s("mo",null,","),s("mn",null,"4"),s("mo",{stretchy:"false"},")"),s("mo",null,","),s("mo",{stretchy:"false"},"("),s("mn",null,"2"),s("mo",null,","),s("mn",null,"3"),s("mo",{stretchy:"false"},")"),s("mo",null,","),s("mo",{stretchy:"false"},"("),s("mn",null,"2"),s("mo",null,","),s("mn",null,"4"),s("mo",{stretchy:"false"},")")]),s("mo",null,".")])],-1))])]),i[46]||(i[46]=e(`
These two types of constraints provide a flexible way to define complex relationships between variables in constraint programming.
julia
using Constraints
+MOI.optimize!(optimizer)
Extension Constraints ​
`,9)),s("p",null,[i[36]||(i[36]=a("These are constraints that are defined by explicitly listing all the tuples of values that satisfy the constraint. They are called extensional because they are defined by the set of values they allow. For example, a binary constraint that specifies that a variable ")),s("mjx-container",m,[(n(),t("svg",c,i[22]||(i[22]=[s("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[s("g",{"data-mml-node":"math"},[s("g",{"data-mml-node":"mi"},[s("path",{"data-c":"1D44B",d:"M42 0H40Q26 0 26 11Q26 15 29 27Q33 41 36 43T55 46Q141 49 190 98Q200 108 306 224T411 342Q302 620 297 625Q288 636 234 637H206Q200 643 200 645T202 664Q206 677 212 683H226Q260 681 347 681Q380 681 408 681T453 682T473 682Q490 682 490 671Q490 670 488 658Q484 643 481 640T465 637Q434 634 411 620L488 426L541 485Q646 598 646 610Q646 628 622 635Q617 635 609 637Q594 637 594 648Q594 650 596 664Q600 677 606 683H618Q619 683 643 683T697 681T738 680Q828 680 837 683H845Q852 676 852 672Q850 647 840 637H824Q790 636 763 628T722 611T698 593L687 584Q687 585 592 480L505 384Q505 383 536 304T601 142T638 56Q648 47 699 46Q734 46 734 37Q734 35 732 23Q728 7 725 4T711 1Q708 1 678 1T589 2Q528 2 496 2T461 1Q444 1 444 10Q444 11 446 25Q448 35 450 39T455 44T464 46T480 47T506 54Q523 62 523 64Q522 64 476 181L429 299Q241 95 236 84Q232 76 232 72Q232 53 261 47Q262 47 267 47T273 46Q276 46 277 46T280 45T283 42T284 35Q284 26 282 19Q279 6 276 4T261 1Q258 1 243 1T201 2T142 2Q64 2 42 0Z",style:{"stroke-width":"3"}})])])],-1)]))),i[23]||(i[23]=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"X")])],-1))]),i[37]||(i[37]=a(" must be either ")),s("mjx-container",u,[(n(),t("svg",C,i[24]||(i[24]=[s("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[s("g",{"data-mml-node":"math"},[s("g",{"data-mml-node":"mn"},[s("path",{"data-c":"31",d:"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z",style:{"stroke-width":"3"}})])])],-1)]))),i[25]||(i[25]=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mn",null,"1")])],-1))]),i[38]||(i[38]=a(" or ")),s("mjx-container",F,[(n(),t("svg",x,i[26]||(i[26]=[s("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[s("g",{"data-mml-node":"math"},[s("g",{"data-mml-node":"mn"},[s("path",{"data-c":"32",d:"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z",style:{"stroke-width":"3"}})])])],-1)]))),i[27]||(i[27]=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mn",null,"2")])],-1))]),i[39]||(i[39]=a(" and a variable ")),s("mjx-container",w,[(n(),t("svg",f,i[28]||(i[28]=[s("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[s("g",{"data-mml-node":"math"},[s("g",{"data-mml-node":"mi"},[s("path",{"data-c":"1D44C",d:"M66 637Q54 637 49 637T39 638T32 641T30 647T33 664T42 682Q44 683 56 683Q104 680 165 680Q288 680 306 683H316Q322 677 322 674T320 656Q316 643 310 637H298Q242 637 242 624Q242 619 292 477T343 333L346 336Q350 340 358 349T379 373T411 410T454 461Q546 568 561 587T577 618Q577 634 545 637Q528 637 528 647Q528 649 530 661Q533 676 535 679T549 683Q551 683 578 682T657 680Q684 680 713 681T746 682Q763 682 763 673Q763 669 760 657T755 643Q753 637 734 637Q662 632 617 587Q608 578 477 424L348 273L322 169Q295 62 295 57Q295 46 363 46Q379 46 384 45T390 35Q390 33 388 23Q384 6 382 4T366 1Q361 1 324 1T232 2Q170 2 138 2T102 1Q84 1 84 9Q84 14 87 24Q88 27 89 30T90 35T91 39T93 42T96 44T101 45T107 45T116 46T129 46Q168 47 180 50T198 63Q201 68 227 171L252 274L129 623Q128 624 127 625T125 627T122 629T118 631T113 633T105 634T96 635T83 636T66 637Z",style:{"stroke-width":"3"}})])])],-1)]))),i[29]||(i[29]=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"Y")])],-1))]),i[40]||(i[40]=a(" must be either ")),s("mjx-container",b,[(n(),t("svg",v,i[30]||(i[30]=[s("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[s("g",{"data-mml-node":"math"},[s("g",{"data-mml-node":"mn"},[s("path",{"data-c":"33",d:"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z",style:{"stroke-width":"3"}})])])],-1)]))),i[31]||(i[31]=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mn",null,"3")])],-1))]),i[41]||(i[41]=a(" or ")),s("mjx-container",H,[(n(),t("svg",B,i[32]||(i[32]=[s("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[s("g",{"data-mml-node":"math"},[s("g",{"data-mml-node":"mn"},[s("path",{"data-c":"34",d:"M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z",style:{"stroke-width":"3"}})])])],-1)]))),i[33]||(i[33]=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mn",null,"4")])],-1))]),i[42]||(i[42]=a(" could be defined extensionally by the set of tuples ")),s("mjx-container",D,[(n(),t("svg",A,i[34]||(i[34]=[l('',1)]))),i[35]||(i[35]=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mrow",{"data-mjx-texclass":"ORD"},[s("mo",{stretchy:"false"},"("),s("mn",null,"1"),s("mo",null,","),s("mn",null,"3"),s("mo",{stretchy:"false"},")"),s("mo",null,","),s("mo",{stretchy:"false"},"("),s("mn",null,"1"),s("mo",null,","),s("mn",null,"4"),s("mo",{stretchy:"false"},")"),s("mo",null,","),s("mo",{stretchy:"false"},"("),s("mn",null,"2"),s("mo",null,","),s("mn",null,"3"),s("mo",{stretchy:"false"},")"),s("mo",null,","),s("mo",{stretchy:"false"},"("),s("mn",null,"2"),s("mo",null,","),s("mn",null,"4"),s("mo",{stretchy:"false"},")")]),s("mo",null,".")])],-1))])]),i[46]||(i[46]=l(`
These two types of constraints provide a flexible way to define complex relationships between variables in constraint programming.
julia
using Constraints
 
 concept(:dist_different, x)
 concept(:dist_different)(x)
julia
# Defines the DistDifferent constraint
@@ -87,4 +87,4 @@ import{_ as l,c as t,a5 as e,j as s,a,o as n}from"./chunks/framework.CJakPlgM.js
 end
 MOI.add_constraint(optimizer, x, CBLS.Intention(y -> abs(y[1] - y[2]) ≠ abs(y[3] - y[4])))
 
-MOI.optimize!(optimizer)
`,2))])}const O=l(h,[["render",V]]);export{z as __pageData,O as default};
+MOI.optimize!(optimizer)
`,2))])}const z=e(h,[["render",V]]);export{J as __pageData,z as default}; diff --git a/dev/assets/constraints_23_comparison_constraints.md.4b0z8qtK.js b/dev/assets/constraints_23_comparison_constraints.md.6Pt2XSoe.js similarity index 98% rename from dev/assets/constraints_23_comparison_constraints.md.4b0z8qtK.js rename to dev/assets/constraints_23_comparison_constraints.md.6Pt2XSoe.js index c6a5235..7f83451 100644 --- a/dev/assets/constraints_23_comparison_constraints.md.4b0z8qtK.js +++ b/dev/assets/constraints_23_comparison_constraints.md.6Pt2XSoe.js @@ -1,4 +1,4 @@ -import{_ as l,c as k,a5 as a,j as i,a as h,G as t,B as p,o as e}from"./chunks/framework.CJakPlgM.js";const b=JSON.parse('{"title":"Constraints.jl: Streamlining Constraint Definition and Integration in Julia","description":"","frontmatter":{},"headers":[],"relativePath":"constraints/23_comparison_constraints.md","filePath":"constraints/23_comparison_constraints.md","lastUpdated":null}'),E={name:"constraints/23_comparison_constraints.md"},r={class:"jldocstring custom-block",open:""},d={class:"jldocstring custom-block",open:""},g={class:"jldocstring custom-block",open:""};function y(o,s,F,C,c,u){const n=p("Badge");return e(),k("div",null,[s[9]||(s[9]=a(`

Constraints.jl: Streamlining Constraint Definition and Integration in Julia ​

julia
using Constraints
+import{_ as l,c as k,a5 as a,j as i,a as h,G as t,B as p,o as e}from"./chunks/framework.CJakPlgM.js";const b=JSON.parse('{"title":"Constraints.jl: Streamlining Constraint Definition and Integration in Julia","description":"","frontmatter":{},"headers":[],"relativePath":"constraints/23_comparison_constraints.md","filePath":"constraints/23_comparison_constraints.md","lastUpdated":null}'),E={name:"constraints/23_comparison_constraints.md"},r={class:"jldocstring custom-block",open:""},d={class:"jldocstring custom-block",open:""},g={class:"jldocstring custom-block",open:""};function y(o,s,F,C,c,u){const n=p("Badge");return e(),k("div",null,[s[9]||(s[9]=a(`
Constraints.jl: Streamlining Constraint Definition and Integration in Julia ​
julia
using Constraints
 
 concept(:all_different, [1,1,1,2]) # false
 concept(:all_different, [1,9,3,2]) # true
julia
using Constraints
@@ -17,7 +17,7 @@ import{_ as l,c as k,a5 as a,j as i,a as h,G as t,B as p,o as e}from"./chunks/fr
 JuMP.optimize!(model)
 @info "All Different" value.(X) value.(Y)
 
-# Note that this example gives a solution for the all_different constraint.
julia
# TODO: How to handle intention in JuMP/MOI
julia
using Constraints
+# Note that this example gives a solution for the all_different constraint.
julia
# TODO: How to handle intention in JuMP/MOI
julia
using Constraints
 
 concept(:all_equal, [1,1,1,2]) #false
 concept(:all_equal, [1,1,1,1]) #true
julia
using Constraints
@@ -35,7 +35,7 @@ import{_ as l,c as k,a5 as a,j as i,a as h,G as t,B as p,o as e}from"./chunks/fr
 JuMP.optimize!(model)
 @info "All Equal" value.(X)
 
-# Note that this example gives a solution for the all_equal constraint.
julia
# TODO: How to handle intention in JuMP/MOI
julia
using Constraints
+# Note that this example gives a solution for the all_equal constraint.
julia
# TODO: How to handle intention in JuMP/MOI
julia
using Constraints
 
 @info concept(:ordered, [1, 2, 3, 4, 4]; op=≤)
 @info concept(:ordered, [1, 2, 3, 3, 5]; op=<)
diff --git a/dev/assets/constraints_23_comparison_constraints.md.4b0z8qtK.lean.js b/dev/assets/constraints_23_comparison_constraints.md.6Pt2XSoe.lean.js
similarity index 98%
rename from dev/assets/constraints_23_comparison_constraints.md.4b0z8qtK.lean.js
rename to dev/assets/constraints_23_comparison_constraints.md.6Pt2XSoe.lean.js
index c6a5235..7f83451 100644
--- a/dev/assets/constraints_23_comparison_constraints.md.4b0z8qtK.lean.js
+++ b/dev/assets/constraints_23_comparison_constraints.md.6Pt2XSoe.lean.js
@@ -1,4 +1,4 @@
-import{_ as l,c as k,a5 as a,j as i,a as h,G as t,B as p,o as e}from"./chunks/framework.CJakPlgM.js";const b=JSON.parse('{"title":"Constraints.jl: Streamlining Constraint Definition and Integration in Julia","description":"","frontmatter":{},"headers":[],"relativePath":"constraints/23_comparison_constraints.md","filePath":"constraints/23_comparison_constraints.md","lastUpdated":null}'),E={name:"constraints/23_comparison_constraints.md"},r={class:"jldocstring custom-block",open:""},d={class:"jldocstring custom-block",open:""},g={class:"jldocstring custom-block",open:""};function y(o,s,F,C,c,u){const n=p("Badge");return e(),k("div",null,[s[9]||(s[9]=a(`
Constraints.jl: Streamlining Constraint Definition and Integration in Julia ​
julia
using Constraints
+import{_ as l,c as k,a5 as a,j as i,a as h,G as t,B as p,o as e}from"./chunks/framework.CJakPlgM.js";const b=JSON.parse('{"title":"Constraints.jl: Streamlining Constraint Definition and Integration in Julia","description":"","frontmatter":{},"headers":[],"relativePath":"constraints/23_comparison_constraints.md","filePath":"constraints/23_comparison_constraints.md","lastUpdated":null}'),E={name:"constraints/23_comparison_constraints.md"},r={class:"jldocstring custom-block",open:""},d={class:"jldocstring custom-block",open:""},g={class:"jldocstring custom-block",open:""};function y(o,s,F,C,c,u){const n=p("Badge");return e(),k("div",null,[s[9]||(s[9]=a(`
Constraints.jl: Streamlining Constraint Definition and Integration in Julia ​
julia
using Constraints
 
 concept(:all_different, [1,1,1,2]) # false
 concept(:all_different, [1,9,3,2]) # true
julia
using Constraints
@@ -17,7 +17,7 @@ import{_ as l,c as k,a5 as a,j as i,a as h,G as t,B as p,o as e}from"./chunks/fr
 JuMP.optimize!(model)
 @info "All Different" value.(X) value.(Y)
 
-# Note that this example gives a solution for the all_different constraint.
julia
# TODO: How to handle intention in JuMP/MOI
julia
using Constraints
+# Note that this example gives a solution for the all_different constraint.
julia
# TODO: How to handle intention in JuMP/MOI
julia
using Constraints
 
 concept(:all_equal, [1,1,1,2]) #false
 concept(:all_equal, [1,1,1,1]) #true
julia
using Constraints
@@ -35,7 +35,7 @@ import{_ as l,c as k,a5 as a,j as i,a as h,G as t,B as p,o as e}from"./chunks/fr
 JuMP.optimize!(model)
 @info "All Equal" value.(X)
 
-# Note that this example gives a solution for the all_equal constraint.
julia
# TODO: How to handle intention in JuMP/MOI
julia
using Constraints
+# Note that this example gives a solution for the all_equal constraint.
julia
# TODO: How to handle intention in JuMP/MOI
julia
using Constraints
 
 @info concept(:ordered, [1, 2, 3, 4, 4]; op=≤)
 @info concept(:ordered, [1, 2, 3, 3, 5]; op=<)
diff --git a/dev/assets/constraints_24_counting_summing_constraints.md.DVkY5sTG.lean.js b/dev/assets/constraints_24_counting_summing_constraints.md.XccROfRE.js
similarity index 98%
rename from dev/assets/constraints_24_counting_summing_constraints.md.DVkY5sTG.lean.js
rename to dev/assets/constraints_24_counting_summing_constraints.md.XccROfRE.js
index faa1337..966bddf 100644
--- a/dev/assets/constraints_24_counting_summing_constraints.md.DVkY5sTG.lean.js
+++ b/dev/assets/constraints_24_counting_summing_constraints.md.XccROfRE.js
@@ -1,4 +1,4 @@
-import{_ as t,c as l,a5 as a,j as i,a as k,G as n,B as p,o as e}from"./chunks/framework.CJakPlgM.js";const b=JSON.parse('{"title":"Constraints.jl: Streamlining Constraint Definition and Integration in Julia","description":"","frontmatter":{},"headers":[],"relativePath":"constraints/24_counting_summing_constraints.md","filePath":"constraints/24_counting_summing_constraints.md","lastUpdated":null}'),E={name:"constraints/24_counting_summing_constraints.md"},d={class:"jldocstring custom-block",open:""},r={class:"jldocstring custom-block",open:""},g={class:"jldocstring custom-block",open:""},y={class:"jldocstring custom-block",open:""};function F(C,s,o,c,B,u){const h=p("Badge");return e(),l("div",null,[s[12]||(s[12]=a(`
Constraints.jl: Streamlining Constraint Definition and Integration in Julia ​
julia
using Constraints
+import{_ as t,c as l,a5 as a,j as i,a as k,G as n,B as p,o as e}from"./chunks/framework.CJakPlgM.js";const b=JSON.parse('{"title":"Constraints.jl: Streamlining Constraint Definition and Integration in Julia","description":"","frontmatter":{},"headers":[],"relativePath":"constraints/24_counting_summing_constraints.md","filePath":"constraints/24_counting_summing_constraints.md","lastUpdated":null}'),E={name:"constraints/24_counting_summing_constraints.md"},d={class:"jldocstring custom-block",open:""},r={class:"jldocstring custom-block",open:""},g={class:"jldocstring custom-block",open:""},y={class:"jldocstring custom-block",open:""};function F(C,s,o,c,B,u){const h=p("Badge");return e(),l("div",null,[s[12]||(s[12]=a(`
Constraints.jl: Streamlining Constraint Definition and Integration in Julia ​
julia
using Constraints
 
 @info concept(:sum, [1, 2, 3, 4, 5]; op = ==, val=15)
 @info concept(:sum, [1, 2, 3, 4, 5]; op = ==, val=2)
@@ -20,7 +20,7 @@ import{_ as t,c as l,a5 as a,j as i,a as k,G as n,B as p,o as e}from"./chunks/fr
 @constraint(model, X in Sum(; op = ==, val = 15))
 @constraint(model, Y in Sum(; op = <=, val = 10))
 JuMP.optimize!(model)
-@info "Sum" value.(X) value.(Y)
julia
# TODO: How to handle intention in JuMP/MOI
julia
using Constraints
+@info "Sum" value.(X) value.(Y)
julia
# TODO: How to handle intention in JuMP/MOI
julia
using Constraints
 
 concept(:count, [1,1,1,2], vals = [1, 1, 1, 2], op = ==, val = 4) # true
 concept(:count, [1,1,1,2], vals = [1, 1, 1, 2], op = ==, val = 5) # false
@@ -54,7 +54,7 @@ import{_ as t,c as l,a5 as a,j as i,a as k,G as n,B as p,o as e}from"./chunks/fr
 @constraint(model, X_at_most in AtMost(vals = [1, 2], val = 1))
 @constraint(model, X_exactly in Exactly(vals = [1, 2], val = 2))
 JuMP.optimize!(model)
-@info "Count" value.(X) value.(X_at_least) value.(X_at_most) value.(X_exactly)
julia
# TODO: How to handle intention in JuMP/MOI
julia
using Constraints
+@info "Count" value.(X) value.(X_at_least) value.(X_at_most) value.(X_exactly)
julia
# TODO: How to handle intention in JuMP/MOI
julia
using Constraints
 
 @info concept(:nvalues, [1, 2, 3, 4, 5]; op = ==, val = 5)
 @info concept(:nvalues, [1, 2, 3, 4, 5]; op = ==, val = 2)
@@ -78,7 +78,7 @@ import{_ as t,c as l,a5 as a,j as i,a as k,G as n,B as p,o as e}from"./chunks/fr
 @constraint(model, Y in NValues(; op = ==, val = 2))
 @constraint(model, Z in NValues(; op = <=, val = 5, vals = [1, 2]))
 JuMP.optimize!(model)
-@info "NValues" value.(X) value.(Y) value.(Z)
julia
# TODO: How to handle intention in JuMP/MOI
julia
using Constraints
+@info "NValues" value.(X) value.(Y) value.(Z)
julia
# TODO: How to handle intention in JuMP/MOI
julia
using Constraints
 
 # [v1, v2, v3], [v1, a1, a2; v2, b1, b2; v3, c1, c2] means v1 occurs between a1 and a2 times in the first array, similar for v2 and v3.
 
diff --git a/dev/assets/constraints_24_counting_summing_constraints.md.DVkY5sTG.js b/dev/assets/constraints_24_counting_summing_constraints.md.XccROfRE.lean.js
similarity index 98%
rename from dev/assets/constraints_24_counting_summing_constraints.md.DVkY5sTG.js
rename to dev/assets/constraints_24_counting_summing_constraints.md.XccROfRE.lean.js
index faa1337..966bddf 100644
--- a/dev/assets/constraints_24_counting_summing_constraints.md.DVkY5sTG.js
+++ b/dev/assets/constraints_24_counting_summing_constraints.md.XccROfRE.lean.js
@@ -1,4 +1,4 @@
-import{_ as t,c as l,a5 as a,j as i,a as k,G as n,B as p,o as e}from"./chunks/framework.CJakPlgM.js";const b=JSON.parse('{"title":"Constraints.jl: Streamlining Constraint Definition and Integration in Julia","description":"","frontmatter":{},"headers":[],"relativePath":"constraints/24_counting_summing_constraints.md","filePath":"constraints/24_counting_summing_constraints.md","lastUpdated":null}'),E={name:"constraints/24_counting_summing_constraints.md"},d={class:"jldocstring custom-block",open:""},r={class:"jldocstring custom-block",open:""},g={class:"jldocstring custom-block",open:""},y={class:"jldocstring custom-block",open:""};function F(C,s,o,c,B,u){const h=p("Badge");return e(),l("div",null,[s[12]||(s[12]=a(`
Constraints.jl: Streamlining Constraint Definition and Integration in Julia ​
julia
using Constraints
+import{_ as t,c as l,a5 as a,j as i,a as k,G as n,B as p,o as e}from"./chunks/framework.CJakPlgM.js";const b=JSON.parse('{"title":"Constraints.jl: Streamlining Constraint Definition and Integration in Julia","description":"","frontmatter":{},"headers":[],"relativePath":"constraints/24_counting_summing_constraints.md","filePath":"constraints/24_counting_summing_constraints.md","lastUpdated":null}'),E={name:"constraints/24_counting_summing_constraints.md"},d={class:"jldocstring custom-block",open:""},r={class:"jldocstring custom-block",open:""},g={class:"jldocstring custom-block",open:""},y={class:"jldocstring custom-block",open:""};function F(C,s,o,c,B,u){const h=p("Badge");return e(),l("div",null,[s[12]||(s[12]=a(`
Constraints.jl: Streamlining Constraint Definition and Integration in Julia ​
julia
using Constraints
 
 @info concept(:sum, [1, 2, 3, 4, 5]; op = ==, val=15)
 @info concept(:sum, [1, 2, 3, 4, 5]; op = ==, val=2)
@@ -20,7 +20,7 @@ import{_ as t,c as l,a5 as a,j as i,a as k,G as n,B as p,o as e}from"./chunks/fr
 @constraint(model, X in Sum(; op = ==, val = 15))
 @constraint(model, Y in Sum(; op = <=, val = 10))
 JuMP.optimize!(model)
-@info "Sum" value.(X) value.(Y)
julia
# TODO: How to handle intention in JuMP/MOI
julia
using Constraints
+@info "Sum" value.(X) value.(Y)
julia
# TODO: How to handle intention in JuMP/MOI
julia
using Constraints
 
 concept(:count, [1,1,1,2], vals = [1, 1, 1, 2], op = ==, val = 4) # true
 concept(:count, [1,1,1,2], vals = [1, 1, 1, 2], op = ==, val = 5) # false
@@ -54,7 +54,7 @@ import{_ as t,c as l,a5 as a,j as i,a as k,G as n,B as p,o as e}from"./chunks/fr
 @constraint(model, X_at_most in AtMost(vals = [1, 2], val = 1))
 @constraint(model, X_exactly in Exactly(vals = [1, 2], val = 2))
 JuMP.optimize!(model)
-@info "Count" value.(X) value.(X_at_least) value.(X_at_most) value.(X_exactly)
julia
# TODO: How to handle intention in JuMP/MOI
julia
using Constraints
+@info "Count" value.(X) value.(X_at_least) value.(X_at_most) value.(X_exactly)
julia
# TODO: How to handle intention in JuMP/MOI
julia
using Constraints
 
 @info concept(:nvalues, [1, 2, 3, 4, 5]; op = ==, val = 5)
 @info concept(:nvalues, [1, 2, 3, 4, 5]; op = ==, val = 2)
@@ -78,7 +78,7 @@ import{_ as t,c as l,a5 as a,j as i,a as k,G as n,B as p,o as e}from"./chunks/fr
 @constraint(model, Y in NValues(; op = ==, val = 2))
 @constraint(model, Z in NValues(; op = <=, val = 5, vals = [1, 2]))
 JuMP.optimize!(model)
-@info "NValues" value.(X) value.(Y) value.(Z)
julia
# TODO: How to handle intention in JuMP/MOI
julia
using Constraints
+@info "NValues" value.(X) value.(Y) value.(Z)
julia
# TODO: How to handle intention in JuMP/MOI
julia
using Constraints
 
 # [v1, v2, v3], [v1, a1, a2; v2, b1, b2; v3, c1, c2] means v1 occurs between a1 and a2 times in the first array, similar for v2 and v3.
 
diff --git a/dev/assets/constraints_25_connection_constraints.md.ajGM2nJs.js b/dev/assets/constraints_25_connection_constraints.md.CrGkCkeo.js
similarity index 98%
rename from dev/assets/constraints_25_connection_constraints.md.ajGM2nJs.js
rename to dev/assets/constraints_25_connection_constraints.md.CrGkCkeo.js
index 46186f4..cde618b 100644
--- a/dev/assets/constraints_25_connection_constraints.md.ajGM2nJs.js
+++ b/dev/assets/constraints_25_connection_constraints.md.CrGkCkeo.js
@@ -1,4 +1,4 @@
-import{_ as t,c as l,a5 as a,j as i,a as h,G as k,B as p,o as e}from"./chunks/framework.CJakPlgM.js";const b=JSON.parse('{"title":"Constraints.jl: Streamlining Constraint Definition and Integration in Julia","description":"","frontmatter":{},"headers":[],"relativePath":"constraints/25_connection_constraints.md","filePath":"constraints/25_connection_constraints.md","lastUpdated":null}'),E={name:"constraints/25_connection_constraints.md"},d={class:"jldocstring custom-block",open:""},r={class:"jldocstring custom-block",open:""},g={class:"jldocstring custom-block",open:""},y={class:"jldocstring custom-block",open:""};function F(C,s,o,c,u,B){const n=p("Badge");return e(),l("div",null,[s[12]||(s[12]=a(`
Constraints.jl: Streamlining Constraint Definition and Integration in Julia ​
julia
using Constraints
+import{_ as t,c as l,a5 as a,j as i,a as h,G as k,B as p,o as e}from"./chunks/framework.CJakPlgM.js";const b=JSON.parse('{"title":"Constraints.jl: Streamlining Constraint Definition and Integration in Julia","description":"","frontmatter":{},"headers":[],"relativePath":"constraints/25_connection_constraints.md","filePath":"constraints/25_connection_constraints.md","lastUpdated":null}'),E={name:"constraints/25_connection_constraints.md"},d={class:"jldocstring custom-block",open:""},r={class:"jldocstring custom-block",open:""},g={class:"jldocstring custom-block",open:""},y={class:"jldocstring custom-block",open:""};function F(C,s,o,c,u,B){const n=p("Badge");return e(),l("div",null,[s[12]||(s[12]=a(`
Constraints.jl: Streamlining Constraint Definition and Integration in Julia ​
julia
using Constraints
 
 concept(:maximum, [1,1,1,2], val = 2, op = ==) # true
 concept(:maximum, [1,2,4,4], val = 2, op = ==) # false
julia
using Constraints
@@ -15,7 +15,7 @@ import{_ as t,c as l,a5 as a,j as i,a as h,G as k,B as p,o as e}from"./chunks/fr
 @variable(model, 1≤X[1:5]≤5, Int)
 @constraint(model, X in Maximum(; op = ==, val = 5))
 optimize!(model)
-@info "Maximum" value.(X)
julia
# TODO: How to handle intention in JuMP/MOI
julia
using Constraints
+@info "Maximum" value.(X)
julia
# TODO: How to handle intention in JuMP/MOI
julia
using Constraints
 
 concept(:minimum, [1,1,1,2], val = 1, op = ==) # true
 concept(:minimum, [1,2,4,4], val = 2, op = ==) # false
julia
using Constraints
@@ -34,7 +34,7 @@ import{_ as t,c as l,a5 as a,j as i,a as h,G as k,B as p,o as e}from"./chunks/fr
 JuMP.optimize!(model)
 @info "Minimum" value.(X)
 
-# Note that this example gives a solution for the minimum constraint.
julia
# TODO: How to handle intention in JuMP/MOI
julia
using Constraints
+# Note that this example gives a solution for the minimum constraint.
julia
# TODO: How to handle intention in JuMP/MOI
julia
using Constraints
 
 @info concept(:element, [1, 2, 3, 4, 5]; id=1, val=1)
 @info concept(:element, [1, 2, 3, 4, 5]; id=1, val=2)
@@ -58,7 +58,7 @@ import{_ as t,c as l,a5 as a,j as i,a as h,G as k,B as p,o as e}from"./chunks/fr
 @constraint(model, Y in Element(; id = 1, val = 1))
 @constraint(model, Z in Element(; id = 2, val = 2))
 JuMP.optimize!(model)
-@info "Element" value.(X) value.(Y) value.(Z)
julia
# TODO: How to handle intention in JuMP/MOI
julia
using Constraints
+@info "Element" value.(X) value.(Y) value.(Z)
julia
# TODO: How to handle intention in JuMP/MOI
julia
using Constraints
 
 @info concept(:channel, [2, 1, 4, 3])
 @info concept(:channel, [1, 2, 3, 4])
diff --git a/dev/assets/constraints_25_connection_constraints.md.ajGM2nJs.lean.js b/dev/assets/constraints_25_connection_constraints.md.CrGkCkeo.lean.js
similarity index 98%
rename from dev/assets/constraints_25_connection_constraints.md.ajGM2nJs.lean.js
rename to dev/assets/constraints_25_connection_constraints.md.CrGkCkeo.lean.js
index 46186f4..cde618b 100644
--- a/dev/assets/constraints_25_connection_constraints.md.ajGM2nJs.lean.js
+++ b/dev/assets/constraints_25_connection_constraints.md.CrGkCkeo.lean.js
@@ -1,4 +1,4 @@
-import{_ as t,c as l,a5 as a,j as i,a as h,G as k,B as p,o as e}from"./chunks/framework.CJakPlgM.js";const b=JSON.parse('{"title":"Constraints.jl: Streamlining Constraint Definition and Integration in Julia","description":"","frontmatter":{},"headers":[],"relativePath":"constraints/25_connection_constraints.md","filePath":"constraints/25_connection_constraints.md","lastUpdated":null}'),E={name:"constraints/25_connection_constraints.md"},d={class:"jldocstring custom-block",open:""},r={class:"jldocstring custom-block",open:""},g={class:"jldocstring custom-block",open:""},y={class:"jldocstring custom-block",open:""};function F(C,s,o,c,u,B){const n=p("Badge");return e(),l("div",null,[s[12]||(s[12]=a(`
Constraints.jl: Streamlining Constraint Definition and Integration in Julia ​
julia
using Constraints
+import{_ as t,c as l,a5 as a,j as i,a as h,G as k,B as p,o as e}from"./chunks/framework.CJakPlgM.js";const b=JSON.parse('{"title":"Constraints.jl: Streamlining Constraint Definition and Integration in Julia","description":"","frontmatter":{},"headers":[],"relativePath":"constraints/25_connection_constraints.md","filePath":"constraints/25_connection_constraints.md","lastUpdated":null}'),E={name:"constraints/25_connection_constraints.md"},d={class:"jldocstring custom-block",open:""},r={class:"jldocstring custom-block",open:""},g={class:"jldocstring custom-block",open:""},y={class:"jldocstring custom-block",open:""};function F(C,s,o,c,u,B){const n=p("Badge");return e(),l("div",null,[s[12]||(s[12]=a(`
Constraints.jl: Streamlining Constraint Definition and Integration in Julia ​
julia
using Constraints
 
 concept(:maximum, [1,1,1,2], val = 2, op = ==) # true
 concept(:maximum, [1,2,4,4], val = 2, op = ==) # false
julia
using Constraints
@@ -15,7 +15,7 @@ import{_ as t,c as l,a5 as a,j as i,a as h,G as k,B as p,o as e}from"./chunks/fr
 @variable(model, 1≤X[1:5]≤5, Int)
 @constraint(model, X in Maximum(; op = ==, val = 5))
 optimize!(model)
-@info "Maximum" value.(X)
julia
# TODO: How to handle intention in JuMP/MOI
julia
using Constraints
+@info "Maximum" value.(X)
julia
# TODO: How to handle intention in JuMP/MOI
julia
using Constraints
 
 concept(:minimum, [1,1,1,2], val = 1, op = ==) # true
 concept(:minimum, [1,2,4,4], val = 2, op = ==) # false
julia
using Constraints
@@ -34,7 +34,7 @@ import{_ as t,c as l,a5 as a,j as i,a as h,G as k,B as p,o as e}from"./chunks/fr
 JuMP.optimize!(model)
 @info "Minimum" value.(X)
 
-# Note that this example gives a solution for the minimum constraint.
julia
# TODO: How to handle intention in JuMP/MOI
julia
using Constraints
+# Note that this example gives a solution for the minimum constraint.
julia
# TODO: How to handle intention in JuMP/MOI
julia
using Constraints
 
 @info concept(:element, [1, 2, 3, 4, 5]; id=1, val=1)
 @info concept(:element, [1, 2, 3, 4, 5]; id=1, val=2)
@@ -58,7 +58,7 @@ import{_ as t,c as l,a5 as a,j as i,a as h,G as k,B as p,o as e}from"./chunks/fr
 @constraint(model, Y in Element(; id = 1, val = 1))
 @constraint(model, Z in Element(; id = 2, val = 2))
 JuMP.optimize!(model)
-@info "Element" value.(X) value.(Y) value.(Z)
julia
# TODO: How to handle intention in JuMP/MOI
julia
using Constraints
+@info "Element" value.(X) value.(Y) value.(Z)
julia
# TODO: How to handle intention in JuMP/MOI
julia
using Constraints
 
 @info concept(:channel, [2, 1, 4, 3])
 @info concept(:channel, [1, 2, 3, 4])
diff --git a/dev/assets/constraints_26_packing_scheduling_constraints.md.CrG8P0jZ.js b/dev/assets/constraints_26_packing_scheduling_constraints.md.C0OPa6mw.js
similarity index 98%
rename from dev/assets/constraints_26_packing_scheduling_constraints.md.CrG8P0jZ.js
rename to dev/assets/constraints_26_packing_scheduling_constraints.md.C0OPa6mw.js
index c220502..47dce76 100644
--- a/dev/assets/constraints_26_packing_scheduling_constraints.md.CrG8P0jZ.js
+++ b/dev/assets/constraints_26_packing_scheduling_constraints.md.C0OPa6mw.js
@@ -1,4 +1,4 @@
-import{_ as t,c as l,a5 as a,j as i,a as k,G as n,B as p,o as e}from"./chunks/framework.CJakPlgM.js";const u=JSON.parse('{"title":"Constraints.jl: Streamlining Constraint Definition and Integration in Julia","description":"","frontmatter":{},"headers":[],"relativePath":"constraints/26_packing_scheduling_constraints.md","filePath":"constraints/26_packing_scheduling_constraints.md","lastUpdated":null}'),E={name:"constraints/26_packing_scheduling_constraints.md"},r={class:"jldocstring custom-block",open:""},d={class:"jldocstring custom-block",open:""};function g(y,s,F,C,o,c){const h=p("Badge");return e(),l("div",null,[s[6]||(s[6]=a(`
Constraints.jl: Streamlining Constraint Definition and Integration in Julia ​
julia
using Constraints
+import{_ as t,c as l,a5 as a,j as i,a as k,G as n,B as p,o as e}from"./chunks/framework.CJakPlgM.js";const u=JSON.parse('{"title":"Constraints.jl: Streamlining Constraint Definition and Integration in Julia","description":"","frontmatter":{},"headers":[],"relativePath":"constraints/26_packing_scheduling_constraints.md","filePath":"constraints/26_packing_scheduling_constraints.md","lastUpdated":null}'),E={name:"constraints/26_packing_scheduling_constraints.md"},r={class:"jldocstring custom-block",open:""},d={class:"jldocstring custom-block",open:""};function g(y,s,F,C,o,c){const h=p("Badge");return e(),l("div",null,[s[6]||(s[6]=a(`
Constraints.jl: Streamlining Constraint Definition and Integration in Julia ​
julia
using Constraints
 
 @info concept(:cumulative, [1, 2, 3, 4, 5]; val = 1)
 @info concept(:cumulative, [1, 2, 2, 4, 5]; val = 1)
@@ -25,7 +25,7 @@ import{_ as t,c as l,a5 as a,j as i,a as k,G as n,B as p,o as e}from"./chunks/fr
 @constraint(model,
     Z in Cumulative(; pair_vars = [3 2 5 4 2; 1 2 1 1 3], op = <, val = 5))
 JuMP.optimize!(model)
-@info "Cumulative" value.(X) value.(Y) value.(Z)
julia
# TODO: How to handle intention in JuMP/MOI
julia
using Constraints
+@info "Cumulative" value.(X) value.(Y) value.(Z)
julia
# TODO: How to handle intention in JuMP/MOI
julia
using Constraints
 
 @info concept(:no_overlap, [1, 2, 3, 4, 5])
 @info concept(:no_overlap, [1, 2, 3, 4, 1])
diff --git a/dev/assets/constraints_26_packing_scheduling_constraints.md.CrG8P0jZ.lean.js b/dev/assets/constraints_26_packing_scheduling_constraints.md.C0OPa6mw.lean.js
similarity index 98%
rename from dev/assets/constraints_26_packing_scheduling_constraints.md.CrG8P0jZ.lean.js
rename to dev/assets/constraints_26_packing_scheduling_constraints.md.C0OPa6mw.lean.js
index c220502..47dce76 100644
--- a/dev/assets/constraints_26_packing_scheduling_constraints.md.CrG8P0jZ.lean.js
+++ b/dev/assets/constraints_26_packing_scheduling_constraints.md.C0OPa6mw.lean.js
@@ -1,4 +1,4 @@
-import{_ as t,c as l,a5 as a,j as i,a as k,G as n,B as p,o as e}from"./chunks/framework.CJakPlgM.js";const u=JSON.parse('{"title":"Constraints.jl: Streamlining Constraint Definition and Integration in Julia","description":"","frontmatter":{},"headers":[],"relativePath":"constraints/26_packing_scheduling_constraints.md","filePath":"constraints/26_packing_scheduling_constraints.md","lastUpdated":null}'),E={name:"constraints/26_packing_scheduling_constraints.md"},r={class:"jldocstring custom-block",open:""},d={class:"jldocstring custom-block",open:""};function g(y,s,F,C,o,c){const h=p("Badge");return e(),l("div",null,[s[6]||(s[6]=a(`
Constraints.jl: Streamlining Constraint Definition and Integration in Julia ​
julia
using Constraints
+import{_ as t,c as l,a5 as a,j as i,a as k,G as n,B as p,o as e}from"./chunks/framework.CJakPlgM.js";const u=JSON.parse('{"title":"Constraints.jl: Streamlining Constraint Definition and Integration in Julia","description":"","frontmatter":{},"headers":[],"relativePath":"constraints/26_packing_scheduling_constraints.md","filePath":"constraints/26_packing_scheduling_constraints.md","lastUpdated":null}'),E={name:"constraints/26_packing_scheduling_constraints.md"},r={class:"jldocstring custom-block",open:""},d={class:"jldocstring custom-block",open:""};function g(y,s,F,C,o,c){const h=p("Badge");return e(),l("div",null,[s[6]||(s[6]=a(`
Constraints.jl: Streamlining Constraint Definition and Integration in Julia ​
julia
using Constraints
 
 @info concept(:cumulative, [1, 2, 3, 4, 5]; val = 1)
 @info concept(:cumulative, [1, 2, 2, 4, 5]; val = 1)
@@ -25,7 +25,7 @@ import{_ as t,c as l,a5 as a,j as i,a as k,G as n,B as p,o as e}from"./chunks/fr
 @constraint(model,
     Z in Cumulative(; pair_vars = [3 2 5 4 2; 1 2 1 1 3], op = <, val = 5))
 JuMP.optimize!(model)
-@info "Cumulative" value.(X) value.(Y) value.(Z)
julia
# TODO: How to handle intention in JuMP/MOI
julia
using Constraints
+@info "Cumulative" value.(X) value.(Y) value.(Z)
julia
# TODO: How to handle intention in JuMP/MOI
julia
using Constraints
 
 @info concept(:no_overlap, [1, 2, 3, 4, 5])
 @info concept(:no_overlap, [1, 2, 3, 4, 1])
diff --git a/dev/assets/cp_30_getting_started.md.QuTvdZuh.js b/dev/assets/cp_30_getting_started.md.B_EkJgkt.js
similarity index 95%
rename from dev/assets/cp_30_getting_started.md.QuTvdZuh.js
rename to dev/assets/cp_30_getting_started.md.B_EkJgkt.js
index 3b984ad..ae2362c 100644
--- a/dev/assets/cp_30_getting_started.md.QuTvdZuh.js
+++ b/dev/assets/cp_30_getting_started.md.B_EkJgkt.js
@@ -1,9 +1,9 @@
-import{_ as n,c as e,a5 as a,j as i,a as t,o as l}from"./chunks/framework.CJakPlgM.js";const y=JSON.parse('{"title":"Getting Started with Julia for CP and Optimization","description":"","frontmatter":{},"headers":[],"relativePath":"cp/30_getting_started.md","filePath":"cp/30_getting_started.md","lastUpdated":null}'),h={name:"cp/30_getting_started.md"},p={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},o={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.439ex"},xmlns:"http://www.w3.org/2000/svg",width:"15.867ex",height:"1.984ex",role:"img",focusable:"false",viewBox:"0 -683 7013.4 877","aria-hidden":"true"},d={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},r={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.439ex"},xmlns:"http://www.w3.org/2000/svg",width:"15.148ex",height:"2.034ex",role:"img",focusable:"false",viewBox:"0 -705 6695.4 899","aria-hidden":"true"},k={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},Q={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"0"},xmlns:"http://www.w3.org/2000/svg",width:"1.928ex",height:"1.545ex",role:"img",focusable:"false",viewBox:"0 -683 852 683","aria-hidden":"true"};function g(c,s,u,T,m,v){return l(),e("div",null,[s[11]||(s[11]=a('
Getting Started with Julia for CP and Optimization ​
Why Julia? ​
  • Discuss the advantages of Julia for computational science and optimization, highlighting its performance and ease of use.
Setting Up Your Julia Environment ​
We encourage users to install Julia through juliaup, a version manager for the Julia language. Please look at the official Julia language download page for further information. Once installed, Julia can be used through various editors (Visual Studio Code), notebooks (Pluto.jl), or command-line (REPL).
Although a part of the CP solvers available within the Julia ecosystem have their own interface, we encourage users to use the JuMP modeling language if possible.
Julia Constraints host several solvers(' interfaces). Due to its flexibility in modeling and solving, we will use LocalSearchSolvers.jl through its JuMP interface CBLS.jl as the basic example. Note that depending on the targeted instances, available hardware, and expectations, it is not necessarily the best choice.
All along the documentation, we will try to provide syntax examples for different setup.
julia
using LocalSearchSolvers
julia
using JuMP, CBLS
julia
# TODO: Add other solvers
Your First Julia CP Model ​
We will start with a classic puzzle game and some of its not that simple variants: the Sudoku.
(From Wikipedia) In classic Sudoku, the objective is to fill a 9 × 9 grid with digits so that each column, each row, and each of the nine 3 × 3 subgrids that compose the grid (also called "boxes", "blocks", or "regions") contains all of the digits from 1 to 9. The puzzle setter provides a partially completed grid, which for a well-posed puzzle has a single solution.
Constraint Programming follows the model-and-solve approach. We first need to model our Sudoku problem.
julia
m = JuMP.Model(CBLS.Optimizer)
julia
# TODO: Add other solvers
But what are the basis of CP models? It is quite simple:
',15)),i("ol",null,[i("li",null,[s[2]||(s[2]=t("A collection ")),i("mjx-container",p,[(l(),e("svg",o,s[0]||(s[0]=[a('',1)]))),s[1]||(s[1]=i("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[i("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[i("mi",null,"X"),i("mo",null,"="),i("msub",null,[i("mi",null,"X"),i("mn",null,"1")]),i("mo",null,","),i("mo",null,"⋯"),i("mo",null,","),i("msub",null,[i("mi",null,"X"),i("mi",null,"n")])])],-1))]),s[3]||(s[3]=t(" of variables with each an associated domain."))])]),s[12]||(s[12]=a('
julia
@variable(m, 1 ≤ X[1:9, 1:9] ≤ 9, Int)
julia
# TODO: Add other solvers
',1)),i("ol",null,[i("li",null,[s[8]||(s[8]=t("A collection of predicates (called constraints) ")),i("mjx-container",d,[(l(),e("svg",r,s[4]||(s[4]=[a('',1)]))),s[5]||(s[5]=i("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[i("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[i("mi",null,"C"),i("mo",null,"="),i("msub",null,[i("mi",null,"C"),i("mn",null,"1")]),i("mo",null,","),i("mo",null,"⋯"),i("mo",null,","),i("msub",null,[i("mi",null,"C"),i("mi",null,"n")])])],-1))]),s[9]||(s[9]=t(" over (subsets of) ")),i("mjx-container",k,[(l(),e("svg",Q,s[6]||(s[6]=[i("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[i("g",{"data-mml-node":"math"},[i("g",{"data-mml-node":"mi"},[i("path",{"data-c":"1D44B",d:"M42 0H40Q26 0 26 11Q26 15 29 27Q33 41 36 43T55 46Q141 49 190 98Q200 108 306 224T411 342Q302 620 297 625Q288 636 234 637H206Q200 643 200 645T202 664Q206 677 212 683H226Q260 681 347 681Q380 681 408 681T453 682T473 682Q490 682 490 671Q490 670 488 658Q484 643 481 640T465 637Q434 634 411 620L488 426L541 485Q646 598 646 610Q646 628 622 635Q617 635 609 637Q594 637 594 648Q594 650 596 664Q600 677 606 683H618Q619 683 643 683T697 681T738 680Q828 680 837 683H845Q852 676 852 672Q850 647 840 637H824Q790 636 763 628T722 611T698 593L687 584Q687 585 592 480L505 384Q505 383 536 304T601 142T638 56Q648 47 699 46Q734 46 734 37Q734 35 732 23Q728 7 725 4T711 1Q708 1 678 1T589 2Q528 2 496 2T461 1Q444 1 444 10Q444 11 446 25Q448 35 450 39T455 44T464 46T480 47T506 54Q523 62 523 64Q522 64 476 181L429 299Q241 95 236 84Q232 76 232 72Q232 53 261 47Q262 47 267 47T273 46Q276 46 277 46T280 45T283 42T284 35Q284 26 282 19Q279 6 276 4T261 1Q258 1 243 1T201 2T142 2Q64 2 42 0Z",style:{"stroke-width":"3"}})])])],-1)]))),s[7]||(s[7]=i("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[i("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[i("mi",null,"X")])],-1))]),s[10]||(s[10]=t("."))])]),s[13]||(s[13]=a(`
When modeling problems as CP, one might define and use their own predicates. However, a large collection of already defined constraints exists. One, if not the most, iconic global constraint is called AllDifferent. It ensures that all variables take distinct values.
Sudoku puzzles can be defined using only this one constraint applied to different subsets of variables.
julia
for i in 1:9
+import{_ as n,c as e,a5 as a,j as i,a as t,o as l}from"./chunks/framework.CJakPlgM.js";const y=JSON.parse('{"title":"Getting Started with Julia for CP and Optimization","description":"","frontmatter":{},"headers":[],"relativePath":"cp/30_getting_started.md","filePath":"cp/30_getting_started.md","lastUpdated":null}'),h={name:"cp/30_getting_started.md"},p={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},o={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.439ex"},xmlns:"http://www.w3.org/2000/svg",width:"15.867ex",height:"1.984ex",role:"img",focusable:"false",viewBox:"0 -683 7013.4 877","aria-hidden":"true"},d={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},r={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.439ex"},xmlns:"http://www.w3.org/2000/svg",width:"15.148ex",height:"2.034ex",role:"img",focusable:"false",viewBox:"0 -705 6695.4 899","aria-hidden":"true"},k={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},Q={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"0"},xmlns:"http://www.w3.org/2000/svg",width:"1.928ex",height:"1.545ex",role:"img",focusable:"false",viewBox:"0 -683 852 683","aria-hidden":"true"};function g(c,s,u,T,m,v){return l(),e("div",null,[s[11]||(s[11]=a('
Getting Started with Julia for CP and Optimization ​
Why Julia? ​
  • Discuss the advantages of Julia for computational science and optimization, highlighting its performance and ease of use.
Setting Up Your Julia Environment ​
We encourage users to install Julia through juliaup, a version manager for the Julia language. Please look at the official Julia language download page for further information. Once installed, Julia can be used through various editors (Visual Studio Code), notebooks (Pluto.jl), or command-line (REPL).
Although a part of the CP solvers available within the Julia ecosystem have their own interface, we encourage users to use the JuMP modeling language if possible.
Julia Constraints host several solvers(' interfaces). Due to its flexibility in modeling and solving, we will use LocalSearchSolvers.jl through its JuMP interface CBLS.jl as the basic example. Note that depending on the targeted instances, available hardware, and expectations, it is not necessarily the best choice.
All along the documentation, we will try to provide syntax examples for different setup.
julia
using LocalSearchSolvers
julia
using JuMP, CBLS
julia
# TODO: Add other solvers
Your First Julia CP Model ​
We will start with a classic puzzle game and some of its not that simple variants: the Sudoku.
(From Wikipedia) In classic Sudoku, the objective is to fill a 9 × 9 grid with digits so that each column, each row, and each of the nine 3 × 3 subgrids that compose the grid (also called "boxes", "blocks", or "regions") contains all of the digits from 1 to 9. The puzzle setter provides a partially completed grid, which for a well-posed puzzle has a single solution.
Constraint Programming follows the model-and-solve approach. We first need to model our Sudoku problem.
julia
m = JuMP.Model(CBLS.Optimizer)
julia
# TODO: Add other solvers
But what are the basis of CP models? It is quite simple:
',15)),i("ol",null,[i("li",null,[s[2]||(s[2]=t("A collection ")),i("mjx-container",p,[(l(),e("svg",o,s[0]||(s[0]=[a('',1)]))),s[1]||(s[1]=i("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[i("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[i("mi",null,"X"),i("mo",null,"="),i("msub",null,[i("mi",null,"X"),i("mn",null,"1")]),i("mo",null,","),i("mo",null,"⋯"),i("mo",null,","),i("msub",null,[i("mi",null,"X"),i("mi",null,"n")])])],-1))]),s[3]||(s[3]=t(" of variables with each an associated domain."))])]),s[12]||(s[12]=a('
julia
@variable(m, 1 ≤ X[1:9, 1:9] ≤ 9, Int)
julia
# TODO: Add other solvers
',1)),i("ol",null,[i("li",null,[s[8]||(s[8]=t("A collection of predicates (called constraints) ")),i("mjx-container",d,[(l(),e("svg",r,s[4]||(s[4]=[a('',1)]))),s[5]||(s[5]=i("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[i("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[i("mi",null,"C"),i("mo",null,"="),i("msub",null,[i("mi",null,"C"),i("mn",null,"1")]),i("mo",null,","),i("mo",null,"⋯"),i("mo",null,","),i("msub",null,[i("mi",null,"C"),i("mi",null,"n")])])],-1))]),s[9]||(s[9]=t(" over (subsets of) ")),i("mjx-container",k,[(l(),e("svg",Q,s[6]||(s[6]=[i("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[i("g",{"data-mml-node":"math"},[i("g",{"data-mml-node":"mi"},[i("path",{"data-c":"1D44B",d:"M42 0H40Q26 0 26 11Q26 15 29 27Q33 41 36 43T55 46Q141 49 190 98Q200 108 306 224T411 342Q302 620 297 625Q288 636 234 637H206Q200 643 200 645T202 664Q206 677 212 683H226Q260 681 347 681Q380 681 408 681T453 682T473 682Q490 682 490 671Q490 670 488 658Q484 643 481 640T465 637Q434 634 411 620L488 426L541 485Q646 598 646 610Q646 628 622 635Q617 635 609 637Q594 637 594 648Q594 650 596 664Q600 677 606 683H618Q619 683 643 683T697 681T738 680Q828 680 837 683H845Q852 676 852 672Q850 647 840 637H824Q790 636 763 628T722 611T698 593L687 584Q687 585 592 480L505 384Q505 383 536 304T601 142T638 56Q648 47 699 46Q734 46 734 37Q734 35 732 23Q728 7 725 4T711 1Q708 1 678 1T589 2Q528 2 496 2T461 1Q444 1 444 10Q444 11 446 25Q448 35 450 39T455 44T464 46T480 47T506 54Q523 62 523 64Q522 64 476 181L429 299Q241 95 236 84Q232 76 232 72Q232 53 261 47Q262 47 267 47T273 46Q276 46 277 46T280 45T283 42T284 35Q284 26 282 19Q279 6 276 4T261 1Q258 1 243 1T201 2T142 2Q64 2 42 0Z",style:{"stroke-width":"3"}})])])],-1)]))),s[7]||(s[7]=i("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[i("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[i("mi",null,"X")])],-1))]),s[10]||(s[10]=t("."))])]),s[13]||(s[13]=a(`
When modeling problems as CP, one might define and use their own predicates. However, a large collection of already defined constraints exists. One, if not the most, iconic global constraint is called AllDifferent. It ensures that all variables take distinct values.
Sudoku puzzles can be defined using only this one constraint applied to different subsets of variables.
julia
for i in 1:9
         @constraint(m, X[i,:] in AllDifferent()) # rows
         @constraint(m, X[:,i] in AllDifferent()) # columns
-end
julia
# TODO: Add other solvers
The last series of AllDifferent constraint is less straight forward. We need to ensure that each 3 × 3 subgrid (block) is filled with distinct values.
julia
for i in 0:2, j in 0:2 # blocks
+end
julia
# TODO: Add other solvers
The last series of AllDifferent constraint is less straight forward. We need to ensure that each 3 × 3 subgrid (block) is filled with distinct values.
julia
for i in 0:2, j in 0:2 # blocks
     @constraint(
         m,
         vec(X[(3i+1):(3(i+1)), (3j+1):(3(j+1))]) in AllDifferent(),
     )
-end
julia
# TODO: Add other solvers
We can now simply run our solver to look for a feasible solution.
julia
optimize!(m)
Note that this is heuristic solver, we might not get a feasible solution! Let's check it out. The value function print the value of a JuMP variable. We can cast it over a collection with the value. syntax.
julia
value.(X)
`,9))])}const E=n(h,[["render",g]]);export{y as __pageData,E as default};
+end
julia
# TODO: Add other solvers
We can now simply run our solver to look for a feasible solution.
julia
optimize!(m)
Note that this is heuristic solver, we might not get a feasible solution! Let's check it out. The value function print the value of a JuMP variable. We can cast it over a collection with the value. syntax.
julia
value.(X)
`,9))])}const E=n(h,[["render",g]]);export{y as __pageData,E as default};
diff --git a/dev/assets/cp_30_getting_started.md.QuTvdZuh.lean.js b/dev/assets/cp_30_getting_started.md.B_EkJgkt.lean.js
similarity index 95%
rename from dev/assets/cp_30_getting_started.md.QuTvdZuh.lean.js
rename to dev/assets/cp_30_getting_started.md.B_EkJgkt.lean.js
index 3b984ad..ae2362c 100644
--- a/dev/assets/cp_30_getting_started.md.QuTvdZuh.lean.js
+++ b/dev/assets/cp_30_getting_started.md.B_EkJgkt.lean.js
@@ -1,9 +1,9 @@
-import{_ as n,c as e,a5 as a,j as i,a as t,o as l}from"./chunks/framework.CJakPlgM.js";const y=JSON.parse('{"title":"Getting Started with Julia for CP and Optimization","description":"","frontmatter":{},"headers":[],"relativePath":"cp/30_getting_started.md","filePath":"cp/30_getting_started.md","lastUpdated":null}'),h={name:"cp/30_getting_started.md"},p={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},o={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.439ex"},xmlns:"http://www.w3.org/2000/svg",width:"15.867ex",height:"1.984ex",role:"img",focusable:"false",viewBox:"0 -683 7013.4 877","aria-hidden":"true"},d={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},r={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.439ex"},xmlns:"http://www.w3.org/2000/svg",width:"15.148ex",height:"2.034ex",role:"img",focusable:"false",viewBox:"0 -705 6695.4 899","aria-hidden":"true"},k={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},Q={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"0"},xmlns:"http://www.w3.org/2000/svg",width:"1.928ex",height:"1.545ex",role:"img",focusable:"false",viewBox:"0 -683 852 683","aria-hidden":"true"};function g(c,s,u,T,m,v){return l(),e("div",null,[s[11]||(s[11]=a('
Getting Started with Julia for CP and Optimization ​
Why Julia? ​
  • Discuss the advantages of Julia for computational science and optimization, highlighting its performance and ease of use.
Setting Up Your Julia Environment ​
We encourage users to install Julia through juliaup, a version manager for the Julia language. Please look at the official Julia language download page for further information. Once installed, Julia can be used through various editors (Visual Studio Code), notebooks (Pluto.jl), or command-line (REPL).
Although a part of the CP solvers available within the Julia ecosystem have their own interface, we encourage users to use the JuMP modeling language if possible.
Julia Constraints host several solvers(' interfaces). Due to its flexibility in modeling and solving, we will use LocalSearchSolvers.jl through its JuMP interface CBLS.jl as the basic example. Note that depending on the targeted instances, available hardware, and expectations, it is not necessarily the best choice.
All along the documentation, we will try to provide syntax examples for different setup.
julia
using LocalSearchSolvers
julia
using JuMP, CBLS
julia
# TODO: Add other solvers
Your First Julia CP Model ​
We will start with a classic puzzle game and some of its not that simple variants: the Sudoku.
(From Wikipedia) In classic Sudoku, the objective is to fill a 9 × 9 grid with digits so that each column, each row, and each of the nine 3 × 3 subgrids that compose the grid (also called "boxes", "blocks", or "regions") contains all of the digits from 1 to 9. The puzzle setter provides a partially completed grid, which for a well-posed puzzle has a single solution.
Constraint Programming follows the model-and-solve approach. We first need to model our Sudoku problem.
julia
m = JuMP.Model(CBLS.Optimizer)
julia
# TODO: Add other solvers
But what are the basis of CP models? It is quite simple:
',15)),i("ol",null,[i("li",null,[s[2]||(s[2]=t("A collection ")),i("mjx-container",p,[(l(),e("svg",o,s[0]||(s[0]=[a('',1)]))),s[1]||(s[1]=i("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[i("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[i("mi",null,"X"),i("mo",null,"="),i("msub",null,[i("mi",null,"X"),i("mn",null,"1")]),i("mo",null,","),i("mo",null,"⋯"),i("mo",null,","),i("msub",null,[i("mi",null,"X"),i("mi",null,"n")])])],-1))]),s[3]||(s[3]=t(" of variables with each an associated domain."))])]),s[12]||(s[12]=a('
julia
@variable(m, 1 ≤ X[1:9, 1:9] ≤ 9, Int)
julia
# TODO: Add other solvers
',1)),i("ol",null,[i("li",null,[s[8]||(s[8]=t("A collection of predicates (called constraints) ")),i("mjx-container",d,[(l(),e("svg",r,s[4]||(s[4]=[a('',1)]))),s[5]||(s[5]=i("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[i("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[i("mi",null,"C"),i("mo",null,"="),i("msub",null,[i("mi",null,"C"),i("mn",null,"1")]),i("mo",null,","),i("mo",null,"⋯"),i("mo",null,","),i("msub",null,[i("mi",null,"C"),i("mi",null,"n")])])],-1))]),s[9]||(s[9]=t(" over (subsets of) ")),i("mjx-container",k,[(l(),e("svg",Q,s[6]||(s[6]=[i("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[i("g",{"data-mml-node":"math"},[i("g",{"data-mml-node":"mi"},[i("path",{"data-c":"1D44B",d:"M42 0H40Q26 0 26 11Q26 15 29 27Q33 41 36 43T55 46Q141 49 190 98Q200 108 306 224T411 342Q302 620 297 625Q288 636 234 637H206Q200 643 200 645T202 664Q206 677 212 683H226Q260 681 347 681Q380 681 408 681T453 682T473 682Q490 682 490 671Q490 670 488 658Q484 643 481 640T465 637Q434 634 411 620L488 426L541 485Q646 598 646 610Q646 628 622 635Q617 635 609 637Q594 637 594 648Q594 650 596 664Q600 677 606 683H618Q619 683 643 683T697 681T738 680Q828 680 837 683H845Q852 676 852 672Q850 647 840 637H824Q790 636 763 628T722 611T698 593L687 584Q687 585 592 480L505 384Q505 383 536 304T601 142T638 56Q648 47 699 46Q734 46 734 37Q734 35 732 23Q728 7 725 4T711 1Q708 1 678 1T589 2Q528 2 496 2T461 1Q444 1 444 10Q444 11 446 25Q448 35 450 39T455 44T464 46T480 47T506 54Q523 62 523 64Q522 64 476 181L429 299Q241 95 236 84Q232 76 232 72Q232 53 261 47Q262 47 267 47T273 46Q276 46 277 46T280 45T283 42T284 35Q284 26 282 19Q279 6 276 4T261 1Q258 1 243 1T201 2T142 2Q64 2 42 0Z",style:{"stroke-width":"3"}})])])],-1)]))),s[7]||(s[7]=i("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[i("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[i("mi",null,"X")])],-1))]),s[10]||(s[10]=t("."))])]),s[13]||(s[13]=a(`
When modeling problems as CP, one might define and use their own predicates. However, a large collection of already defined constraints exists. One, if not the most, iconic global constraint is called AllDifferent. It ensures that all variables take distinct values.
Sudoku puzzles can be defined using only this one constraint applied to different subsets of variables.
julia
for i in 1:9
+import{_ as n,c as e,a5 as a,j as i,a as t,o as l}from"./chunks/framework.CJakPlgM.js";const y=JSON.parse('{"title":"Getting Started with Julia for CP and Optimization","description":"","frontmatter":{},"headers":[],"relativePath":"cp/30_getting_started.md","filePath":"cp/30_getting_started.md","lastUpdated":null}'),h={name:"cp/30_getting_started.md"},p={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},o={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.439ex"},xmlns:"http://www.w3.org/2000/svg",width:"15.867ex",height:"1.984ex",role:"img",focusable:"false",viewBox:"0 -683 7013.4 877","aria-hidden":"true"},d={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},r={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.439ex"},xmlns:"http://www.w3.org/2000/svg",width:"15.148ex",height:"2.034ex",role:"img",focusable:"false",viewBox:"0 -705 6695.4 899","aria-hidden":"true"},k={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},Q={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"0"},xmlns:"http://www.w3.org/2000/svg",width:"1.928ex",height:"1.545ex",role:"img",focusable:"false",viewBox:"0 -683 852 683","aria-hidden":"true"};function g(c,s,u,T,m,v){return l(),e("div",null,[s[11]||(s[11]=a('
Getting Started with Julia for CP and Optimization ​
Why Julia? ​
  • Discuss the advantages of Julia for computational science and optimization, highlighting its performance and ease of use.
Setting Up Your Julia Environment ​
We encourage users to install Julia through juliaup, a version manager for the Julia language. Please look at the official Julia language download page for further information. Once installed, Julia can be used through various editors (Visual Studio Code), notebooks (Pluto.jl), or command-line (REPL).
Although a part of the CP solvers available within the Julia ecosystem have their own interface, we encourage users to use the JuMP modeling language if possible.
Julia Constraints host several solvers(' interfaces). Due to its flexibility in modeling and solving, we will use LocalSearchSolvers.jl through its JuMP interface CBLS.jl as the basic example. Note that depending on the targeted instances, available hardware, and expectations, it is not necessarily the best choice.
All along the documentation, we will try to provide syntax examples for different setup.
julia
using LocalSearchSolvers
julia
using JuMP, CBLS
julia
# TODO: Add other solvers
Your First Julia CP Model ​
We will start with a classic puzzle game and some of its not that simple variants: the Sudoku.
(From Wikipedia) In classic Sudoku, the objective is to fill a 9 × 9 grid with digits so that each column, each row, and each of the nine 3 × 3 subgrids that compose the grid (also called "boxes", "blocks", or "regions") contains all of the digits from 1 to 9. The puzzle setter provides a partially completed grid, which for a well-posed puzzle has a single solution.
Constraint Programming follows the model-and-solve approach. We first need to model our Sudoku problem.
julia
m = JuMP.Model(CBLS.Optimizer)
julia
# TODO: Add other solvers
But what are the basis of CP models? It is quite simple:
',15)),i("ol",null,[i("li",null,[s[2]||(s[2]=t("A collection ")),i("mjx-container",p,[(l(),e("svg",o,s[0]||(s[0]=[a('',1)]))),s[1]||(s[1]=i("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[i("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[i("mi",null,"X"),i("mo",null,"="),i("msub",null,[i("mi",null,"X"),i("mn",null,"1")]),i("mo",null,","),i("mo",null,"⋯"),i("mo",null,","),i("msub",null,[i("mi",null,"X"),i("mi",null,"n")])])],-1))]),s[3]||(s[3]=t(" of variables with each an associated domain."))])]),s[12]||(s[12]=a('
julia
@variable(m, 1 ≤ X[1:9, 1:9] ≤ 9, Int)
julia
# TODO: Add other solvers
',1)),i("ol",null,[i("li",null,[s[8]||(s[8]=t("A collection of predicates (called constraints) ")),i("mjx-container",d,[(l(),e("svg",r,s[4]||(s[4]=[a('',1)]))),s[5]||(s[5]=i("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[i("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[i("mi",null,"C"),i("mo",null,"="),i("msub",null,[i("mi",null,"C"),i("mn",null,"1")]),i("mo",null,","),i("mo",null,"⋯"),i("mo",null,","),i("msub",null,[i("mi",null,"C"),i("mi",null,"n")])])],-1))]),s[9]||(s[9]=t(" over (subsets of) ")),i("mjx-container",k,[(l(),e("svg",Q,s[6]||(s[6]=[i("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[i("g",{"data-mml-node":"math"},[i("g",{"data-mml-node":"mi"},[i("path",{"data-c":"1D44B",d:"M42 0H40Q26 0 26 11Q26 15 29 27Q33 41 36 43T55 46Q141 49 190 98Q200 108 306 224T411 342Q302 620 297 625Q288 636 234 637H206Q200 643 200 645T202 664Q206 677 212 683H226Q260 681 347 681Q380 681 408 681T453 682T473 682Q490 682 490 671Q490 670 488 658Q484 643 481 640T465 637Q434 634 411 620L488 426L541 485Q646 598 646 610Q646 628 622 635Q617 635 609 637Q594 637 594 648Q594 650 596 664Q600 677 606 683H618Q619 683 643 683T697 681T738 680Q828 680 837 683H845Q852 676 852 672Q850 647 840 637H824Q790 636 763 628T722 611T698 593L687 584Q687 585 592 480L505 384Q505 383 536 304T601 142T638 56Q648 47 699 46Q734 46 734 37Q734 35 732 23Q728 7 725 4T711 1Q708 1 678 1T589 2Q528 2 496 2T461 1Q444 1 444 10Q444 11 446 25Q448 35 450 39T455 44T464 46T480 47T506 54Q523 62 523 64Q522 64 476 181L429 299Q241 95 236 84Q232 76 232 72Q232 53 261 47Q262 47 267 47T273 46Q276 46 277 46T280 45T283 42T284 35Q284 26 282 19Q279 6 276 4T261 1Q258 1 243 1T201 2T142 2Q64 2 42 0Z",style:{"stroke-width":"3"}})])])],-1)]))),s[7]||(s[7]=i("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[i("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[i("mi",null,"X")])],-1))]),s[10]||(s[10]=t("."))])]),s[13]||(s[13]=a(`
When modeling problems as CP, one might define and use their own predicates. However, a large collection of already defined constraints exists. One, if not the most, iconic global constraint is called AllDifferent. It ensures that all variables take distinct values.
Sudoku puzzles can be defined using only this one constraint applied to different subsets of variables.
julia
for i in 1:9
         @constraint(m, X[i,:] in AllDifferent()) # rows
         @constraint(m, X[:,i] in AllDifferent()) # columns
-end
julia
# TODO: Add other solvers
The last series of AllDifferent constraint is less straight forward. We need to ensure that each 3 × 3 subgrid (block) is filled with distinct values.
julia
for i in 0:2, j in 0:2 # blocks
+end
julia
# TODO: Add other solvers
The last series of AllDifferent constraint is less straight forward. We need to ensure that each 3 × 3 subgrid (block) is filled with distinct values.
julia
for i in 0:2, j in 0:2 # blocks
     @constraint(
         m,
         vec(X[(3i+1):(3(i+1)), (3j+1):(3(j+1))]) in AllDifferent(),
     )
-end
julia
# TODO: Add other solvers
We can now simply run our solver to look for a feasible solution.
julia
optimize!(m)
Note that this is heuristic solver, we might not get a feasible solution! Let's check it out. The value function print the value of a JuMP variable. We can cast it over a collection with the value. syntax.
julia
value.(X)
`,9))])}const E=n(h,[["render",g]]);export{y as __pageData,E as default};
+end
julia
# TODO: Add other solvers
We can now simply run our solver to look for a feasible solution.
julia
optimize!(m)
Note that this is heuristic solver, we might not get a feasible solution! Let's check it out. The value function print the value of a JuMP variable. We can cast it over a collection with the value. syntax.
julia
value.(X)
`,9))])}const E=n(h,[["render",g]]);export{y as __pageData,E as default};
diff --git a/dev/assets/solvers_10_cbls.md.BCa7hnj8.js b/dev/assets/solvers_10_cbls.md.CdQMlrVz.js
similarity index 63%
rename from dev/assets/solvers_10_cbls.md.BCa7hnj8.js
rename to dev/assets/solvers_10_cbls.md.CdQMlrVz.js
index 397544a..0c632d5 100644
--- a/dev/assets/solvers_10_cbls.md.BCa7hnj8.js
+++ b/dev/assets/solvers_10_cbls.md.CdQMlrVz.js
@@ -5,4 +5,4 @@ import{_ as n,c as p,j as i,a as t,G as e,a5 as l,B as r,o}from"./chunks/framewo
 @objective(model, ScalarFunction(f))
 
 # Generic use
-@objective(model, ScalarFunction(f, X))
source
`,7))]),i("details",ts,[i("summary",null,[s[140]||(s[140]=i("a",{id:"CBLS.Sum",href:"#CBLS.Sum"},[i("span",{class:"jlbinding"},"CBLS.Sum")],-1)),s[141]||(s[141]=t()),e(a,{type:"info",class:"jlObjectType jlType",text:"Type"})]),s[142]||(s[142]=i("p",null,[t("Global constraint ensuring that the sum of the variables in "),i("code",null,"x"),t(" satisfies a given condition.")],-1)),s[143]||(s[143]=i("p",null,[i("a",{href:"https://github.com/JuliaConstraints/CBLS.jl/blob/v0.2.2/src/constraints/sum.jl#L46-L48",target:"_blank",rel:"noreferrer"},"source")],-1))]),i("details",as,[i("summary",null,[s[144]||(s[144]=i("a",{id:"CBLS.Supports",href:"#CBLS.Supports"},[i("span",{class:"jlbinding"},"CBLS.Supports")],-1)),s[145]||(s[145]=t()),e(a,{type:"info",class:"jlObjectType jlType",text:"Type"})]),s[146]||(s[146]=l('
Global constraint ensuring that the tuple x matches a configuration listed within the support set pair_vars. This constraint is derived from the extension model, specifying that x must be one of the explicitly defined supported configurations: x ∈ pair_vars. It is utilized to directly declare the tuples that are valid and should be included in the solution space.
julia
@constraint(model, X in Supports(; pair_vars))
source
',3))]),i("details",es,[i("summary",null,[s[147]||(s[147]=i("a",{id:"Base.copy-Tuple{CBLS.MOIError}",href:"#Base.copy-Tuple{CBLS.MOIError}"},[i("span",{class:"jlbinding"},"Base.copy")],-1)),s[148]||(s[148]=t()),e(a,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[149]||(s[149]=l('
julia
Base.copy(set::MOIError) = begin
DOCSTRING
source
',3))]),i("details",ls,[i("summary",null,[s[150]||(s[150]=i("a",{id:"Base.copy-Tuple{CBLS.MOIIntention}",href:"#Base.copy-Tuple{CBLS.MOIIntention}"},[i("span",{class:"jlbinding"},"Base.copy")],-1)),s[151]||(s[151]=t()),e(a,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[152]||(s[152]=l('
julia
Base.copy(set::MOIIntention)
Copy an intention set.
Arguments
  • set::MOIIntention: The intention set to be copied.
Returns
  • MOIIntention: A copy of the intention set.
source
',7))]),i("details",ns,[i("summary",null,[s[153]||(s[153]=i("a",{id:"Base.copy-Tuple{DiscreteSet}",href:"#Base.copy-Tuple{DiscreteSet}"},[i("span",{class:"jlbinding"},"Base.copy")],-1)),s[154]||(s[154]=t()),e(a,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[155]||(s[155]=l('
julia
Base.copy(set::DiscreteSet)
Copy a discrete set.
Arguments
  • set::DiscreteSet: The discrete set to be copied.
Returns
  • DiscreteSet: A copy of the discrete set.
source
',7))]),i("details",ps,[i("summary",null,[s[156]||(s[156]=i("a",{id:"Base.copy-Tuple{F} where F<:Function",href:"#Base.copy-Tuple{F} where F<:Function"},[i("span",{class:"jlbinding"},"Base.copy")],-1)),s[157]||(s[157]=t()),e(a,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[158]||(s[158]=l('
julia
Base.copy(op::F) where {F <: Function}
Copy a function.
Arguments
  • op::F: The function to be copied.
Returns
  • F: The copied function.
source
',7))]),i("details",rs,[i("summary",null,[s[159]||(s[159]=i("a",{id:"Base.copy-Tuple{Nothing}",href:"#Base.copy-Tuple{Nothing}"},[i("span",{class:"jlbinding"},"Base.copy")],-1)),s[160]||(s[160]=t()),e(a,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[161]||(s[161]=l('
julia
Base.copy(::Nothing)
Copy a Nothing value.
Arguments
  • ::Nothing: The Nothing value to be copied.
Returns
  • Nothing: The copied Nothing value.
source
',7))]),i("details",os,[i("summary",null,[s[162]||(s[162]=i("a",{id:"JuMP.build_variable-Union{Tuple{T}, Tuple{Function, JuMP.VariableInfo, T}} where T<:MathOptInterface.AbstractScalarSet",href:"#JuMP.build_variable-Union{Tuple{T}, Tuple{Function, JuMP.VariableInfo, T}} where T<:MathOptInterface.AbstractScalarSet"},[i("span",{class:"jlbinding"},"JuMP.build_variable")],-1)),s[163]||(s[163]=t()),e(a,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[164]||(s[164]=l('
julia
JuMP.build_variable(::Function, info::JuMP.VariableInfo, set::T) where T <: MOI.AbstractScalarSet
Create a variable constrained by a scalar set.
Arguments
  • info::JuMP.VariableInfo: Information about the variable to be created.
  • set::T where T <: MOI.AbstractScalarSet: The set defining the constraints on the variable.
Returns
  • JuMP.VariableConstrainedOnCreation: A variable constrained by the specified set.
source
',7))]),i("details",hs,[i("summary",null,[s[165]||(s[165]=i("a",{id:"JuMP.moi_set-Tuple{Intention, Int64}",href:"#JuMP.moi_set-Tuple{Intention, Int64}"},[i("span",{class:"jlbinding"},"JuMP.moi_set")],-1)),s[166]||(s[166]=t()),e(a,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[167]||(s[167]=l('
julia
JuMP.moi_set(set::Intention, dim::Int) -> MOIIntention
Convert an Intention set to a MOIIntention set.
Arguments
  • set::Intention: The intention set to be converted.
  • dim::Int: The dimension of the vector set.
Returns
  • MOIIntention: The converted MOIIntention set.
source
',7))]),i("details",ds,[i("summary",null,[s[168]||(s[168]=i("a",{id:"JuMP.moi_set-Tuple{Predicate, Int64}",href:"#JuMP.moi_set-Tuple{Predicate, Int64}"},[i("span",{class:"jlbinding"},"JuMP.moi_set")],-1)),s[169]||(s[169]=t()),e(a,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[170]||(s[170]=l('
julia
JuMP.moi_set(set::Predicate, dim::Int) -> MOIIntention
Convert a Predicate set to a MOIIntention set.
Arguments
  • set::Predicate: The predicate set to be converted.
  • dim::Int: The dimension of the vector set.
Returns
  • MOIIntention: The converted MOIIntention set.
source
',7))]),i("details",ks,[i("summary",null,[s[171]||(s[171]=i("a",{id:"MathOptInterface.add_constraint-Union{Tuple{F}, Tuple{CBLS.Optimizer, MathOptInterface.VectorOfVariables, CBLS.MOIError{F}}} where F<:Function",href:"#MathOptInterface.add_constraint-Union{Tuple{F}, Tuple{CBLS.Optimizer, MathOptInterface.VectorOfVariables, CBLS.MOIError{F}}} where F<:Function"},[i("span",{class:"jlbinding"},"MathOptInterface.add_constraint")],-1)),s[172]||(s[172]=t()),e(a,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[173]||(s[173]=l('
julia
MOI.add_constraint(optimizer::Optimizer, vars::MOI.VectorOfVariables, set::MOIError)
DOCSTRING
Arguments:
  • optimizer: DESCRIPTION
  • vars: DESCRIPTION
  • set: DESCRIPTION
source
',5))]),i("details",gs,[i("summary",null,[s[174]||(s[174]=i("a",{id:"MathOptInterface.add_constraint-Union{Tuple{F}, Tuple{CBLS.Optimizer, MathOptInterface.VectorOfVariables, CBLS.MOIIntention{F}}} where F<:Function",href:"#MathOptInterface.add_constraint-Union{Tuple{F}, Tuple{CBLS.Optimizer, MathOptInterface.VectorOfVariables, CBLS.MOIIntention{F}}} where F<:Function"},[i("span",{class:"jlbinding"},"MathOptInterface.add_constraint")],-1)),s[175]||(s[175]=t()),e(a,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[176]||(s[176]=l('
julia
MOI.add_constraint(optimizer::Optimizer, vars::MOI.VectorOfVariables, set::MOIIntention{F}) where {F <: Function}
Add an intention constraint to the optimizer.
Arguments
  • optimizer::Optimizer: The optimizer instance.
  • vars::MOI.VectorOfVariables: The variables for the constraint.
  • set::MOIIntention{F}: The intention set defining the constraint.
Returns
  • CI{VOV, MOIIntention{F}}: The constraint index.
source
',7))]),i("details",us,[i("summary",null,[s[177]||(s[177]=i("a",{id:"MathOptInterface.add_constraint-Union{Tuple{T}, Tuple{CBLS.Optimizer, MathOptInterface.VariableIndex, DiscreteSet{T}}} where T<:Number",href:"#MathOptInterface.add_constraint-Union{Tuple{T}, Tuple{CBLS.Optimizer, MathOptInterface.VariableIndex, DiscreteSet{T}}} where T<:Number"},[i("span",{class:"jlbinding"},"MathOptInterface.add_constraint")],-1)),s[178]||(s[178]=t()),e(a,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[179]||(s[179]=l('
julia
MOI.add_constraint(optimizer::Optimizer, v::VI, set::DiscreteSet{T}) where T <: Number
DOCSTRING
Arguments:
  • optimizer: DESCRIPTION
  • v: DESCRIPTION
  • set: DESCRIPTION
source
',5))]),i("details",cs,[i("summary",null,[s[180]||(s[180]=i("a",{id:"MathOptInterface.add_variable-Tuple{CBLS.Optimizer}",href:"#MathOptInterface.add_variable-Tuple{CBLS.Optimizer}"},[i("span",{class:"jlbinding"},"MathOptInterface.add_variable")],-1)),s[181]||(s[181]=t()),e(a,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[182]||(s[182]=l('
julia
MOI.add_variable(model::Optimizer) = begin
DOCSTRING
source
',3))]),i("details",ys,[i("summary",null,[s[183]||(s[183]=i("a",{id:"MathOptInterface.copy_to-Tuple{CBLS.Optimizer, MathOptInterface.ModelLike}",href:"#MathOptInterface.copy_to-Tuple{CBLS.Optimizer, MathOptInterface.ModelLike}"},[i("span",{class:"jlbinding"},"MathOptInterface.copy_to")],-1)),s[184]||(s[184]=t()),e(a,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[185]||(s[185]=l('
julia
MOI.copy_to(model::Optimizer, src::MOI.ModelLike)
Copy the source model to the optimizer.
Arguments
  • model::Optimizer: The optimizer instance.
  • src::MOI.ModelLike: The source model to be copied.
Returns
  • Nothing
source
',7))]),i("details",bs,[i("summary",null,[s[186]||(s[186]=i("a",{id:"MathOptInterface.empty!-Tuple{Any}",href:"#MathOptInterface.empty!-Tuple{Any}"},[i("span",{class:"jlbinding"},"MathOptInterface.empty!")],-1)),s[187]||(s[187]=t()),e(a,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[188]||(s[188]=l('
julia
MOI.empty!(opt)
Empty the optimizer.
Arguments
  • opt::Optimizer: The optimizer instance.
Returns
  • Nothing
source
',7))]),i("details",Es,[i("summary",null,[s[189]||(s[189]=i("a",{id:"MathOptInterface.get-Tuple{CBLS.Optimizer, MathOptInterface.SolverName}",href:"#MathOptInterface.get-Tuple{CBLS.Optimizer, MathOptInterface.SolverName}"},[i("span",{class:"jlbinding"},"MathOptInterface.get")],-1)),s[190]||(s[190]=t()),e(a,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[191]||(s[191]=l('
julia
MOI.get(::Optimizer, ::MOI.SolverName)
Get the name of the solver.
Arguments
  • ::Optimizer: The optimizer instance.
Returns
  • String: The name of the solver.
source
',7))]),i("details",Cs,[i("summary",null,[s[192]||(s[192]=i("a",{id:"MathOptInterface.get-Tuple{CBLS.Optimizer, MathOptInterface.SolverVersion}",href:"#MathOptInterface.get-Tuple{CBLS.Optimizer, MathOptInterface.SolverVersion}"},[i("span",{class:"jlbinding"},"MathOptInterface.get")],-1)),s[193]||(s[193]=t()),e(a,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[194]||(s[194]=l('
julia
Moi.get(::Optimizer, ::MOI.SolverVersion)
Get the version of the solver, here LocalSearchSolvers.jl.
source
',3))]),i("details",ms,[i("summary",null,[s[195]||(s[195]=i("a",{id:"MathOptInterface.is_empty-Tuple{CBLS.Optimizer}",href:"#MathOptInterface.is_empty-Tuple{CBLS.Optimizer}"},[i("span",{class:"jlbinding"},"MathOptInterface.is_empty")],-1)),s[196]||(s[196]=t()),e(a,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[197]||(s[197]=l('
julia
MOI.is_empty(model::Optimizer)
Check if the model is empty.
Arguments
  • model::Optimizer: The optimizer instance.
Returns
  • Bool: True if the model is empty, false otherwise.
source
',7))]),i("details",Fs,[i("summary",null,[s[198]||(s[198]=i("a",{id:"MathOptInterface.is_valid-Tuple{CBLS.Optimizer, MathOptInterface.ConstraintIndex{MathOptInterface.VariableIndex, MathOptInterface.Integer}}",href:"#MathOptInterface.is_valid-Tuple{CBLS.Optimizer, MathOptInterface.ConstraintIndex{MathOptInterface.VariableIndex, MathOptInterface.Integer}}"},[i("span",{class:"jlbinding"},"MathOptInterface.is_valid")],-1)),s[199]||(s[199]=t()),e(a,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[200]||(s[200]=l('
julia
MOI.is_valid(optimizer::Optimizer, index::CI{VI, MOI.Integer})
Check if an index is valid for the optimizer.
Arguments
  • optimizer::Optimizer: The optimizer instance.
  • index::CI{VI, MOI.Integer}: The index to be checked.
Returns
  • Bool: True if the index is valid, false otherwise.
source
',7))]),i("details",js,[i("summary",null,[s[201]||(s[201]=i("a",{id:"MathOptInterface.optimize!-Tuple{CBLS.Optimizer}",href:"#MathOptInterface.optimize!-Tuple{CBLS.Optimizer}"},[i("span",{class:"jlbinding"},"MathOptInterface.optimize!")],-1)),s[202]||(s[202]=t()),e(a,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[203]||(s[203]=l('
julia
MOI.optimize!(model::Optimizer)
Optimize the model using the optimizer.
Arguments
  • model::Optimizer: The optimizer instance.
Returns
  • Nothing
source
',7))]),i("details",vs,[i("summary",null,[s[204]||(s[204]=i("a",{id:"MathOptInterface.set",href:"#MathOptInterface.set"},[i("span",{class:"jlbinding"},"MathOptInterface.set")],-1)),s[205]||(s[205]=t()),e(a,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[206]||(s[206]=l('
julia
MOI.set(::Optimizer, ::MOI.Silent, bool = true)
Set the verbosity of the solver.
Arguments
  • ::Optimizer: The optimizer instance.
  • ::MOI.Silent: The silent option for the solver.
  • bool::Bool: Whether to set the solver to silent mode.
Returns
  • Nothing
source
',7))]),i("details",fs,[i("summary",null,[s[207]||(s[207]=i("a",{id:"MathOptInterface.set-Tuple{CBLS.Optimizer, MathOptInterface.RawOptimizerAttribute, Any}",href:"#MathOptInterface.set-Tuple{CBLS.Optimizer, MathOptInterface.RawOptimizerAttribute, Any}"},[i("span",{class:"jlbinding"},"MathOptInterface.set")],-1)),s[208]||(s[208]=t()),e(a,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[209]||(s[209]=l('
julia
MOI.set(model::Optimizer, p::MOI.RawOptimizerAttribute, value)
Set a RawOptimizerAttribute to value
source
',3))]),i("details",Bs,[i("summary",null,[s[210]||(s[210]=i("a",{id:"MathOptInterface.set-Tuple{CBLS.Optimizer, MathOptInterface.TimeLimitSec, Union{Nothing, Float64}}",href:"#MathOptInterface.set-Tuple{CBLS.Optimizer, MathOptInterface.TimeLimitSec, Union{Nothing, Float64}}"},[i("span",{class:"jlbinding"},"MathOptInterface.set")],-1)),s[211]||(s[211]=t()),e(a,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[212]||(s[212]=l('
julia
MOI.set(model::Optimizer, ::MOI.TimeLimitSec, value::Union{Nothing,Float64})
Set the time limit
source
',3))]),i("details",Os,[i("summary",null,[s[213]||(s[213]=i("a",{id:"MathOptInterface.supports_constraint-Union{Tuple{F}, Tuple{CBLS.Optimizer, Type{MathOptInterface.VectorOfVariables}, Type{CBLS.MOIError{F}}}} where F<:Function",href:"#MathOptInterface.supports_constraint-Union{Tuple{F}, Tuple{CBLS.Optimizer, Type{MathOptInterface.VectorOfVariables}, Type{CBLS.MOIError{F}}}} where F<:Function"},[i("span",{class:"jlbinding"},"MathOptInterface.supports_constraint")],-1)),s[214]||(s[214]=t()),e(a,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[215]||(s[215]=l('
julia
MOI.supports_constraint(::Optimizer, ::Type{VOV}, ::Type{MOIError}) = begin
DOCSTRING
Arguments:
  • ``: DESCRIPTION
  • ``: DESCRIPTION
  • ``: DESCRIPTION
source
',5))]),i("details",Ls,[i("summary",null,[s[216]||(s[216]=i("a",{id:"MathOptInterface.supports_constraint-Union{Tuple{F}, Tuple{CBLS.Optimizer, Type{MathOptInterface.VectorOfVariables}, Type{CBLS.MOIIntention{F}}}} where F<:Function",href:"#MathOptInterface.supports_constraint-Union{Tuple{F}, Tuple{CBLS.Optimizer, Type{MathOptInterface.VectorOfVariables}, Type{CBLS.MOIIntention{F}}}} where F<:Function"},[i("span",{class:"jlbinding"},"MathOptInterface.supports_constraint")],-1)),s[217]||(s[217]=t()),e(a,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[218]||(s[218]=l('
julia
MOI.supports_constraint(::Optimizer, ::Type{VOV}, ::Type{MOIIntention{F}}) where {F <: Function}
Check if the optimizer supports a given intention constraint.
Arguments
  • ::Optimizer: The optimizer instance.
  • ::Type{VOV}: The type of the variable.
  • ::Type{MOIIntention{F}}: The type of the intention.
Returns
  • Bool: True if the optimizer supports the constraint, false otherwise.
source
',7))]),i("details",Ss,[i("summary",null,[s[219]||(s[219]=i("a",{id:"MathOptInterface.supports_incremental_interface-Tuple{CBLS.Optimizer}",href:"#MathOptInterface.supports_incremental_interface-Tuple{CBLS.Optimizer}"},[i("span",{class:"jlbinding"},"MathOptInterface.supports_incremental_interface")],-1)),s[220]||(s[220]=t()),e(a,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[221]||(s[221]=l('
julia
MOI.supports_incremental_interface(::Optimizer)
Check if the optimizer supports incremental interface.
Arguments
  • ::Optimizer: The optimizer instance.
Returns
  • Bool: True if the optimizer supports incremental interface, false otherwise.
source
',7))])])}const Ns=n(h,[["render",Is]]);export{Vs as __pageData,Ns as default};
+@objective(model, ScalarFunction(f, X))
source
`,7))]),i("details",ts,[i("summary",null,[s[140]||(s[140]=i("a",{id:"CBLS.Sum",href:"#CBLS.Sum"},[i("span",{class:"jlbinding"},"CBLS.Sum")],-1)),s[141]||(s[141]=t()),e(a,{type:"info",class:"jlObjectType jlType",text:"Type"})]),s[142]||(s[142]=i("p",null,[t("Global constraint ensuring that the sum of the variables in "),i("code",null,"x"),t(" satisfies a given condition.")],-1)),s[143]||(s[143]=i("p",null,[i("a",{href:"https://github.com/JuliaConstraints/CBLS.jl/blob/v0.2.2/src/constraints/sum.jl#L46-L48",target:"_blank",rel:"noreferrer"},"source")],-1))]),i("details",as,[i("summary",null,[s[144]||(s[144]=i("a",{id:"CBLS.Supports",href:"#CBLS.Supports"},[i("span",{class:"jlbinding"},"CBLS.Supports")],-1)),s[145]||(s[145]=t()),e(a,{type:"info",class:"jlObjectType jlType",text:"Type"})]),s[146]||(s[146]=l('
Global constraint ensuring that the tuple x matches a configuration listed within the support set pair_vars. This constraint is derived from the extension model, specifying that x must be one of the explicitly defined supported configurations: x ∈ pair_vars. It is utilized to directly declare the tuples that are valid and should be included in the solution space.
julia
@constraint(model, X in Supports(; pair_vars))
source
',3))]),i("details",es,[i("summary",null,[s[147]||(s[147]=i("a",{id:"Base.copy-Tuple{CBLS.DiscreteSet}",href:"#Base.copy-Tuple{CBLS.DiscreteSet}"},[i("span",{class:"jlbinding"},"Base.copy")],-1)),s[148]||(s[148]=t()),e(a,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[149]||(s[149]=l('
julia
Base.copy(set::DiscreteSet)
Copy a discrete set.
Arguments
  • set::DiscreteSet: The discrete set to be copied.
Returns
  • DiscreteSet: A copy of the discrete set.
source
',7))]),i("details",ls,[i("summary",null,[s[150]||(s[150]=i("a",{id:"Base.copy-Tuple{CBLS.MOIError}",href:"#Base.copy-Tuple{CBLS.MOIError}"},[i("span",{class:"jlbinding"},"Base.copy")],-1)),s[151]||(s[151]=t()),e(a,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[152]||(s[152]=l('
julia
Base.copy(set::MOIError) = begin
DOCSTRING
source
',3))]),i("details",ns,[i("summary",null,[s[153]||(s[153]=i("a",{id:"Base.copy-Tuple{CBLS.MOIIntention}",href:"#Base.copy-Tuple{CBLS.MOIIntention}"},[i("span",{class:"jlbinding"},"Base.copy")],-1)),s[154]||(s[154]=t()),e(a,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[155]||(s[155]=l('
julia
Base.copy(set::MOIIntention)
Copy an intention set.
Arguments
  • set::MOIIntention: The intention set to be copied.
Returns
  • MOIIntention: A copy of the intention set.
source
',7))]),i("details",ps,[i("summary",null,[s[156]||(s[156]=i("a",{id:"Base.copy-Tuple{F} where F<:Function",href:"#Base.copy-Tuple{F} where F<:Function"},[i("span",{class:"jlbinding"},"Base.copy")],-1)),s[157]||(s[157]=t()),e(a,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[158]||(s[158]=l('
julia
Base.copy(op::F) where {F <: Function}
Copy a function.
Arguments
  • op::F: The function to be copied.
Returns
  • F: The copied function.
source
',7))]),i("details",rs,[i("summary",null,[s[159]||(s[159]=i("a",{id:"Base.copy-Tuple{Nothing}",href:"#Base.copy-Tuple{Nothing}"},[i("span",{class:"jlbinding"},"Base.copy")],-1)),s[160]||(s[160]=t()),e(a,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[161]||(s[161]=l('
julia
Base.copy(::Nothing)
Copy a Nothing value.
Arguments
  • ::Nothing: The Nothing value to be copied.
Returns
  • Nothing: The copied Nothing value.
source
',7))]),i("details",os,[i("summary",null,[s[162]||(s[162]=i("a",{id:"JuMP.build_variable-Union{Tuple{T}, Tuple{Function, JuMP.VariableInfo, T}} where T<:MathOptInterface.AbstractScalarSet",href:"#JuMP.build_variable-Union{Tuple{T}, Tuple{Function, JuMP.VariableInfo, T}} where T<:MathOptInterface.AbstractScalarSet"},[i("span",{class:"jlbinding"},"JuMP.build_variable")],-1)),s[163]||(s[163]=t()),e(a,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[164]||(s[164]=l('
julia
JuMP.build_variable(::Function, info::JuMP.VariableInfo, set::T) where T <: MOI.AbstractScalarSet
Create a variable constrained by a scalar set.
Arguments
  • info::JuMP.VariableInfo: Information about the variable to be created.
  • set::T where T <: MOI.AbstractScalarSet: The set defining the constraints on the variable.
Returns
  • JuMP.VariableConstrainedOnCreation: A variable constrained by the specified set.
source
',7))]),i("details",hs,[i("summary",null,[s[165]||(s[165]=i("a",{id:"JuMP.moi_set-Tuple{CBLS.Intention, Int64}",href:"#JuMP.moi_set-Tuple{CBLS.Intention, Int64}"},[i("span",{class:"jlbinding"},"JuMP.moi_set")],-1)),s[166]||(s[166]=t()),e(a,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[167]||(s[167]=l('
julia
JuMP.moi_set(set::Intention, dim::Int) -> MOIIntention
Convert an Intention set to a MOIIntention set.
Arguments
  • set::Intention: The intention set to be converted.
  • dim::Int: The dimension of the vector set.
Returns
  • MOIIntention: The converted MOIIntention set.
source
',7))]),i("details",ds,[i("summary",null,[s[168]||(s[168]=i("a",{id:"JuMP.moi_set-Tuple{Predicate, Int64}",href:"#JuMP.moi_set-Tuple{Predicate, Int64}"},[i("span",{class:"jlbinding"},"JuMP.moi_set")],-1)),s[169]||(s[169]=t()),e(a,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[170]||(s[170]=l('
julia
JuMP.moi_set(set::Predicate, dim::Int) -> MOIIntention
Convert a Predicate set to a MOIIntention set.
Arguments
  • set::Predicate: The predicate set to be converted.
  • dim::Int: The dimension of the vector set.
Returns
  • MOIIntention: The converted MOIIntention set.
source
',7))]),i("details",ks,[i("summary",null,[s[171]||(s[171]=i("a",{id:"MathOptInterface.add_constraint-Union{Tuple{F}, Tuple{CBLS.Optimizer, MathOptInterface.VectorOfVariables, CBLS.MOIError{F}}} where F<:Function",href:"#MathOptInterface.add_constraint-Union{Tuple{F}, Tuple{CBLS.Optimizer, MathOptInterface.VectorOfVariables, CBLS.MOIError{F}}} where F<:Function"},[i("span",{class:"jlbinding"},"MathOptInterface.add_constraint")],-1)),s[172]||(s[172]=t()),e(a,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[173]||(s[173]=l('
julia
MOI.add_constraint(optimizer::Optimizer, vars::MOI.VectorOfVariables, set::MOIError)
DOCSTRING
Arguments:
  • optimizer: DESCRIPTION
  • vars: DESCRIPTION
  • set: DESCRIPTION
source
',5))]),i("details",gs,[i("summary",null,[s[174]||(s[174]=i("a",{id:"MathOptInterface.add_constraint-Union{Tuple{F}, Tuple{CBLS.Optimizer, MathOptInterface.VectorOfVariables, CBLS.MOIIntention{F}}} where F<:Function",href:"#MathOptInterface.add_constraint-Union{Tuple{F}, Tuple{CBLS.Optimizer, MathOptInterface.VectorOfVariables, CBLS.MOIIntention{F}}} where F<:Function"},[i("span",{class:"jlbinding"},"MathOptInterface.add_constraint")],-1)),s[175]||(s[175]=t()),e(a,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[176]||(s[176]=l('
julia
MOI.add_constraint(optimizer::Optimizer, vars::MOI.VectorOfVariables, set::MOIIntention{F}) where {F <: Function}
Add an intention constraint to the optimizer.
Arguments
  • optimizer::Optimizer: The optimizer instance.
  • vars::MOI.VectorOfVariables: The variables for the constraint.
  • set::MOIIntention{F}: The intention set defining the constraint.
Returns
  • CI{VOV, MOIIntention{F}}: The constraint index.
source
',7))]),i("details",us,[i("summary",null,[s[177]||(s[177]=i("a",{id:"MathOptInterface.add_constraint-Union{Tuple{T}, Tuple{CBLS.Optimizer, MathOptInterface.VariableIndex, CBLS.DiscreteSet{T}}} where T<:Number",href:"#MathOptInterface.add_constraint-Union{Tuple{T}, Tuple{CBLS.Optimizer, MathOptInterface.VariableIndex, CBLS.DiscreteSet{T}}} where T<:Number"},[i("span",{class:"jlbinding"},"MathOptInterface.add_constraint")],-1)),s[178]||(s[178]=t()),e(a,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[179]||(s[179]=l('
julia
MOI.add_constraint(optimizer::Optimizer, v::VI, set::DiscreteSet{T}) where T <: Number
DOCSTRING
Arguments:
  • optimizer: DESCRIPTION
  • v: DESCRIPTION
  • set: DESCRIPTION
source
',5))]),i("details",cs,[i("summary",null,[s[180]||(s[180]=i("a",{id:"MathOptInterface.add_variable-Tuple{CBLS.Optimizer}",href:"#MathOptInterface.add_variable-Tuple{CBLS.Optimizer}"},[i("span",{class:"jlbinding"},"MathOptInterface.add_variable")],-1)),s[181]||(s[181]=t()),e(a,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[182]||(s[182]=l('
julia
MOI.add_variable(model::Optimizer) = begin
DOCSTRING
source
',3))]),i("details",ys,[i("summary",null,[s[183]||(s[183]=i("a",{id:"MathOptInterface.copy_to-Tuple{CBLS.Optimizer, MathOptInterface.ModelLike}",href:"#MathOptInterface.copy_to-Tuple{CBLS.Optimizer, MathOptInterface.ModelLike}"},[i("span",{class:"jlbinding"},"MathOptInterface.copy_to")],-1)),s[184]||(s[184]=t()),e(a,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[185]||(s[185]=l('
julia
MOI.copy_to(model::Optimizer, src::MOI.ModelLike)
Copy the source model to the optimizer.
Arguments
  • model::Optimizer: The optimizer instance.
  • src::MOI.ModelLike: The source model to be copied.
Returns
  • Nothing
source
',7))]),i("details",bs,[i("summary",null,[s[186]||(s[186]=i("a",{id:"MathOptInterface.empty!-Tuple{Any}",href:"#MathOptInterface.empty!-Tuple{Any}"},[i("span",{class:"jlbinding"},"MathOptInterface.empty!")],-1)),s[187]||(s[187]=t()),e(a,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[188]||(s[188]=l('
julia
MOI.empty!(opt)
Empty the optimizer.
Arguments
  • opt::Optimizer: The optimizer instance.
Returns
  • Nothing
source
',7))]),i("details",Es,[i("summary",null,[s[189]||(s[189]=i("a",{id:"MathOptInterface.get-Tuple{CBLS.Optimizer, MathOptInterface.SolverName}",href:"#MathOptInterface.get-Tuple{CBLS.Optimizer, MathOptInterface.SolverName}"},[i("span",{class:"jlbinding"},"MathOptInterface.get")],-1)),s[190]||(s[190]=t()),e(a,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[191]||(s[191]=l('
julia
MOI.get(::Optimizer, ::MOI.SolverName)
Get the name of the solver.
Arguments
  • ::Optimizer: The optimizer instance.
Returns
  • String: The name of the solver.
source
',7))]),i("details",Cs,[i("summary",null,[s[192]||(s[192]=i("a",{id:"MathOptInterface.get-Tuple{CBLS.Optimizer, MathOptInterface.SolverVersion}",href:"#MathOptInterface.get-Tuple{CBLS.Optimizer, MathOptInterface.SolverVersion}"},[i("span",{class:"jlbinding"},"MathOptInterface.get")],-1)),s[193]||(s[193]=t()),e(a,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[194]||(s[194]=l('
julia
Moi.get(::Optimizer, ::MOI.SolverVersion)
Get the version of the solver, here LocalSearchSolvers.jl.
source
',3))]),i("details",ms,[i("summary",null,[s[195]||(s[195]=i("a",{id:"MathOptInterface.is_empty-Tuple{CBLS.Optimizer}",href:"#MathOptInterface.is_empty-Tuple{CBLS.Optimizer}"},[i("span",{class:"jlbinding"},"MathOptInterface.is_empty")],-1)),s[196]||(s[196]=t()),e(a,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[197]||(s[197]=l('
julia
MOI.is_empty(model::Optimizer)
Check if the model is empty.
Arguments
  • model::Optimizer: The optimizer instance.
Returns
  • Bool: True if the model is empty, false otherwise.
source
',7))]),i("details",Fs,[i("summary",null,[s[198]||(s[198]=i("a",{id:"MathOptInterface.is_valid-Tuple{CBLS.Optimizer, MathOptInterface.ConstraintIndex{MathOptInterface.VariableIndex, MathOptInterface.Integer}}",href:"#MathOptInterface.is_valid-Tuple{CBLS.Optimizer, MathOptInterface.ConstraintIndex{MathOptInterface.VariableIndex, MathOptInterface.Integer}}"},[i("span",{class:"jlbinding"},"MathOptInterface.is_valid")],-1)),s[199]||(s[199]=t()),e(a,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[200]||(s[200]=l('
julia
MOI.is_valid(optimizer::Optimizer, index::CI{VI, MOI.Integer})
Check if an index is valid for the optimizer.
Arguments
  • optimizer::Optimizer: The optimizer instance.
  • index::CI{VI, MOI.Integer}: The index to be checked.
Returns
  • Bool: True if the index is valid, false otherwise.
source
',7))]),i("details",js,[i("summary",null,[s[201]||(s[201]=i("a",{id:"MathOptInterface.optimize!-Tuple{CBLS.Optimizer}",href:"#MathOptInterface.optimize!-Tuple{CBLS.Optimizer}"},[i("span",{class:"jlbinding"},"MathOptInterface.optimize!")],-1)),s[202]||(s[202]=t()),e(a,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[203]||(s[203]=l('
julia
MOI.optimize!(model::Optimizer)
Optimize the model using the optimizer.
Arguments
  • model::Optimizer: The optimizer instance.
Returns
  • Nothing
source
',7))]),i("details",vs,[i("summary",null,[s[204]||(s[204]=i("a",{id:"MathOptInterface.set",href:"#MathOptInterface.set"},[i("span",{class:"jlbinding"},"MathOptInterface.set")],-1)),s[205]||(s[205]=t()),e(a,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[206]||(s[206]=l('
julia
MOI.set(::Optimizer, ::MOI.Silent, bool = true)
Set the verbosity of the solver.
Arguments
  • ::Optimizer: The optimizer instance.
  • ::MOI.Silent: The silent option for the solver.
  • bool::Bool: Whether to set the solver to silent mode.
Returns
  • Nothing
source
',7))]),i("details",fs,[i("summary",null,[s[207]||(s[207]=i("a",{id:"MathOptInterface.set-Tuple{CBLS.Optimizer, MathOptInterface.RawOptimizerAttribute, Any}",href:"#MathOptInterface.set-Tuple{CBLS.Optimizer, MathOptInterface.RawOptimizerAttribute, Any}"},[i("span",{class:"jlbinding"},"MathOptInterface.set")],-1)),s[208]||(s[208]=t()),e(a,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[209]||(s[209]=l('
julia
MOI.set(model::Optimizer, p::MOI.RawOptimizerAttribute, value)
Set a RawOptimizerAttribute to value
source
',3))]),i("details",Bs,[i("summary",null,[s[210]||(s[210]=i("a",{id:"MathOptInterface.set-Tuple{CBLS.Optimizer, MathOptInterface.TimeLimitSec, Union{Nothing, Float64}}",href:"#MathOptInterface.set-Tuple{CBLS.Optimizer, MathOptInterface.TimeLimitSec, Union{Nothing, Float64}}"},[i("span",{class:"jlbinding"},"MathOptInterface.set")],-1)),s[211]||(s[211]=t()),e(a,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[212]||(s[212]=l('
julia
MOI.set(model::Optimizer, ::MOI.TimeLimitSec, value::Union{Nothing,Float64})
Set the time limit
source
',3))]),i("details",Os,[i("summary",null,[s[213]||(s[213]=i("a",{id:"MathOptInterface.supports_constraint-Union{Tuple{F}, Tuple{CBLS.Optimizer, Type{MathOptInterface.VectorOfVariables}, Type{CBLS.MOIError{F}}}} where F<:Function",href:"#MathOptInterface.supports_constraint-Union{Tuple{F}, Tuple{CBLS.Optimizer, Type{MathOptInterface.VectorOfVariables}, Type{CBLS.MOIError{F}}}} where F<:Function"},[i("span",{class:"jlbinding"},"MathOptInterface.supports_constraint")],-1)),s[214]||(s[214]=t()),e(a,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[215]||(s[215]=l('
julia
MOI.supports_constraint(::Optimizer, ::Type{VOV}, ::Type{MOIError}) = begin
DOCSTRING
Arguments:
  • ``: DESCRIPTION
  • ``: DESCRIPTION
  • ``: DESCRIPTION
source
',5))]),i("details",Ls,[i("summary",null,[s[216]||(s[216]=i("a",{id:"MathOptInterface.supports_constraint-Union{Tuple{F}, Tuple{CBLS.Optimizer, Type{MathOptInterface.VectorOfVariables}, Type{CBLS.MOIIntention{F}}}} where F<:Function",href:"#MathOptInterface.supports_constraint-Union{Tuple{F}, Tuple{CBLS.Optimizer, Type{MathOptInterface.VectorOfVariables}, Type{CBLS.MOIIntention{F}}}} where F<:Function"},[i("span",{class:"jlbinding"},"MathOptInterface.supports_constraint")],-1)),s[217]||(s[217]=t()),e(a,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[218]||(s[218]=l('
julia
MOI.supports_constraint(::Optimizer, ::Type{VOV}, ::Type{MOIIntention{F}}) where {F <: Function}
Check if the optimizer supports a given intention constraint.
Arguments
  • ::Optimizer: The optimizer instance.
  • ::Type{VOV}: The type of the variable.
  • ::Type{MOIIntention{F}}: The type of the intention.
Returns
  • Bool: True if the optimizer supports the constraint, false otherwise.
source
',7))]),i("details",Ss,[i("summary",null,[s[219]||(s[219]=i("a",{id:"MathOptInterface.supports_incremental_interface-Tuple{CBLS.Optimizer}",href:"#MathOptInterface.supports_incremental_interface-Tuple{CBLS.Optimizer}"},[i("span",{class:"jlbinding"},"MathOptInterface.supports_incremental_interface")],-1)),s[220]||(s[220]=t()),e(a,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[221]||(s[221]=l('
julia
MOI.supports_incremental_interface(::Optimizer)
Check if the optimizer supports incremental interface.
Arguments
  • ::Optimizer: The optimizer instance.
Returns
  • Bool: True if the optimizer supports incremental interface, false otherwise.
source
',7))])])}const Ns=n(h,[["render",Is]]);export{Vs as __pageData,Ns as default};
diff --git a/dev/assets/solvers_10_cbls.md.BCa7hnj8.lean.js b/dev/assets/solvers_10_cbls.md.CdQMlrVz.lean.js
similarity index 63%
rename from dev/assets/solvers_10_cbls.md.BCa7hnj8.lean.js
rename to dev/assets/solvers_10_cbls.md.CdQMlrVz.lean.js
index 397544a..0c632d5 100644
--- a/dev/assets/solvers_10_cbls.md.BCa7hnj8.lean.js
+++ b/dev/assets/solvers_10_cbls.md.CdQMlrVz.lean.js
@@ -5,4 +5,4 @@ import{_ as n,c as p,j as i,a as t,G as e,a5 as l,B as r,o}from"./chunks/framewo
 @objective(model, ScalarFunction(f))
 
 # Generic use
-@objective(model, ScalarFunction(f, X))
source
`,7))]),i("details",ts,[i("summary",null,[s[140]||(s[140]=i("a",{id:"CBLS.Sum",href:"#CBLS.Sum"},[i("span",{class:"jlbinding"},"CBLS.Sum")],-1)),s[141]||(s[141]=t()),e(a,{type:"info",class:"jlObjectType jlType",text:"Type"})]),s[142]||(s[142]=i("p",null,[t("Global constraint ensuring that the sum of the variables in "),i("code",null,"x"),t(" satisfies a given condition.")],-1)),s[143]||(s[143]=i("p",null,[i("a",{href:"https://github.com/JuliaConstraints/CBLS.jl/blob/v0.2.2/src/constraints/sum.jl#L46-L48",target:"_blank",rel:"noreferrer"},"source")],-1))]),i("details",as,[i("summary",null,[s[144]||(s[144]=i("a",{id:"CBLS.Supports",href:"#CBLS.Supports"},[i("span",{class:"jlbinding"},"CBLS.Supports")],-1)),s[145]||(s[145]=t()),e(a,{type:"info",class:"jlObjectType jlType",text:"Type"})]),s[146]||(s[146]=l('
Global constraint ensuring that the tuple x matches a configuration listed within the support set pair_vars. This constraint is derived from the extension model, specifying that x must be one of the explicitly defined supported configurations: x ∈ pair_vars. It is utilized to directly declare the tuples that are valid and should be included in the solution space.
julia
@constraint(model, X in Supports(; pair_vars))
source
',3))]),i("details",es,[i("summary",null,[s[147]||(s[147]=i("a",{id:"Base.copy-Tuple{CBLS.MOIError}",href:"#Base.copy-Tuple{CBLS.MOIError}"},[i("span",{class:"jlbinding"},"Base.copy")],-1)),s[148]||(s[148]=t()),e(a,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[149]||(s[149]=l('
julia
Base.copy(set::MOIError) = begin
DOCSTRING
source
',3))]),i("details",ls,[i("summary",null,[s[150]||(s[150]=i("a",{id:"Base.copy-Tuple{CBLS.MOIIntention}",href:"#Base.copy-Tuple{CBLS.MOIIntention}"},[i("span",{class:"jlbinding"},"Base.copy")],-1)),s[151]||(s[151]=t()),e(a,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[152]||(s[152]=l('
julia
Base.copy(set::MOIIntention)
Copy an intention set.
Arguments
  • set::MOIIntention: The intention set to be copied.
Returns
  • MOIIntention: A copy of the intention set.
source
',7))]),i("details",ns,[i("summary",null,[s[153]||(s[153]=i("a",{id:"Base.copy-Tuple{DiscreteSet}",href:"#Base.copy-Tuple{DiscreteSet}"},[i("span",{class:"jlbinding"},"Base.copy")],-1)),s[154]||(s[154]=t()),e(a,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[155]||(s[155]=l('
julia
Base.copy(set::DiscreteSet)
Copy a discrete set.
Arguments
  • set::DiscreteSet: The discrete set to be copied.
Returns
  • DiscreteSet: A copy of the discrete set.
source
',7))]),i("details",ps,[i("summary",null,[s[156]||(s[156]=i("a",{id:"Base.copy-Tuple{F} where F<:Function",href:"#Base.copy-Tuple{F} where F<:Function"},[i("span",{class:"jlbinding"},"Base.copy")],-1)),s[157]||(s[157]=t()),e(a,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[158]||(s[158]=l('
julia
Base.copy(op::F) where {F <: Function}
Copy a function.
Arguments
  • op::F: The function to be copied.
Returns
  • F: The copied function.
source
',7))]),i("details",rs,[i("summary",null,[s[159]||(s[159]=i("a",{id:"Base.copy-Tuple{Nothing}",href:"#Base.copy-Tuple{Nothing}"},[i("span",{class:"jlbinding"},"Base.copy")],-1)),s[160]||(s[160]=t()),e(a,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[161]||(s[161]=l('
julia
Base.copy(::Nothing)
Copy a Nothing value.
Arguments
  • ::Nothing: The Nothing value to be copied.
Returns
  • Nothing: The copied Nothing value.
source
',7))]),i("details",os,[i("summary",null,[s[162]||(s[162]=i("a",{id:"JuMP.build_variable-Union{Tuple{T}, Tuple{Function, JuMP.VariableInfo, T}} where T<:MathOptInterface.AbstractScalarSet",href:"#JuMP.build_variable-Union{Tuple{T}, Tuple{Function, JuMP.VariableInfo, T}} where T<:MathOptInterface.AbstractScalarSet"},[i("span",{class:"jlbinding"},"JuMP.build_variable")],-1)),s[163]||(s[163]=t()),e(a,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[164]||(s[164]=l('
julia
JuMP.build_variable(::Function, info::JuMP.VariableInfo, set::T) where T <: MOI.AbstractScalarSet
Create a variable constrained by a scalar set.
Arguments
  • info::JuMP.VariableInfo: Information about the variable to be created.
  • set::T where T <: MOI.AbstractScalarSet: The set defining the constraints on the variable.
Returns
  • JuMP.VariableConstrainedOnCreation: A variable constrained by the specified set.
source
',7))]),i("details",hs,[i("summary",null,[s[165]||(s[165]=i("a",{id:"JuMP.moi_set-Tuple{Intention, Int64}",href:"#JuMP.moi_set-Tuple{Intention, Int64}"},[i("span",{class:"jlbinding"},"JuMP.moi_set")],-1)),s[166]||(s[166]=t()),e(a,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[167]||(s[167]=l('
julia
JuMP.moi_set(set::Intention, dim::Int) -> MOIIntention
Convert an Intention set to a MOIIntention set.
Arguments
  • set::Intention: The intention set to be converted.
  • dim::Int: The dimension of the vector set.
Returns
  • MOIIntention: The converted MOIIntention set.
source
',7))]),i("details",ds,[i("summary",null,[s[168]||(s[168]=i("a",{id:"JuMP.moi_set-Tuple{Predicate, Int64}",href:"#JuMP.moi_set-Tuple{Predicate, Int64}"},[i("span",{class:"jlbinding"},"JuMP.moi_set")],-1)),s[169]||(s[169]=t()),e(a,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[170]||(s[170]=l('
julia
JuMP.moi_set(set::Predicate, dim::Int) -> MOIIntention
Convert a Predicate set to a MOIIntention set.
Arguments
  • set::Predicate: The predicate set to be converted.
  • dim::Int: The dimension of the vector set.
Returns
  • MOIIntention: The converted MOIIntention set.
source
',7))]),i("details",ks,[i("summary",null,[s[171]||(s[171]=i("a",{id:"MathOptInterface.add_constraint-Union{Tuple{F}, Tuple{CBLS.Optimizer, MathOptInterface.VectorOfVariables, CBLS.MOIError{F}}} where F<:Function",href:"#MathOptInterface.add_constraint-Union{Tuple{F}, Tuple{CBLS.Optimizer, MathOptInterface.VectorOfVariables, CBLS.MOIError{F}}} where F<:Function"},[i("span",{class:"jlbinding"},"MathOptInterface.add_constraint")],-1)),s[172]||(s[172]=t()),e(a,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[173]||(s[173]=l('
julia
MOI.add_constraint(optimizer::Optimizer, vars::MOI.VectorOfVariables, set::MOIError)
DOCSTRING
Arguments:
  • optimizer: DESCRIPTION
  • vars: DESCRIPTION
  • set: DESCRIPTION
source
',5))]),i("details",gs,[i("summary",null,[s[174]||(s[174]=i("a",{id:"MathOptInterface.add_constraint-Union{Tuple{F}, Tuple{CBLS.Optimizer, MathOptInterface.VectorOfVariables, CBLS.MOIIntention{F}}} where F<:Function",href:"#MathOptInterface.add_constraint-Union{Tuple{F}, Tuple{CBLS.Optimizer, MathOptInterface.VectorOfVariables, CBLS.MOIIntention{F}}} where F<:Function"},[i("span",{class:"jlbinding"},"MathOptInterface.add_constraint")],-1)),s[175]||(s[175]=t()),e(a,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[176]||(s[176]=l('
julia
MOI.add_constraint(optimizer::Optimizer, vars::MOI.VectorOfVariables, set::MOIIntention{F}) where {F <: Function}
Add an intention constraint to the optimizer.
Arguments
  • optimizer::Optimizer: The optimizer instance.
  • vars::MOI.VectorOfVariables: The variables for the constraint.
  • set::MOIIntention{F}: The intention set defining the constraint.
Returns
  • CI{VOV, MOIIntention{F}}: The constraint index.
source
',7))]),i("details",us,[i("summary",null,[s[177]||(s[177]=i("a",{id:"MathOptInterface.add_constraint-Union{Tuple{T}, Tuple{CBLS.Optimizer, MathOptInterface.VariableIndex, DiscreteSet{T}}} where T<:Number",href:"#MathOptInterface.add_constraint-Union{Tuple{T}, Tuple{CBLS.Optimizer, MathOptInterface.VariableIndex, DiscreteSet{T}}} where T<:Number"},[i("span",{class:"jlbinding"},"MathOptInterface.add_constraint")],-1)),s[178]||(s[178]=t()),e(a,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[179]||(s[179]=l('
julia
MOI.add_constraint(optimizer::Optimizer, v::VI, set::DiscreteSet{T}) where T <: Number
DOCSTRING
Arguments:
  • optimizer: DESCRIPTION
  • v: DESCRIPTION
  • set: DESCRIPTION
source
',5))]),i("details",cs,[i("summary",null,[s[180]||(s[180]=i("a",{id:"MathOptInterface.add_variable-Tuple{CBLS.Optimizer}",href:"#MathOptInterface.add_variable-Tuple{CBLS.Optimizer}"},[i("span",{class:"jlbinding"},"MathOptInterface.add_variable")],-1)),s[181]||(s[181]=t()),e(a,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[182]||(s[182]=l('
julia
MOI.add_variable(model::Optimizer) = begin
DOCSTRING
source
',3))]),i("details",ys,[i("summary",null,[s[183]||(s[183]=i("a",{id:"MathOptInterface.copy_to-Tuple{CBLS.Optimizer, MathOptInterface.ModelLike}",href:"#MathOptInterface.copy_to-Tuple{CBLS.Optimizer, MathOptInterface.ModelLike}"},[i("span",{class:"jlbinding"},"MathOptInterface.copy_to")],-1)),s[184]||(s[184]=t()),e(a,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[185]||(s[185]=l('
julia
MOI.copy_to(model::Optimizer, src::MOI.ModelLike)
Copy the source model to the optimizer.
Arguments
  • model::Optimizer: The optimizer instance.
  • src::MOI.ModelLike: The source model to be copied.
Returns
  • Nothing
source
',7))]),i("details",bs,[i("summary",null,[s[186]||(s[186]=i("a",{id:"MathOptInterface.empty!-Tuple{Any}",href:"#MathOptInterface.empty!-Tuple{Any}"},[i("span",{class:"jlbinding"},"MathOptInterface.empty!")],-1)),s[187]||(s[187]=t()),e(a,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[188]||(s[188]=l('
julia
MOI.empty!(opt)
Empty the optimizer.
Arguments
  • opt::Optimizer: The optimizer instance.
Returns
  • Nothing
source
',7))]),i("details",Es,[i("summary",null,[s[189]||(s[189]=i("a",{id:"MathOptInterface.get-Tuple{CBLS.Optimizer, MathOptInterface.SolverName}",href:"#MathOptInterface.get-Tuple{CBLS.Optimizer, MathOptInterface.SolverName}"},[i("span",{class:"jlbinding"},"MathOptInterface.get")],-1)),s[190]||(s[190]=t()),e(a,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[191]||(s[191]=l('
julia
MOI.get(::Optimizer, ::MOI.SolverName)
Get the name of the solver.
Arguments
  • ::Optimizer: The optimizer instance.
Returns
  • String: The name of the solver.
source
',7))]),i("details",Cs,[i("summary",null,[s[192]||(s[192]=i("a",{id:"MathOptInterface.get-Tuple{CBLS.Optimizer, MathOptInterface.SolverVersion}",href:"#MathOptInterface.get-Tuple{CBLS.Optimizer, MathOptInterface.SolverVersion}"},[i("span",{class:"jlbinding"},"MathOptInterface.get")],-1)),s[193]||(s[193]=t()),e(a,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[194]||(s[194]=l('
julia
Moi.get(::Optimizer, ::MOI.SolverVersion)
Get the version of the solver, here LocalSearchSolvers.jl.
source
',3))]),i("details",ms,[i("summary",null,[s[195]||(s[195]=i("a",{id:"MathOptInterface.is_empty-Tuple{CBLS.Optimizer}",href:"#MathOptInterface.is_empty-Tuple{CBLS.Optimizer}"},[i("span",{class:"jlbinding"},"MathOptInterface.is_empty")],-1)),s[196]||(s[196]=t()),e(a,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[197]||(s[197]=l('
julia
MOI.is_empty(model::Optimizer)
Check if the model is empty.
Arguments
  • model::Optimizer: The optimizer instance.
Returns
  • Bool: True if the model is empty, false otherwise.
source
',7))]),i("details",Fs,[i("summary",null,[s[198]||(s[198]=i("a",{id:"MathOptInterface.is_valid-Tuple{CBLS.Optimizer, MathOptInterface.ConstraintIndex{MathOptInterface.VariableIndex, MathOptInterface.Integer}}",href:"#MathOptInterface.is_valid-Tuple{CBLS.Optimizer, MathOptInterface.ConstraintIndex{MathOptInterface.VariableIndex, MathOptInterface.Integer}}"},[i("span",{class:"jlbinding"},"MathOptInterface.is_valid")],-1)),s[199]||(s[199]=t()),e(a,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[200]||(s[200]=l('
julia
MOI.is_valid(optimizer::Optimizer, index::CI{VI, MOI.Integer})
Check if an index is valid for the optimizer.
Arguments
  • optimizer::Optimizer: The optimizer instance.
  • index::CI{VI, MOI.Integer}: The index to be checked.
Returns
  • Bool: True if the index is valid, false otherwise.
source
',7))]),i("details",js,[i("summary",null,[s[201]||(s[201]=i("a",{id:"MathOptInterface.optimize!-Tuple{CBLS.Optimizer}",href:"#MathOptInterface.optimize!-Tuple{CBLS.Optimizer}"},[i("span",{class:"jlbinding"},"MathOptInterface.optimize!")],-1)),s[202]||(s[202]=t()),e(a,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[203]||(s[203]=l('
julia
MOI.optimize!(model::Optimizer)
Optimize the model using the optimizer.
Arguments
  • model::Optimizer: The optimizer instance.
Returns
  • Nothing
source
',7))]),i("details",vs,[i("summary",null,[s[204]||(s[204]=i("a",{id:"MathOptInterface.set",href:"#MathOptInterface.set"},[i("span",{class:"jlbinding"},"MathOptInterface.set")],-1)),s[205]||(s[205]=t()),e(a,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[206]||(s[206]=l('
julia
MOI.set(::Optimizer, ::MOI.Silent, bool = true)
Set the verbosity of the solver.
Arguments
  • ::Optimizer: The optimizer instance.
  • ::MOI.Silent: The silent option for the solver.
  • bool::Bool: Whether to set the solver to silent mode.
Returns
  • Nothing
source
',7))]),i("details",fs,[i("summary",null,[s[207]||(s[207]=i("a",{id:"MathOptInterface.set-Tuple{CBLS.Optimizer, MathOptInterface.RawOptimizerAttribute, Any}",href:"#MathOptInterface.set-Tuple{CBLS.Optimizer, MathOptInterface.RawOptimizerAttribute, Any}"},[i("span",{class:"jlbinding"},"MathOptInterface.set")],-1)),s[208]||(s[208]=t()),e(a,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[209]||(s[209]=l('
julia
MOI.set(model::Optimizer, p::MOI.RawOptimizerAttribute, value)
Set a RawOptimizerAttribute to value
source
',3))]),i("details",Bs,[i("summary",null,[s[210]||(s[210]=i("a",{id:"MathOptInterface.set-Tuple{CBLS.Optimizer, MathOptInterface.TimeLimitSec, Union{Nothing, Float64}}",href:"#MathOptInterface.set-Tuple{CBLS.Optimizer, MathOptInterface.TimeLimitSec, Union{Nothing, Float64}}"},[i("span",{class:"jlbinding"},"MathOptInterface.set")],-1)),s[211]||(s[211]=t()),e(a,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[212]||(s[212]=l('
julia
MOI.set(model::Optimizer, ::MOI.TimeLimitSec, value::Union{Nothing,Float64})
Set the time limit
source
',3))]),i("details",Os,[i("summary",null,[s[213]||(s[213]=i("a",{id:"MathOptInterface.supports_constraint-Union{Tuple{F}, Tuple{CBLS.Optimizer, Type{MathOptInterface.VectorOfVariables}, Type{CBLS.MOIError{F}}}} where F<:Function",href:"#MathOptInterface.supports_constraint-Union{Tuple{F}, Tuple{CBLS.Optimizer, Type{MathOptInterface.VectorOfVariables}, Type{CBLS.MOIError{F}}}} where F<:Function"},[i("span",{class:"jlbinding"},"MathOptInterface.supports_constraint")],-1)),s[214]||(s[214]=t()),e(a,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[215]||(s[215]=l('
julia
MOI.supports_constraint(::Optimizer, ::Type{VOV}, ::Type{MOIError}) = begin
DOCSTRING
Arguments:
  • ``: DESCRIPTION
  • ``: DESCRIPTION
  • ``: DESCRIPTION
source
',5))]),i("details",Ls,[i("summary",null,[s[216]||(s[216]=i("a",{id:"MathOptInterface.supports_constraint-Union{Tuple{F}, Tuple{CBLS.Optimizer, Type{MathOptInterface.VectorOfVariables}, Type{CBLS.MOIIntention{F}}}} where F<:Function",href:"#MathOptInterface.supports_constraint-Union{Tuple{F}, Tuple{CBLS.Optimizer, Type{MathOptInterface.VectorOfVariables}, Type{CBLS.MOIIntention{F}}}} where F<:Function"},[i("span",{class:"jlbinding"},"MathOptInterface.supports_constraint")],-1)),s[217]||(s[217]=t()),e(a,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[218]||(s[218]=l('
julia
MOI.supports_constraint(::Optimizer, ::Type{VOV}, ::Type{MOIIntention{F}}) where {F <: Function}
Check if the optimizer supports a given intention constraint.
Arguments
  • ::Optimizer: The optimizer instance.
  • ::Type{VOV}: The type of the variable.
  • ::Type{MOIIntention{F}}: The type of the intention.
Returns
  • Bool: True if the optimizer supports the constraint, false otherwise.
source
',7))]),i("details",Ss,[i("summary",null,[s[219]||(s[219]=i("a",{id:"MathOptInterface.supports_incremental_interface-Tuple{CBLS.Optimizer}",href:"#MathOptInterface.supports_incremental_interface-Tuple{CBLS.Optimizer}"},[i("span",{class:"jlbinding"},"MathOptInterface.supports_incremental_interface")],-1)),s[220]||(s[220]=t()),e(a,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[221]||(s[221]=l('
julia
MOI.supports_incremental_interface(::Optimizer)
Check if the optimizer supports incremental interface.
Arguments
  • ::Optimizer: The optimizer instance.
Returns
  • Bool: True if the optimizer supports incremental interface, false otherwise.
source
',7))])])}const Ns=n(h,[["render",Is]]);export{Vs as __pageData,Ns as default};
+@objective(model, ScalarFunction(f, X))
source
`,7))]),i("details",ts,[i("summary",null,[s[140]||(s[140]=i("a",{id:"CBLS.Sum",href:"#CBLS.Sum"},[i("span",{class:"jlbinding"},"CBLS.Sum")],-1)),s[141]||(s[141]=t()),e(a,{type:"info",class:"jlObjectType jlType",text:"Type"})]),s[142]||(s[142]=i("p",null,[t("Global constraint ensuring that the sum of the variables in "),i("code",null,"x"),t(" satisfies a given condition.")],-1)),s[143]||(s[143]=i("p",null,[i("a",{href:"https://github.com/JuliaConstraints/CBLS.jl/blob/v0.2.2/src/constraints/sum.jl#L46-L48",target:"_blank",rel:"noreferrer"},"source")],-1))]),i("details",as,[i("summary",null,[s[144]||(s[144]=i("a",{id:"CBLS.Supports",href:"#CBLS.Supports"},[i("span",{class:"jlbinding"},"CBLS.Supports")],-1)),s[145]||(s[145]=t()),e(a,{type:"info",class:"jlObjectType jlType",text:"Type"})]),s[146]||(s[146]=l('
Global constraint ensuring that the tuple x matches a configuration listed within the support set pair_vars. This constraint is derived from the extension model, specifying that x must be one of the explicitly defined supported configurations: x ∈ pair_vars. It is utilized to directly declare the tuples that are valid and should be included in the solution space.
julia
@constraint(model, X in Supports(; pair_vars))
source
',3))]),i("details",es,[i("summary",null,[s[147]||(s[147]=i("a",{id:"Base.copy-Tuple{CBLS.DiscreteSet}",href:"#Base.copy-Tuple{CBLS.DiscreteSet}"},[i("span",{class:"jlbinding"},"Base.copy")],-1)),s[148]||(s[148]=t()),e(a,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[149]||(s[149]=l('
julia
Base.copy(set::DiscreteSet)
Copy a discrete set.
Arguments
  • set::DiscreteSet: The discrete set to be copied.
Returns
  • DiscreteSet: A copy of the discrete set.
source
',7))]),i("details",ls,[i("summary",null,[s[150]||(s[150]=i("a",{id:"Base.copy-Tuple{CBLS.MOIError}",href:"#Base.copy-Tuple{CBLS.MOIError}"},[i("span",{class:"jlbinding"},"Base.copy")],-1)),s[151]||(s[151]=t()),e(a,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[152]||(s[152]=l('
julia
Base.copy(set::MOIError) = begin
DOCSTRING
source
',3))]),i("details",ns,[i("summary",null,[s[153]||(s[153]=i("a",{id:"Base.copy-Tuple{CBLS.MOIIntention}",href:"#Base.copy-Tuple{CBLS.MOIIntention}"},[i("span",{class:"jlbinding"},"Base.copy")],-1)),s[154]||(s[154]=t()),e(a,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[155]||(s[155]=l('
julia
Base.copy(set::MOIIntention)
Copy an intention set.
Arguments
  • set::MOIIntention: The intention set to be copied.
Returns
  • MOIIntention: A copy of the intention set.
source
',7))]),i("details",ps,[i("summary",null,[s[156]||(s[156]=i("a",{id:"Base.copy-Tuple{F} where F<:Function",href:"#Base.copy-Tuple{F} where F<:Function"},[i("span",{class:"jlbinding"},"Base.copy")],-1)),s[157]||(s[157]=t()),e(a,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[158]||(s[158]=l('
julia
Base.copy(op::F) where {F <: Function}
Copy a function.
Arguments
  • op::F: The function to be copied.
Returns
  • F: The copied function.
source
',7))]),i("details",rs,[i("summary",null,[s[159]||(s[159]=i("a",{id:"Base.copy-Tuple{Nothing}",href:"#Base.copy-Tuple{Nothing}"},[i("span",{class:"jlbinding"},"Base.copy")],-1)),s[160]||(s[160]=t()),e(a,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[161]||(s[161]=l('
julia
Base.copy(::Nothing)
Copy a Nothing value.
Arguments
  • ::Nothing: The Nothing value to be copied.
Returns
  • Nothing: The copied Nothing value.
source
',7))]),i("details",os,[i("summary",null,[s[162]||(s[162]=i("a",{id:"JuMP.build_variable-Union{Tuple{T}, Tuple{Function, JuMP.VariableInfo, T}} where T<:MathOptInterface.AbstractScalarSet",href:"#JuMP.build_variable-Union{Tuple{T}, Tuple{Function, JuMP.VariableInfo, T}} where T<:MathOptInterface.AbstractScalarSet"},[i("span",{class:"jlbinding"},"JuMP.build_variable")],-1)),s[163]||(s[163]=t()),e(a,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[164]||(s[164]=l('
julia
JuMP.build_variable(::Function, info::JuMP.VariableInfo, set::T) where T <: MOI.AbstractScalarSet
Create a variable constrained by a scalar set.
Arguments
  • info::JuMP.VariableInfo: Information about the variable to be created.
  • set::T where T <: MOI.AbstractScalarSet: The set defining the constraints on the variable.
Returns
  • JuMP.VariableConstrainedOnCreation: A variable constrained by the specified set.
source
',7))]),i("details",hs,[i("summary",null,[s[165]||(s[165]=i("a",{id:"JuMP.moi_set-Tuple{CBLS.Intention, Int64}",href:"#JuMP.moi_set-Tuple{CBLS.Intention, Int64}"},[i("span",{class:"jlbinding"},"JuMP.moi_set")],-1)),s[166]||(s[166]=t()),e(a,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[167]||(s[167]=l('
julia
JuMP.moi_set(set::Intention, dim::Int) -> MOIIntention
Convert an Intention set to a MOIIntention set.
Arguments
  • set::Intention: The intention set to be converted.
  • dim::Int: The dimension of the vector set.
Returns
  • MOIIntention: The converted MOIIntention set.
source
',7))]),i("details",ds,[i("summary",null,[s[168]||(s[168]=i("a",{id:"JuMP.moi_set-Tuple{Predicate, Int64}",href:"#JuMP.moi_set-Tuple{Predicate, Int64}"},[i("span",{class:"jlbinding"},"JuMP.moi_set")],-1)),s[169]||(s[169]=t()),e(a,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[170]||(s[170]=l('
julia
JuMP.moi_set(set::Predicate, dim::Int) -> MOIIntention
Convert a Predicate set to a MOIIntention set.
Arguments
  • set::Predicate: The predicate set to be converted.
  • dim::Int: The dimension of the vector set.
Returns
  • MOIIntention: The converted MOIIntention set.
source
',7))]),i("details",ks,[i("summary",null,[s[171]||(s[171]=i("a",{id:"MathOptInterface.add_constraint-Union{Tuple{F}, Tuple{CBLS.Optimizer, MathOptInterface.VectorOfVariables, CBLS.MOIError{F}}} where F<:Function",href:"#MathOptInterface.add_constraint-Union{Tuple{F}, Tuple{CBLS.Optimizer, MathOptInterface.VectorOfVariables, CBLS.MOIError{F}}} where F<:Function"},[i("span",{class:"jlbinding"},"MathOptInterface.add_constraint")],-1)),s[172]||(s[172]=t()),e(a,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[173]||(s[173]=l('
julia
MOI.add_constraint(optimizer::Optimizer, vars::MOI.VectorOfVariables, set::MOIError)
DOCSTRING
Arguments:
  • optimizer: DESCRIPTION
  • vars: DESCRIPTION
  • set: DESCRIPTION
source
',5))]),i("details",gs,[i("summary",null,[s[174]||(s[174]=i("a",{id:"MathOptInterface.add_constraint-Union{Tuple{F}, Tuple{CBLS.Optimizer, MathOptInterface.VectorOfVariables, CBLS.MOIIntention{F}}} where F<:Function",href:"#MathOptInterface.add_constraint-Union{Tuple{F}, Tuple{CBLS.Optimizer, MathOptInterface.VectorOfVariables, CBLS.MOIIntention{F}}} where F<:Function"},[i("span",{class:"jlbinding"},"MathOptInterface.add_constraint")],-1)),s[175]||(s[175]=t()),e(a,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[176]||(s[176]=l('
julia
MOI.add_constraint(optimizer::Optimizer, vars::MOI.VectorOfVariables, set::MOIIntention{F}) where {F <: Function}
Add an intention constraint to the optimizer.
Arguments
  • optimizer::Optimizer: The optimizer instance.
  • vars::MOI.VectorOfVariables: The variables for the constraint.
  • set::MOIIntention{F}: The intention set defining the constraint.
Returns
  • CI{VOV, MOIIntention{F}}: The constraint index.
source
',7))]),i("details",us,[i("summary",null,[s[177]||(s[177]=i("a",{id:"MathOptInterface.add_constraint-Union{Tuple{T}, Tuple{CBLS.Optimizer, MathOptInterface.VariableIndex, CBLS.DiscreteSet{T}}} where T<:Number",href:"#MathOptInterface.add_constraint-Union{Tuple{T}, Tuple{CBLS.Optimizer, MathOptInterface.VariableIndex, CBLS.DiscreteSet{T}}} where T<:Number"},[i("span",{class:"jlbinding"},"MathOptInterface.add_constraint")],-1)),s[178]||(s[178]=t()),e(a,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[179]||(s[179]=l('
julia
MOI.add_constraint(optimizer::Optimizer, v::VI, set::DiscreteSet{T}) where T <: Number
DOCSTRING
Arguments:
  • optimizer: DESCRIPTION
  • v: DESCRIPTION
  • set: DESCRIPTION
source
',5))]),i("details",cs,[i("summary",null,[s[180]||(s[180]=i("a",{id:"MathOptInterface.add_variable-Tuple{CBLS.Optimizer}",href:"#MathOptInterface.add_variable-Tuple{CBLS.Optimizer}"},[i("span",{class:"jlbinding"},"MathOptInterface.add_variable")],-1)),s[181]||(s[181]=t()),e(a,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[182]||(s[182]=l('
julia
MOI.add_variable(model::Optimizer) = begin
DOCSTRING
source
',3))]),i("details",ys,[i("summary",null,[s[183]||(s[183]=i("a",{id:"MathOptInterface.copy_to-Tuple{CBLS.Optimizer, MathOptInterface.ModelLike}",href:"#MathOptInterface.copy_to-Tuple{CBLS.Optimizer, MathOptInterface.ModelLike}"},[i("span",{class:"jlbinding"},"MathOptInterface.copy_to")],-1)),s[184]||(s[184]=t()),e(a,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[185]||(s[185]=l('
julia
MOI.copy_to(model::Optimizer, src::MOI.ModelLike)
Copy the source model to the optimizer.
Arguments
  • model::Optimizer: The optimizer instance.
  • src::MOI.ModelLike: The source model to be copied.
Returns
  • Nothing
source
',7))]),i("details",bs,[i("summary",null,[s[186]||(s[186]=i("a",{id:"MathOptInterface.empty!-Tuple{Any}",href:"#MathOptInterface.empty!-Tuple{Any}"},[i("span",{class:"jlbinding"},"MathOptInterface.empty!")],-1)),s[187]||(s[187]=t()),e(a,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[188]||(s[188]=l('
julia
MOI.empty!(opt)
Empty the optimizer.
Arguments
  • opt::Optimizer: The optimizer instance.
Returns
  • Nothing
source
',7))]),i("details",Es,[i("summary",null,[s[189]||(s[189]=i("a",{id:"MathOptInterface.get-Tuple{CBLS.Optimizer, MathOptInterface.SolverName}",href:"#MathOptInterface.get-Tuple{CBLS.Optimizer, MathOptInterface.SolverName}"},[i("span",{class:"jlbinding"},"MathOptInterface.get")],-1)),s[190]||(s[190]=t()),e(a,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[191]||(s[191]=l('
julia
MOI.get(::Optimizer, ::MOI.SolverName)
Get the name of the solver.
Arguments
  • ::Optimizer: The optimizer instance.
Returns
  • String: The name of the solver.
source
',7))]),i("details",Cs,[i("summary",null,[s[192]||(s[192]=i("a",{id:"MathOptInterface.get-Tuple{CBLS.Optimizer, MathOptInterface.SolverVersion}",href:"#MathOptInterface.get-Tuple{CBLS.Optimizer, MathOptInterface.SolverVersion}"},[i("span",{class:"jlbinding"},"MathOptInterface.get")],-1)),s[193]||(s[193]=t()),e(a,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[194]||(s[194]=l('
julia
Moi.get(::Optimizer, ::MOI.SolverVersion)
Get the version of the solver, here LocalSearchSolvers.jl.
source
',3))]),i("details",ms,[i("summary",null,[s[195]||(s[195]=i("a",{id:"MathOptInterface.is_empty-Tuple{CBLS.Optimizer}",href:"#MathOptInterface.is_empty-Tuple{CBLS.Optimizer}"},[i("span",{class:"jlbinding"},"MathOptInterface.is_empty")],-1)),s[196]||(s[196]=t()),e(a,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[197]||(s[197]=l('
julia
MOI.is_empty(model::Optimizer)
Check if the model is empty.
Arguments
  • model::Optimizer: The optimizer instance.
Returns
  • Bool: True if the model is empty, false otherwise.
source
',7))]),i("details",Fs,[i("summary",null,[s[198]||(s[198]=i("a",{id:"MathOptInterface.is_valid-Tuple{CBLS.Optimizer, MathOptInterface.ConstraintIndex{MathOptInterface.VariableIndex, MathOptInterface.Integer}}",href:"#MathOptInterface.is_valid-Tuple{CBLS.Optimizer, MathOptInterface.ConstraintIndex{MathOptInterface.VariableIndex, MathOptInterface.Integer}}"},[i("span",{class:"jlbinding"},"MathOptInterface.is_valid")],-1)),s[199]||(s[199]=t()),e(a,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[200]||(s[200]=l('
julia
MOI.is_valid(optimizer::Optimizer, index::CI{VI, MOI.Integer})
Check if an index is valid for the optimizer.
Arguments
  • optimizer::Optimizer: The optimizer instance.
  • index::CI{VI, MOI.Integer}: The index to be checked.
Returns
  • Bool: True if the index is valid, false otherwise.
source
',7))]),i("details",js,[i("summary",null,[s[201]||(s[201]=i("a",{id:"MathOptInterface.optimize!-Tuple{CBLS.Optimizer}",href:"#MathOptInterface.optimize!-Tuple{CBLS.Optimizer}"},[i("span",{class:"jlbinding"},"MathOptInterface.optimize!")],-1)),s[202]||(s[202]=t()),e(a,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[203]||(s[203]=l('
julia
MOI.optimize!(model::Optimizer)
Optimize the model using the optimizer.
Arguments
  • model::Optimizer: The optimizer instance.
Returns
  • Nothing
source
',7))]),i("details",vs,[i("summary",null,[s[204]||(s[204]=i("a",{id:"MathOptInterface.set",href:"#MathOptInterface.set"},[i("span",{class:"jlbinding"},"MathOptInterface.set")],-1)),s[205]||(s[205]=t()),e(a,{type:"info",class:"jlObjectType jlFunction",text:"Function"})]),s[206]||(s[206]=l('
julia
MOI.set(::Optimizer, ::MOI.Silent, bool = true)
Set the verbosity of the solver.
Arguments
  • ::Optimizer: The optimizer instance.
  • ::MOI.Silent: The silent option for the solver.
  • bool::Bool: Whether to set the solver to silent mode.
Returns
  • Nothing
source
',7))]),i("details",fs,[i("summary",null,[s[207]||(s[207]=i("a",{id:"MathOptInterface.set-Tuple{CBLS.Optimizer, MathOptInterface.RawOptimizerAttribute, Any}",href:"#MathOptInterface.set-Tuple{CBLS.Optimizer, MathOptInterface.RawOptimizerAttribute, Any}"},[i("span",{class:"jlbinding"},"MathOptInterface.set")],-1)),s[208]||(s[208]=t()),e(a,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[209]||(s[209]=l('
julia
MOI.set(model::Optimizer, p::MOI.RawOptimizerAttribute, value)
Set a RawOptimizerAttribute to value
source
',3))]),i("details",Bs,[i("summary",null,[s[210]||(s[210]=i("a",{id:"MathOptInterface.set-Tuple{CBLS.Optimizer, MathOptInterface.TimeLimitSec, Union{Nothing, Float64}}",href:"#MathOptInterface.set-Tuple{CBLS.Optimizer, MathOptInterface.TimeLimitSec, Union{Nothing, Float64}}"},[i("span",{class:"jlbinding"},"MathOptInterface.set")],-1)),s[211]||(s[211]=t()),e(a,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[212]||(s[212]=l('
julia
MOI.set(model::Optimizer, ::MOI.TimeLimitSec, value::Union{Nothing,Float64})
Set the time limit
source
',3))]),i("details",Os,[i("summary",null,[s[213]||(s[213]=i("a",{id:"MathOptInterface.supports_constraint-Union{Tuple{F}, Tuple{CBLS.Optimizer, Type{MathOptInterface.VectorOfVariables}, Type{CBLS.MOIError{F}}}} where F<:Function",href:"#MathOptInterface.supports_constraint-Union{Tuple{F}, Tuple{CBLS.Optimizer, Type{MathOptInterface.VectorOfVariables}, Type{CBLS.MOIError{F}}}} where F<:Function"},[i("span",{class:"jlbinding"},"MathOptInterface.supports_constraint")],-1)),s[214]||(s[214]=t()),e(a,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[215]||(s[215]=l('
julia
MOI.supports_constraint(::Optimizer, ::Type{VOV}, ::Type{MOIError}) = begin
DOCSTRING
Arguments:
  • ``: DESCRIPTION
  • ``: DESCRIPTION
  • ``: DESCRIPTION
source
',5))]),i("details",Ls,[i("summary",null,[s[216]||(s[216]=i("a",{id:"MathOptInterface.supports_constraint-Union{Tuple{F}, Tuple{CBLS.Optimizer, Type{MathOptInterface.VectorOfVariables}, Type{CBLS.MOIIntention{F}}}} where F<:Function",href:"#MathOptInterface.supports_constraint-Union{Tuple{F}, Tuple{CBLS.Optimizer, Type{MathOptInterface.VectorOfVariables}, Type{CBLS.MOIIntention{F}}}} where F<:Function"},[i("span",{class:"jlbinding"},"MathOptInterface.supports_constraint")],-1)),s[217]||(s[217]=t()),e(a,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[218]||(s[218]=l('
julia
MOI.supports_constraint(::Optimizer, ::Type{VOV}, ::Type{MOIIntention{F}}) where {F <: Function}
Check if the optimizer supports a given intention constraint.
Arguments
  • ::Optimizer: The optimizer instance.
  • ::Type{VOV}: The type of the variable.
  • ::Type{MOIIntention{F}}: The type of the intention.
Returns
  • Bool: True if the optimizer supports the constraint, false otherwise.
source
',7))]),i("details",Ss,[i("summary",null,[s[219]||(s[219]=i("a",{id:"MathOptInterface.supports_incremental_interface-Tuple{CBLS.Optimizer}",href:"#MathOptInterface.supports_incremental_interface-Tuple{CBLS.Optimizer}"},[i("span",{class:"jlbinding"},"MathOptInterface.supports_incremental_interface")],-1)),s[220]||(s[220]=t()),e(a,{type:"info",class:"jlObjectType jlMethod",text:"Method"})]),s[221]||(s[221]=l('
julia
MOI.supports_incremental_interface(::Optimizer)
Check if the optimizer supports incremental interface.
Arguments
  • ::Optimizer: The optimizer instance.
Returns
  • Bool: True if the optimizer supports incremental interface, false otherwise.
source
',7))])])}const Ns=n(h,[["render",Is]]);export{Vs as __pageData,Ns as default};
diff --git a/dev/assets/solvers_40_constraint_explorer.md.CjuNUjfR.js b/dev/assets/solvers_40_constraint_explorer.md.CjuNUjfR.js
deleted file mode 100644
index 44626ff..0000000
--- a/dev/assets/solvers_40_constraint_explorer.md.CjuNUjfR.js
+++ /dev/null
@@ -1 +0,0 @@
-import{_ as o,c as a,j as e,a as r,o as n}from"./chunks/framework.CJakPlgM.js";const m=JSON.parse('{"title":"ConstraintExplorer.jl","description":"","frontmatter":{},"headers":[],"relativePath":"solvers/40_constraint_explorer.md","filePath":"solvers/40_constraint_explorer.md","lastUpdated":null}'),l={name:"solvers/40_constraint_explorer.md"};function s(i,t,c,p,d,_){return n(),a("div",null,t[0]||(t[0]=[e("h1",{id:"constraintexplorer-jl",tabindex:"-1"},[r("ConstraintExplorer.jl "),e("a",{class:"header-anchor",href:"#constraintexplorer-jl","aria-label":'Permalink to "ConstraintExplorer.jl"'},"​")],-1),e("p",null,[r("Documentation for "),e("code",null,"ConstraintExplorer.jl"),r(".")],-1)]))}const f=o(l,[["render",s]]);export{m as __pageData,f as default};
diff --git a/dev/assets/solvers_40_constraint_explorer.md.CjuNUjfR.lean.js b/dev/assets/solvers_40_constraint_explorer.md.CjuNUjfR.lean.js
deleted file mode 100644
index 44626ff..0000000
--- a/dev/assets/solvers_40_constraint_explorer.md.CjuNUjfR.lean.js
+++ /dev/null
@@ -1 +0,0 @@
-import{_ as o,c as a,j as e,a as r,o as n}from"./chunks/framework.CJakPlgM.js";const m=JSON.parse('{"title":"ConstraintExplorer.jl","description":"","frontmatter":{},"headers":[],"relativePath":"solvers/40_constraint_explorer.md","filePath":"solvers/40_constraint_explorer.md","lastUpdated":null}'),l={name:"solvers/40_constraint_explorer.md"};function s(i,t,c,p,d,_){return n(),a("div",null,t[0]||(t[0]=[e("h1",{id:"constraintexplorer-jl",tabindex:"-1"},[r("ConstraintExplorer.jl "),e("a",{class:"header-anchor",href:"#constraintexplorer-jl","aria-label":'Permalink to "ConstraintExplorer.jl"'},"​")],-1),e("p",null,[r("Documentation for "),e("code",null,"ConstraintExplorer.jl"),r(".")],-1)]))}const f=o(l,[["render",s]]);export{m as __pageData,f as default};
diff --git a/dev/assets/solvers_40_constraint_explorer.md.DrX4zrKv.js b/dev/assets/solvers_40_constraint_explorer.md.DrX4zrKv.js
new file mode 100644
index 0000000..b593be8
--- /dev/null
+++ b/dev/assets/solvers_40_constraint_explorer.md.DrX4zrKv.js
@@ -0,0 +1 @@
+import{_ as r,c as l,j as t,a as i,G as n,a5 as e,B as o,o as p}from"./chunks/framework.CJakPlgM.js";const x=JSON.parse('{"title":"ConstraintExplorer.jl","description":"","frontmatter":{},"headers":[],"relativePath":"solvers/40_constraint_explorer.md","filePath":"solvers/40_constraint_explorer.md","lastUpdated":null}'),h={name:"solvers/40_constraint_explorer.md"},d={class:"jldocstring custom-block",open:""},k={class:"jldocstring custom-block",open:""};function c(g,s,u,E,C,y){const a=o("Badge");return p(),l("div",null,[s[6]||(s[6]=t("h1",{id:"constraintexplorer-jl",tabindex:"-1"},[i("ConstraintExplorer.jl "),t("a",{class:"header-anchor",href:"#constraintexplorer-jl","aria-label":'Permalink to "ConstraintExplorer.jl"'},"​")],-1)),s[7]||(s[7]=t("p",null,[i("Documentation for "),t("code",null,"ConstraintExplorer.jl"),i(".")],-1)),t("details",d,[t("summary",null,[s[0]||(s[0]=t("a",{id:"ConstraintExplorer.MOIInstantiation",href:"#ConstraintExplorer.MOIInstantiation"},[t("span",{class:"jlbinding"},"ConstraintExplorer.MOIInstantiation")],-1)),s[1]||(s[1]=i()),n(a,{type:"info",class:"jlObjectType jlType",text:"Type"})]),s[2]||(s[2]=e('
julia
MOIInstantiation{T <: Number, V <: Vector{T}} <: MOI.AbstractVectorSet
DOCSTRING
source
',3))]),t("details",k,[t("summary",null,[s[3]||(s[3]=t("a",{id:"ConstraintExplorer.MOISupports",href:"#ConstraintExplorer.MOISupports"},[t("span",{class:"jlbinding"},"ConstraintExplorer.MOISupports")],-1)),s[4]||(s[4]=i()),n(a,{type:"info",class:"jlObjectType jlType",text:"Type"})]),s[5]||(s[5]=e('
julia
MOISupports{T <: Number, V <: Vector{Vector{T}}} <: MOI.AbstractVectorSet
DOCSTRING
source
',3))])])}const m=r(h,[["render",c]]);export{x as __pageData,m as default};
diff --git a/dev/assets/solvers_40_constraint_explorer.md.DrX4zrKv.lean.js b/dev/assets/solvers_40_constraint_explorer.md.DrX4zrKv.lean.js
new file mode 100644
index 0000000..b593be8
--- /dev/null
+++ b/dev/assets/solvers_40_constraint_explorer.md.DrX4zrKv.lean.js
@@ -0,0 +1 @@
+import{_ as r,c as l,j as t,a as i,G as n,a5 as e,B as o,o as p}from"./chunks/framework.CJakPlgM.js";const x=JSON.parse('{"title":"ConstraintExplorer.jl","description":"","frontmatter":{},"headers":[],"relativePath":"solvers/40_constraint_explorer.md","filePath":"solvers/40_constraint_explorer.md","lastUpdated":null}'),h={name:"solvers/40_constraint_explorer.md"},d={class:"jldocstring custom-block",open:""},k={class:"jldocstring custom-block",open:""};function c(g,s,u,E,C,y){const a=o("Badge");return p(),l("div",null,[s[6]||(s[6]=t("h1",{id:"constraintexplorer-jl",tabindex:"-1"},[i("ConstraintExplorer.jl "),t("a",{class:"header-anchor",href:"#constraintexplorer-jl","aria-label":'Permalink to "ConstraintExplorer.jl"'},"​")],-1)),s[7]||(s[7]=t("p",null,[i("Documentation for "),t("code",null,"ConstraintExplorer.jl"),i(".")],-1)),t("details",d,[t("summary",null,[s[0]||(s[0]=t("a",{id:"ConstraintExplorer.MOIInstantiation",href:"#ConstraintExplorer.MOIInstantiation"},[t("span",{class:"jlbinding"},"ConstraintExplorer.MOIInstantiation")],-1)),s[1]||(s[1]=i()),n(a,{type:"info",class:"jlObjectType jlType",text:"Type"})]),s[2]||(s[2]=e('
julia
MOIInstantiation{T <: Number, V <: Vector{T}} <: MOI.AbstractVectorSet
DOCSTRING
source
',3))]),t("details",k,[t("summary",null,[s[3]||(s[3]=t("a",{id:"ConstraintExplorer.MOISupports",href:"#ConstraintExplorer.MOISupports"},[t("span",{class:"jlbinding"},"ConstraintExplorer.MOISupports")],-1)),s[4]||(s[4]=i()),n(a,{type:"info",class:"jlObjectType jlType",text:"Type"})]),s[5]||(s[5]=e('
julia
MOISupports{T <: Number, V <: Vector{Vector{T}}} <: MOI.AbstractVectorSet
DOCSTRING
source
',3))])])}const m=r(h,[["render",c]]);export{x as __pageData,m as default};
diff --git a/dev/constraints/00_intro.html b/dev/constraints/00_intro.html
index f68a348..649d646 100644
--- a/dev/constraints/00_intro.html
+++ b/dev/constraints/00_intro.html
@@ -8,9 +8,9 @@
     
     
     
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Julia Constraints
Appearance
Introduction to basics constraint-based modeling tools ​
Constraint programming (CP) is a high-level paradigm for solving combinatorial problems, and Julia Constraints provides an efficient and flexible framework for developing constraint-based models.
All along this documentation, we will present code example base on the syntaxes of Julia Constraints internals (JC-API), of Julia for Mathematical Programming (JuMP ), of MathOptInterface (MOI), and, when relevant, of other standards such as XCSP.
Terminology ​
Warning
Terminology in Optimization varies strongly between different methods and communities. In this doc we try to be consistent with the following principles (in bold).
  • Constraint: A general mathematical predicate involving variables.
  • Constraint Instantiation: The application of a constraint to specific variables.
  • Configuration: A specific assignment of values to the variables.
  • Constraint Satisfaction/Violation: Whether a configuration meets or fails a constraint.
Constraint ​
Definition: A constraint is a formal mathematical statement that expresses a condition or a relation between a set of variables. It can be seen as a predicate that the variables must satisfy.
Example: Consider the constraint x+y≤10. This constraint involves two variables, x and y, and specifies that their sum must not exceed 10.
Constraint Instantiation ​
Definition: A constraint instantiation refers to a specific application of a generic constraint to a particular subset of variables from a problem. It is essentially the constraint applied with the actual variables of the problem.
Example: Given the generic constraint x+y≤10, if we have variables x1 and x2 in our problem, then the instantiated constraint would be x1+x2≤10.
Configuration ​
Definition: A configuration, also known as an assignment, is a specific set of values assigned to the variables in their respective domains. It represents a possible state of the variables.
Example: For variables x and y with domains [0,10], a configuration could be x=3 and y=2.
Constraint Satisfaction or Violation by a Configuration ​
Definition: This refers to whether a specific configuration (set of variable assignments) satisfies or violates a given constraint instantiation. A constraint is satisfied if the configuration makes the constraint true; otherwise, it is violated (false).
Example: Given the constraint instantiation x+y≤10 and the configuration x=3 and y=2, the constraint is satisfied because 3+2=5, which is less than or equal to 10. However, for the configuration x=6 and y=5, the constraint is violated because 6+5=11, which exceeds 10.
Domain-defined variables ​
In CP, variables are defined through their domain. ConstraintDomains.jl supports various types of domains such as discrete ones (sets, range, etc.), or continuous intervals, and custom domains.
A versatile constraints' API ​
Constraints.jl implements a wide range of generic and core constraints, ensuring compatibility with XCSP3-core standards and providing a user-friendly interface. It includes features extracted from the learning blocks of Julia Constraints to leverage most of each constraint characteristics.
A collection of models ​
The ConstraintModels.jl catalog offers a collection of predefined models and templates for constructing complex constraint satisfaction problems (CSPs) and optimization models. This resource provides reusable components to streamline the modeling process.
Contributions with new models are more than welcome!
Internal Aspects ​
Several internal components are crucial for the efficient functioning of Julia Constraints. ConstraintCommons.jl provides shared functionalities and utilities used across different parts of the framework, contributing to its robust performance and extensibility. However, it is unlikely to be of direct use to most users.

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diff --git a/dev/constraints/10_variables_and_domains.html b/dev/constraints/10_variables_and_domains.html
index b7be054..b855420 100644
--- a/dev/constraints/10_variables_and_domains.html
+++ b/dev/constraints/10_variables_and_domains.html
@@ -8,16 +8,16 @@
     
     
     
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Julia Constraints
Appearance
Defining Variables and Exploring Domains ​
ConstraintDomains.jl stands as the standard way to define variables and explore domains within the Julia Constraints ecosystem. This package provides the infrastructure necessary for specifying both discrete and continuous domains. Explorations features are mainly related to the learning about constraints aspect and will be detailed in that chapter.
Variables and their domains can also be defined through MOI and JuMP syntaxes in their respective models.
Implementing the AbstractDomain Interface ​
At the foundation of ConstraintDomains.jl is the AbstractDomain type, an abstract supertype for all domain types. Implementations of AbstractDomain must provide methods for checking membership (∈), generating random elements (rand), and determining the domain's size or range (length). These functionalities are essential for defining the behavior and properties of variable domains within constraint models.
ConstraintDomains.AbstractDomain Type
julia
AbstractDomain
An abstract super type for any domain type. A domain type D <: AbstractDomain must implement the following methods to properly interface AbstractDomain.
  • Base.∈(val, ::D)
  • Base.rand(::D)
  • Base.length(::D) that is the number of elements in a discrete domain, and the distance between bounds or similar for a continuous domain
Additionally, if the domain is used in a dynamic context, it can extend
  • add!(::D, args)
  • delete!(::D, args)
where args depends on D's structure
source
Discrete Domains ​
Optimization in discrete spaces has been the core of Constraint Programming since its inception. We provide three kinds of discrete domains.
SetDomain ​
A SetDomain is simply a Set of unordered numerical values.
julia
using ConstraintDomains
+    
Julia Constraints
Appearance
Defining Variables and Exploring Domains ​
ConstraintDomains.jl stands as the standard way to define variables and explore domains within the Julia Constraints ecosystem. This package provides the infrastructure necessary for specifying both discrete and continuous domains. Explorations features are mainly related to the learning about constraints aspect and will be detailed in that chapter.
Variables and their domains can also be defined through MOI and JuMP syntaxes in their respective models.
Implementing the AbstractDomain Interface ​
At the foundation of ConstraintDomains.jl is the AbstractDomain type, an abstract supertype for all domain types. Implementations of AbstractDomain must provide methods for checking membership (∈), generating random elements (rand), and determining the domain's size or range (length). These functionalities are essential for defining the behavior and properties of variable domains within constraint models.
ConstraintDomains.AbstractDomain Type
julia
AbstractDomain
An abstract super type for any domain type. A domain type D <: AbstractDomain must implement the following methods to properly interface AbstractDomain.
  • Base.∈(val, ::D)
  • Base.rand(::D)
  • Base.length(::D) that is the number of elements in a discrete domain, and the distance between bounds or similar for a continuous domain
Additionally, if the domain is used in a dynamic context, it can extend
  • add!(::D, args)
  • delete!(::D, args)
where args depends on D's structure
source
Discrete Domains ​
Optimization in discrete spaces has been the core of Constraint Programming since its inception. We provide three kinds of discrete domains.
SetDomain ​
A SetDomain is simply a Set of unordered numerical values.
julia
using ConstraintDomains
 
 d1 = domain([53.69, 89.2, 0.12])
 d2 = domain([2//3, 89//123])
@@ -44,7 +44,7 @@
 MOI.add_constraint(optimizer, v3, CBLS.DiscreteSet(4.3))
 
 v4 = MOI.add_variable(optimizer)
-MOI.add_constraint(optimizer, v4, CBLS.DiscreteSet([1, 42, 3.14]))
RangeDomain ​
A range domain allows for minimal storage and more efficient operation on discrete sets defined as Range in Julia. It is not recommended for dynamic domains (it will be replaced with SetDomain as soon as a non-extremal element is removed).
julia
using ConstraintDomains
+MOI.add_constraint(optimizer, v4, CBLS.DiscreteSet([1, 42, 3.14]))
RangeDomain ​
A range domain allows for minimal storage and more efficient operation on discrete sets defined as Range in Julia. It is not recommended for dynamic domains (it will be replaced with SetDomain as soon as a non-extremal element is removed).
julia
using ConstraintDomains
 
 d1 = domain(1:5)
 d2 = domain(0.4:0.1:1.3)
julia
## To be implemented
@@ -64,12 +64,12 @@
 
 # v2 = MOI.add_variable(optimizer)
 
-# MOI.add_constraint(optimizer, v1, MOI.RangeSet(0.4:0.1:1.3))
Arbitrary Domains ​
As odd as it may sound, we provide a constructor for sets of elements making up arbitrary, possibly non-numerical, domains.
Until some practical examples are implemented, this structure will mainly be a placeholder with default behavior.
Continuous Domains ​
Numerous problems cannot be challenged without expressing at least part of their domains as continuous variables. In Julia Constraints we provide such domains as (set of) intervals.
julia
using ConstraintDomains, Intervals
+# MOI.add_constraint(optimizer, v1, MOI.RangeSet(0.4:0.1:1.3))
Arbitrary Domains ​
As odd as it may sound, we provide a constructor for sets of elements making up arbitrary, possibly non-numerical, domains.
Until some practical examples are implemented, this structure will mainly be a placeholder with default behavior.
Continuous Domains ​
Numerous problems cannot be challenged without expressing at least part of their domains as continuous variables. In Julia Constraints we provide such domains as (set of) intervals.
julia
using ConstraintDomains, Intervals
 
 d1 = domain(Interval{Open,Closed}(3.2, true), (42, false))
 d2 = domain(3.2..42)
 d3 = domain([3.2..42, 63.2..324.1])
julia
## see MOI.Interval
julia
## see MOI.Interval

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\ No newline at end of file
diff --git a/dev/constraints/20_constraints.html b/dev/constraints/20_constraints.html
index 5c8a553..6ad41e7 100644
--- a/dev/constraints/20_constraints.html
+++ b/dev/constraints/20_constraints.html
@@ -8,9 +8,9 @@
     
     
     
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@@ -27,7 +27,7 @@
     :val, # one scalar value
     :vals, # a list of scalar values (independent of the input vector size)
 ]
source
We provide a couple of methods to navigate the usual constraints extracted from XCSP3-Core.
Constraints.USUAL_CONSTRAINTS Constant
julia
USUAL_CONSTRAINTS::Dict
Dictionary that contains all the usual constraints defined in Constraint.jl. It is based on XCSP3-core specifications available at https://arxiv.org/abs/2009.00514
Adding a new constraint is as simple as defining a new function with the same name as the constraint and using the @usual macro to define it. The macro will take care of adding the new constraint to the USUAL_CONSTRAINTS dictionary.
Example
julia
@usual concept_all_different(x; vals=nothing) = xcsp_all_different(list=x, except=vals)
source
Constraints.describe Function
julia
describe(constraints::Dict{Symbol,Constraint}=USUAL_CONSTRAINTS; width=150)
Return a pretty table with the description of the constraints in constraints.
Arguments
  • constraints::Dict{Symbol,Constraint}: dictionary of constraints to describe. Default is USUAL_CONSTRAINTS.
  • width::Int: width of the table.
Example
julia
describe()
source
Constraints.constraints_parameters Function
julia
constraints_parameters(C=USUAL_CONSTRAINTS)
Return a pretty table with the parameters of the constraints in C.
Arguments
  • C::Dict{Symbol,Constraint}: dictionary of constraints. Default is USUAL_CONSTRAINTS.
Example
julia
constraints_parameters()
source
Constraints.constraints_descriptions Function
julia
constraints_descriptions(C=USUAL_CONSTRAINTS)
Return a pretty table with the descriptions of the constraints in C.
Arguments
  • C::Dict{Symbol,Constraint}: dictionary of constraints. Default is USUAL_CONSTRAINTS.
Example
julia
constraints_descriptions()
source
Concepts, Error Functions, and QUBO matrices ​
One major use of this collection of usual constraint is to extract the concept or the error function (error_f) of a given constraint.
Constraints.concept Function
julia
concept(c::Constraint)
Return the concept (function) of constraint c. concept(c::Constraint, x...; param = nothing) Apply the concept of c to values x and optionally param.
source
julia
concept(s::Symbol, args...; kargs...)
Return the concept of the constraint s applied to args and kargs. This is a shortcut for concept(USUAL_CONSTRAINTS[s])(args...; kargs...).
Arguments
  • s::Symbol: the constraint name.
  • args...: the arguments to apply the concept to.
  • kargs...: the keyword arguments to apply the concept to.
Example
julia
concept(:all_different, [1, 2, 3])
source
Note that the error function is a finer estimation of how much a constraint is violated or not. By default, the error_f method simply return 0. if the constraint is satisfied or 1. otherwise.
Efficient versions of error_f are either hand-coded or generated through CompositionalNetworks.jl.
Constraints.error_f Function
julia
error_f(c::Constraint)
Return the error function of constraint c. error_f(c::Constraint, x; param = nothing) Apply the error function of c to values x and optionally param.
source
Finally, another use is to provide QUBO matrices of those usual constraints through QUBOConstraints.jl. The syntax and interface for this feature are still a work in progress.

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diff --git a/dev/constraints/21_generic_constraints.html b/dev/constraints/21_generic_constraints.html
index 3e906f2..2a68b6d 100644
--- a/dev/constraints/21_generic_constraints.html
+++ b/dev/constraints/21_generic_constraints.html
@@ -8,11 +8,11 @@
     
     
     
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@@ -28,7 +28,7 @@
 @usual concept_dist_different(x) = xcsp_intention(
     list = x,
     predicate = predicate_dist_different
-)
Please check the section dedicated to the Golomb Ruler problem to see a use for this constraint. <!– TODO: Golomb Ruler –>
APIs ​
Note that the intention constraint is not directly available through the JC-API in Constraints.jl. It is designed as such since defining a constraint through a predicate is the natural way.
We provide here a usage example for the :dist_different constraint, previously added to the USUAL_CONSTRAINTS collection.
Higher level modeling language such as JuMP should provide an Intention interface.
julia
using Constraints
+)
Please check the section dedicated to the Golomb Ruler problem to see a use for this constraint. <!– TODO: Golomb Ruler –>
APIs ​
Note that the intention constraint is not directly available through the JC-API in Constraints.jl. It is designed as such since defining a constraint through a predicate is the natural way.
We provide here a usage example for the :dist_different constraint, previously added to the USUAL_CONSTRAINTS collection.
Higher level modeling language such as JuMP should provide an Intention interface.
julia
using Constraints
 
 concept(:dist_different, x)
 concept(:dist_different)(x)
julia
# Defines the DistDifferent constraint
@@ -67,7 +67,7 @@
 end
 MOI.add_constraint(optimizer, x, CBLS.Intention(y -> abs(y[1] - y[2]) ≠ abs(y[3] - y[4])))
 
-MOI.optimize!(optimizer)
Extension Constraints ​
These are constraints that are defined by explicitly listing all the tuples of values that satisfy the constraint. They are called extensional because they are defined by the set of values they allow. For example, a binary constraint that specifies that a variable X must be either 1 or 2 and a variable Y must be either 3 or 4 could be defined extensionally by the set of tuples (1,3),(1,4),(2,3),(2,4).
These two types of constraints provide a flexible way to define complex relationships between variables in constraint programming.
julia
using Constraints
+MOI.optimize!(optimizer)
Extension Constraints ​
These are constraints that are defined by explicitly listing all the tuples of values that satisfy the constraint. They are called extensional because they are defined by the set of values they allow. For example, a binary constraint that specifies that a variable X must be either 1 or 2 and a variable Y must be either 3 or 4 could be defined extensionally by the set of tuples (1,3),(1,4),(2,3),(2,4).
These two types of constraints provide a flexible way to define complex relationships between variables in constraint programming.
julia
using Constraints
 
 concept(:dist_different, x)
 concept(:dist_different)(x)
julia
# Defines the DistDifferent constraint
@@ -107,7 +107,7 @@
 MOI.add_constraint(optimizer, x, CBLS.Intention(y -> abs(y[1] - y[2]) ≠ abs(y[3] - y[4])))
 
 MOI.optimize!(optimizer)

-    
+    
     
   
 
\ No newline at end of file
diff --git a/dev/constraints/22_language_constraints.html b/dev/constraints/22_language_constraints.html
index 00e950a..fa161df 100644
--- a/dev/constraints/22_language_constraints.html
+++ b/dev/constraints/22_language_constraints.html
@@ -8,9 +8,9 @@
     
     
     
-    
+    
     
-    
+    
     
     
     
@@ -63,7 +63,7 @@
 c([2,1,2]; language = a)
 c([1,0,2]; language = a)
 c([0,1,2]; language = a)
source

-    
+    
     
   
 
\ No newline at end of file
diff --git a/dev/constraints/23_comparison_constraints.html b/dev/constraints/23_comparison_constraints.html
index 7815d91..e6022b0 100644
--- a/dev/constraints/23_comparison_constraints.html
+++ b/dev/constraints/23_comparison_constraints.html
@@ -8,16 +8,16 @@
     
     
     
-    
+    
     
-    
+    
     
-    
+    
     
     
   
   
-    
Julia Constraints
Appearance
Constraints.jl: Streamlining Constraint Definition and Integration in Julia ​
julia
using Constraints
+    
Julia Constraints
Appearance
Constraints.jl: Streamlining Constraint Definition and Integration in Julia ​
julia
using Constraints
 
 concept(:all_different, [1,1,1,2]) # false
 concept(:all_different, [1,9,3,2]) # true
julia
using Constraints
@@ -36,7 +36,7 @@
 JuMP.optimize!(model)
 @info "All Different" value.(X) value.(Y)
 
-# Note that this example gives a solution for the all_different constraint.
julia
# TODO: How to handle intention in JuMP/MOI
julia
using Constraints
+# Note that this example gives a solution for the all_different constraint.
julia
# TODO: How to handle intention in JuMP/MOI
julia
using Constraints
 
 concept(:all_equal, [1,1,1,2]) #false
 concept(:all_equal, [1,1,1,1]) #true
julia
using Constraints
@@ -54,7 +54,7 @@
 JuMP.optimize!(model)
 @info "All Equal" value.(X)
 
-# Note that this example gives a solution for the all_equal constraint.
julia
# TODO: How to handle intention in JuMP/MOI
julia
using Constraints
+# Note that this example gives a solution for the all_equal constraint.
julia
# TODO: How to handle intention in JuMP/MOI
julia
using Constraints
 
 @info concept(:ordered, [1, 2, 3, 4, 4]; op=≤)
 @info concept(:ordered, [1, 2, 3, 3, 5]; op=<)
@@ -99,7 +99,7 @@
 c([1, 2, 3, 4, 5]; op=<)
 !c([1, 2, 3, 4, 3]; op=≤)
 !c([1, 2, 3, 4, 3]; op=<)
source

-    
+    
     
   
 
\ No newline at end of file
diff --git a/dev/constraints/24_counting_summing_constraints.html b/dev/constraints/24_counting_summing_constraints.html
index 0e3aebe..ce8ff5c 100644
--- a/dev/constraints/24_counting_summing_constraints.html
+++ b/dev/constraints/24_counting_summing_constraints.html
@@ -8,16 +8,16 @@
     
     
     
-    
+    
     
-    
+    
     
-    
+    
     
     
   
   
-    
Julia Constraints
Appearance
Constraints.jl: Streamlining Constraint Definition and Integration in Julia ​
julia
using Constraints
+    
Julia Constraints
Appearance
Constraints.jl: Streamlining Constraint Definition and Integration in Julia ​
julia
using Constraints
 
 @info concept(:sum, [1, 2, 3, 4, 5]; op = ==, val=15)
 @info concept(:sum, [1, 2, 3, 4, 5]; op = ==, val=2)
@@ -39,7 +39,7 @@
 @constraint(model, X in Sum(; op = ==, val = 15))
 @constraint(model, Y in Sum(; op = <=, val = 10))
 JuMP.optimize!(model)
-@info "Sum" value.(X) value.(Y)
julia
# TODO: How to handle intention in JuMP/MOI
julia
using Constraints
+@info "Sum" value.(X) value.(Y)
julia
# TODO: How to handle intention in JuMP/MOI
julia
using Constraints
 
 concept(:count, [1,1,1,2], vals = [1, 1, 1, 2], op = ==, val = 4) # true
 concept(:count, [1,1,1,2], vals = [1, 1, 1, 2], op = ==, val = 5) # false
@@ -73,7 +73,7 @@
 @constraint(model, X_at_most in AtMost(vals = [1, 2], val = 1))
 @constraint(model, X_exactly in Exactly(vals = [1, 2], val = 2))
 JuMP.optimize!(model)
-@info "Count" value.(X) value.(X_at_least) value.(X_at_most) value.(X_exactly)
julia
# TODO: How to handle intention in JuMP/MOI
julia
using Constraints
+@info "Count" value.(X) value.(X_at_least) value.(X_at_most) value.(X_exactly)
julia
# TODO: How to handle intention in JuMP/MOI
julia
using Constraints
 
 @info concept(:nvalues, [1, 2, 3, 4, 5]; op = ==, val = 5)
 @info concept(:nvalues, [1, 2, 3, 4, 5]; op = ==, val = 2)
@@ -97,7 +97,7 @@
 @constraint(model, Y in NValues(; op = ==, val = 2))
 @constraint(model, Z in NValues(; op = <=, val = 5, vals = [1, 2]))
 JuMP.optimize!(model)
-@info "NValues" value.(X) value.(Y) value.(Z)
julia
# TODO: How to handle intention in JuMP/MOI
julia
using Constraints
+@info "NValues" value.(X) value.(Y) value.(Z)
julia
# TODO: How to handle intention in JuMP/MOI
julia
using Constraints
 
 # [v1, v2, v3], [v1, a1, a2; v2, b1, b2; v3, c1, c2] means v1 occurs between a1 and a2 times in the first array, similar for v2 and v3.
 
@@ -163,7 +163,7 @@
 
 co = concept(:cardinality_open)
 co([8, 5, 10, 10]; vals=[2 0 1; 5 1 3; 10 2 3])
source

-    
+    
     
   
 
\ No newline at end of file
diff --git a/dev/constraints/25_connection_constraints.html b/dev/constraints/25_connection_constraints.html
index 99b6cbb..b719a24 100644
--- a/dev/constraints/25_connection_constraints.html
+++ b/dev/constraints/25_connection_constraints.html
@@ -8,16 +8,16 @@
     
     
     
-    
+    
     
-    
+    
     
-    
+    
     
     
   
   
-    
Julia Constraints
Appearance
Constraints.jl: Streamlining Constraint Definition and Integration in Julia ​
julia
using Constraints
+    
Julia Constraints
Appearance
Constraints.jl: Streamlining Constraint Definition and Integration in Julia ​
julia
using Constraints
 
 concept(:maximum, [1,1,1,2], val = 2, op = ==) # true
 concept(:maximum, [1,2,4,4], val = 2, op = ==) # false
julia
using Constraints
@@ -34,7 +34,7 @@
 @variable(model, 1≤X[1:5]≤5, Int)
 @constraint(model, X in Maximum(; op = ==, val = 5))
 optimize!(model)
-@info "Maximum" value.(X)
julia
# TODO: How to handle intention in JuMP/MOI
julia
using Constraints
+@info "Maximum" value.(X)
julia
# TODO: How to handle intention in JuMP/MOI
julia
using Constraints
 
 concept(:minimum, [1,1,1,2], val = 1, op = ==) # true
 concept(:minimum, [1,2,4,4], val = 2, op = ==) # false
julia
using Constraints
@@ -53,7 +53,7 @@
 JuMP.optimize!(model)
 @info "Minimum" value.(X)
 
-# Note that this example gives a solution for the minimum constraint.
julia
# TODO: How to handle intention in JuMP/MOI
julia
using Constraints
+# Note that this example gives a solution for the minimum constraint.
julia
# TODO: How to handle intention in JuMP/MOI
julia
using Constraints
 
 @info concept(:element, [1, 2, 3, 4, 5]; id=1, val=1)
 @info concept(:element, [1, 2, 3, 4, 5]; id=1, val=2)
@@ -77,7 +77,7 @@
 @constraint(model, Y in Element(; id = 1, val = 1))
 @constraint(model, Z in Element(; id = 2, val = 2))
 JuMP.optimize!(model)
-@info "Element" value.(X) value.(Y) value.(Z)
julia
# TODO: How to handle intention in JuMP/MOI
julia
using Constraints
+@info "Element" value.(X) value.(Y) value.(Z)
julia
# TODO: How to handle intention in JuMP/MOI
julia
using Constraints
 
 @info concept(:channel, [2, 1, 4, 3])
 @info concept(:channel, [1, 2, 3, 4])
@@ -126,7 +126,7 @@
 c([2, 1, 4, 3, 5, 2, 1, 4, 5, 3]; dim=2)
 c([false, false, true, false]; id=3)
 c([false, false, true, false]; id=1)
source

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+    
     
   
 
\ No newline at end of file
diff --git a/dev/constraints/26_packing_scheduling_constraints.html b/dev/constraints/26_packing_scheduling_constraints.html
index 9eb61a2..cf3583e 100644
--- a/dev/constraints/26_packing_scheduling_constraints.html
+++ b/dev/constraints/26_packing_scheduling_constraints.html
@@ -8,16 +8,16 @@
     
     
     
-    
+    
     
-    
+    
     
-    
+    
     
     
   
   
-    
Julia Constraints
Appearance
Constraints.jl: Streamlining Constraint Definition and Integration in Julia ​
julia
using Constraints
+    
Julia Constraints
Appearance
Constraints.jl: Streamlining Constraint Definition and Integration in Julia ​
julia
using Constraints
 
 @info concept(:cumulative, [1, 2, 3, 4, 5]; val = 1)
 @info concept(:cumulative, [1, 2, 2, 4, 5]; val = 1)
@@ -44,7 +44,7 @@
 @constraint(model,
     Z in Cumulative(; pair_vars = [3 2 5 4 2; 1 2 1 1 3], op = <, val = 5))
 JuMP.optimize!(model)
-@info "Cumulative" value.(X) value.(Y) value.(Z)
julia
# TODO: How to handle intention in JuMP/MOI
julia
using Constraints
+@info "Cumulative" value.(X) value.(Y) value.(Z)
julia
# TODO: How to handle intention in JuMP/MOI
julia
using Constraints
 
 @info concept(:no_overlap, [1, 2, 3, 4, 5])
 @info concept(:no_overlap, [1, 2, 3, 4, 1])
@@ -88,7 +88,7 @@
 c([1, 2, 4, 6, 3]; pair_vars = [1, 1, 3, 1, 1])
 c([1, 1, 1, 3, 5, 2, 7, 7, 5, 12, 8, 7]; pair_vars = [2, 4, 1, 4 ,2 ,3, 5, 1, 2, 3, 3, 2], dim = 3)
 c([1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4]; pair_vars = [2, 4, 1, 4 ,2 ,3, 5, 1, 2, 3, 3, 2], dim = 3)
source

-    
+    
     
   
 
\ No newline at end of file
diff --git a/dev/constraints/27_graph_constraints.html b/dev/constraints/27_graph_constraints.html
index 80b481d..5d69511 100644
--- a/dev/constraints/27_graph_constraints.html
+++ b/dev/constraints/27_graph_constraints.html
@@ -8,9 +8,9 @@
     
     
     
-    
+    
     
-    
+    
     
     
     
@@ -24,7 +24,7 @@
 c([2, 3, 4, 1])
 c([2, 3, 1, 4]; op = ==, val = 3)
 c([4, 3, 1, 3]; op = >, val = 0)
source

-    
+    
     
   
 
\ No newline at end of file
diff --git a/dev/constraints/28_elementary_constraints.html b/dev/constraints/28_elementary_constraints.html
index 7060ca1..7e04a8d 100644
--- a/dev/constraints/28_elementary_constraints.html
+++ b/dev/constraints/28_elementary_constraints.html
@@ -8,9 +8,9 @@
     
     
     
-    
+    
     
-    
+    
     
     
     
@@ -22,7 +22,7 @@
 
 c([1, 2, 3, 4, 5]; pair_vars=[1, 2, 3, 4, 5])
 c([1, 2, 3, 4, 5]; pair_vars=[1, 2, 3, 4, 6])
source

-    
+    
     
   
 
\ No newline at end of file
diff --git a/dev/constraints/40_constraint_models.html b/dev/constraints/40_constraint_models.html
index 13f0b67..24c4734 100644
--- a/dev/constraints/40_constraint_models.html
+++ b/dev/constraints/40_constraint_models.html
@@ -8,9 +8,9 @@
     
     
     
-    
+    
     
-    
+    
     
     
     
@@ -47,7 +47,7 @@
 # Retrieve and display the values
 solution = value.(grid)
 display(solution, Val(:sudoku))
source

-    
+    
     
   
 
\ No newline at end of file
diff --git a/dev/constraints/60_constraint_commons.html b/dev/constraints/60_constraint_commons.html
index 492f81f..49b97c4 100644
--- a/dev/constraints/60_constraint_commons.html
+++ b/dev/constraints/60_constraint_commons.html
@@ -8,9 +8,9 @@
     
     
     
-    
+    
     
-    
+    
     
     
     
@@ -27,7 +27,7 @@
     :val, # one scalar value
     :vals, # a list of scalar values (independent of the input vector size)
 ]
source
ConstraintCommons.extract_parameters Function
julia
extract_parameters(m::Union{Method, Function}; parameters)
Extracts the intersection between the kargs of m and parameters (defaults to USUAL_CONSTRAINT_PARAMETERS).
source
julia
extract_parameters(s::Symbol, constraints_dict=USUAL_CONSTRAINTS; parameters=ConstraintCommons.USUAL_CONSTRAINT_PARAMETERS)
Return the parameters of the constraint s in constraints_dict.
Arguments
  • s::Symbol: the constraint name.
  • constraints_dict::Dict{Symbol,Constraint}: dictionary of constraints. Default is USUAL_CONSTRAINTS.
  • parameters::Vector{Symbol}: vector of parameters. Default is ConstraintCommons.USUAL_CONSTRAINT_PARAMETERS.
Example
julia
extract_parameters(:all_different)
source
Performances ​
Bench Evolution ParametersChair Evolution Parameters
Languages ​
XCSP3 considers two kinds of structure to recognize languages as core constraints: Automata, Multivalued Decision Diagrams (MMDs).
ConstraintCommons.AbstractMultivaluedDecisionDiagram Type
julia
AbstractMultivaluedDecisionDiagram
An abstract interface for Multivalued Decision Diagrams (MDD) used in Julia Constraints packages. Requirements:
  • accept(a<:AbstractMultivaluedDecisionDiagram, word): return true if a accepts word.
source
ConstraintCommons.MDD Type
julia
MDD{S,T} <: AbstractMultivaluedDecisionDiagram
A minimal implementation of a multivalued decision diagram structure.
source
ConstraintCommons.AbstractAutomaton Type
julia
AbstractAutomaton
An abstract interface for automata used in Julia Constraints packages. Requirements:
  • accept(a<:AbstractAutomaton, word): return true if a accepts word.
source
ConstraintCommons.Automaton Type
julia
Automaton{S, T, F <: Union{S, Vector{S}, Set{S}}} <: AbstractAutomaton
A minimal implementation of a deterministic automaton structure.
source
ConstraintCommons.accept Function
julia
accept(a::Union{Automaton, MDD}, w)
Return true if a accepts the word w and false otherwise.
source
julia
ConstraintCommons.accept(fa::FakeAutomaton, word)
Implement the accept methods for FakeAutomaton.
source
ConstraintCommons.at_end Function
julia
at_end(a::Automaton, s)
Internal method used by accept with Automaton.
source
Performances ​
Bench Evolution Automata
Chair Evolution Automata
Bench Evolution Diagrams
Chair Evolution Diagrams
Extensions ​
We extend some operations for Nothing and Symbol.
ConstraintCommons.symcon Function
julia
symcon(s1::Symbol, s2::Symbol, connector::AbstractString="_")
Extends * to Symbols multiplication by connecting the symbols by an _.
source
ConstraintCommons.consin Function
julia
consin(::Any, ::Nothing)
Extends Base.in (or ∈) when the set is nothing. Returns false.
source
ConstraintCommons.consisempty Function
julia
consisempty(::Nothing)
Extends Base.isempty when the set is nothing. Returns true.
source
Performances ​
Bench Evolution Nothing
Chair Evolution Nothing
Bench Evolution Symbols
Chair Evolution Symbols
Sampling ​
During our constraint learning processes, we use sampling to efficiently make partial exploration of search spaces. The following are some examples of sampling utilities.
ConstraintCommons.oversample Function
julia
oversample(X, f)
Oversample elements of X until the boolean function f has as many true and false configurations.
source
Performances ​
Bench EvolutionChair Evolution
Extrema ​
We need to compute the difference between extrema of various kind of collections in several situations.
ConstraintCommons.δ_extrema Function
julia
δ_extrema(X...)
Compute both the difference between the maximum and the minimum of over all the collections of X.
source
Performances ​
Bench EvolutionChair Evolution
Dictionaries ​
We provide the ever-useful incsert! function for dictionaries.
ConstraintCommons.incsert! Function
julia
incsert!(d::Union{AbstractDict, AbstractDictionary}, ind, val = 1)
Increase or insert a counter in a dictionary-based collection. The counter insertion defaults to val = 1.
source
Performances ​
Bench EvolutionChair Evolution

-    
+    
     
   
 
\ No newline at end of file
diff --git a/dev/constraints/61_pattern_folds.html b/dev/constraints/61_pattern_folds.html
index c42308b..e781151 100644
--- a/dev/constraints/61_pattern_folds.html
+++ b/dev/constraints/61_pattern_folds.html
@@ -8,9 +8,9 @@
     
     
     
-    
+    
     
-    
+    
     
     
     
@@ -19,7 +19,7 @@
   
     
Julia Constraints
Appearance
PatternFolds.jl ​
Documentation for PatternFolds.jl.
PatternFolds.PatternFold Type
julia
PatternFold{T, P}
A Union type used as an interface for folded patterns such as VectorFold. To implement the interface and inherit from it, a new structure MyFold{T[,P]} must define three fields:
  • pattern::P. Note that both length(::P) and rand(::P) methods must be available
  • gap::TS
  • folds::int
Finally one can redefine PatternFold
julia
PatternFold{T} = Union{AbstractVectorFold{T}, IntervalsFold{T}, MyFold{T[,P]}}
source
PatternFolds.AbstractVectorFold Type
julia
AbstractVectorFold{T, P}
An abstract type used as an interface for folded vectors such as VectorFold. To implement the interface and inherit from it, a new structure must define three fields:
  • pattern::P. Note that both length(::P) and rand(::P) methods must be available
  • gap::T
  • folds::int
source
PatternFolds.IVectorFold Type
julia
VectorFold{T,V <: AbstractVector{T}}
A folded vector structure that extends the methods of AbstractVector to a folded structure.
source
PatternFolds.VectorFold Type
julia
VectorFold{T,V <: AbstractVector{T}}
A mutable structure for folded vector that extends the methods of AbstractVector. Compared to IVectorFold, this tructure is about 20% faster using iterators. Note that this structure keep an active pointer to the current unfolded pattern. However, its external behavior is similar to IVectorFold.
source
Base.iterate Method
julia
iterate(iter)
Extends iterate methods from Base to allow forward and reverse iteration on both VectorFold and MVectorFold.
source
Base.length Method
julia
length(pf<:PatternFold)
Return the length of pf if unfolded.
source
Base.rand Method
julia
rand(pf<:PatternFold)
Returns a random value of pf as if it was unfolded.
source
Base.rand Method
julia
Base.rand(::Vector{AbstractVectorFold})
 Extend the `Base.rand` function to `Vector{AbstractVectorFold}`.
source
Base.rand Method
julia
Base.rand(::Vector{IntervalsFold})
Extend the Base.rand function to Vector{IntervalsFold}.
source
PatternFolds.fold Method
julia
fold(v::V, depth = 0)
returns a suitable VectorFold, which when unfolded gives the Vector V.
source
PatternFolds.folds Method
julia
folds(<:PatternFold)
Return the number of folds. An infinite folded pattern returns 0.
source
PatternFolds.gap Method
julia
gap(<:PatternFold)
Return the gap between the starts of consecutive folds.
source
PatternFolds.make_vector_fold Function
julia
make_vector_fold(pattern, gap, fold, kind = :mutable)
A dispatcher to construct a folded vector. The kind of vector can be set to either :mutable (default) or :immutable. The default is faster in most cases but it depends on the pattern, gap, and fold parameters. For critical code, it is recommended to benchmark both options.
source
PatternFolds.pattern Method
julia
pattern(vf, index)
Return the element at index in the original pattern.
source
PatternFolds.pattern Method
julia
pattern(<:PatternFold)
Return the pattern of any PatternFold. The pattern defines the occurrences of the first fold.
source
PatternFolds.pattern_length Method
julia
pattern_length(pf<:PatternFold)
Return the length of the basic pattern of pf.
source
PatternFolds.reset_pattern! Method
julia
reset_pattern!(<:PatternFold)
Reset the unfolded pattern to the first fold.
source
PatternFolds.set_fold! Function
julia
set_fold!(mvf::VectorFold, new_fold = mvf.current + 1)
Set the unfolded pattern to new_fold. By default move the next fold after current.
source
PatternFolds.unfold Method
julia
unfold(vf::VectorFold; from=1, to=folds(vf))
Construct the unfolded version of vf (with the same type as pattern(vf)) based. Please note that using an iterator on vf avoid memory allocation, which is not the case of unfold.
source

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\ No newline at end of file
diff --git a/dev/constraints/62_constraint_domains.html b/dev/constraints/62_constraint_domains.html
index 5bcce66..708ce38 100644
--- a/dev/constraints/62_constraint_domains.html
+++ b/dev/constraints/62_constraint_domains.html
@@ -8,9 +8,9 @@
     
     
     
-    
+    
     
-    
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@@ -65,7 +65,7 @@
 solutions, non_solutions = explore(domains, allunique)
source
Performances ​
Bench Evolution ExplorationChair Evolution Exploration
Parameters ​
ConstraintDomains.BoolParameterDomain Type
julia
BoolParameterDomain <: AbstractDomain
A domain to store boolean values. It is used to generate random parameters.
source
ConstraintDomains.DimParameterDomain Type
julia
DimParameterDomain <: AbstractDomain
A domain to store dimensions. It is used to generate random parameters.
source
ConstraintDomains.IdParameterDomain Type
julia
IdParameterDomain <: AbstractDomain
A domain to store ids. It is used to generate random parameters.
source
ConstraintDomains.FakeAutomaton Type
julia
FakeAutomaton{T} <: ConstraintCommons.AbstractAutomaton
A structure to generate pseudo automaton enough for parameter exploration.
source
ConstraintCommons.accept Function
julia
accept(a::Union{Automaton, MDD}, w)
Return true if a accepts the word w and false otherwise.
source
julia
ConstraintCommons.accept(fa::FakeAutomaton, word)
Implement the accept methods for FakeAutomaton.
source
ConstraintDomains.fake_automaton Function
julia
fake_automaton(d)
Construct a FakeAutomaton.
source
ConstraintDomains.LanguageParameterDomain Type
julia
LanguageParameterDomain <: AbstractDomain
A domain to store languages. It is used to generate random parameters.
source
ConstraintDomains.OpParameterDomain Type
julia
OpParameterDomain{T} <: AbstractDomain
A domain to store operators. It is used to generate random parameters.
source
ConstraintDomains.PairVarsParameterDomain Type
julia
PairVarsParameterDomain{T} <: AbstractDomain
A domain to store values paired with variables. It is used to generate random parameters.
source
ConstraintDomains.ValParameterDomain Type
julia
ValParameterDomain{T} <: AbstractDomain
A domain to store one value. It is used to generate random parameters.
source
ConstraintDomains.ValsParameterDomain Type
julia
ValsParameterDomain{T} <: AbstractDomain
A domain to store values. It is used to generate random parameters.
source
Base.rand Function
julia
Base.rand(::Vector{IntervalsFold})
Extend the Base.rand function to Vector{IntervalsFold}.
source
julia
rand(pf<:PatternFold)
Returns a random value of pf as if it was unfolded.
source
julia
Base.rand(::Vector{AbstractVectorFold})
 Extend the `Base.rand` function to `Vector{AbstractVectorFold}`.
source
julia
Base.rand(d::Union{Vector{D},Set{D}, D}) where {D<:AbstractDomain}
Extends Base.rand to (a collection of) domains.
source
julia
Base.rand(itv::Intervals)
 Base.rand(itv::Intervals, i)
Return a random value from itv, specifically from the ith interval if i is specified.
source
julia
Base.rand(d::D) where D <: DiscreteDomain
Draw randomly a point in d.
source
julia
Base.rand(fa::FakeAutomaton)
Extends Base.rand. Currently simply returns fa.
source
ConstraintDomains.generate_parameters Function
julia
generate_parameters(d<:AbstractDomain, param)
Generates random parameters based on the domain d and the kind of parameters param.
source

-    
+    
     
   
 
\ No newline at end of file
diff --git a/dev/constraints/63_constraints_jl.html b/dev/constraints/63_constraints_jl.html
index 8c0fd07..ceb32ae 100644
--- a/dev/constraints/63_constraints_jl.html
+++ b/dev/constraints/63_constraints_jl.html
@@ -8,9 +8,9 @@
     
     
     
-    
+    
     
-    
+    
     
     
     
@@ -27,7 +27,7 @@
     :val, # one scalar value
     :vals, # a list of scalar values (independent of the input vector size)
 ]

source

Concepts, Error Functions, and QUBO matrices ​

One major use of this collection of usual constraint is to extract the concept or the error function (error_f) of a given constraint.

Constraints.concept Function
julia
concept(c::Constraint)

Return the concept (function) of constraint c. concept(c::Constraint, x...; param = nothing) Apply the concept of c to values x and optionally param.

source

julia
concept(s::Symbol, args...; kargs...)

Return the concept of the constraint s applied to args and kargs. This is a shortcut for concept(USUAL_CONSTRAINTS[s])(args...; kargs...).

Arguments

  • s::Symbol: the constraint name.

  • args...: the arguments to apply the concept to.

  • kargs...: the keyword arguments to apply the concept to.

Example

julia
concept(:all_different, [1, 2, 3])

source

Note that the error function is a finer estimation of how much a constraint is violated or not. By default, the error_f method simply return 0. if the constraint is satisfied or 1. otherwise.

Efficient versions of error_r are either hand-coded or generated through CompositionalNetworks.jl.

Constraints.error_f Function
julia
error_f(c::Constraint)

Return the error function of constraint c. error_f(c::Constraint, x; param = nothing) Apply the error function of c to values x and optionally param.

source

Finally, another use is to provide QUBO matrices of those usual constraints through QUBOConstraints.jl. The syntax and interface for this feature are still a work in progress.

Usual Constraints ​

We provide a couple of methods to navigate the usual constraints extracted from XCSP3-Core.

Constraints.USUAL_CONSTRAINTS Constant
julia
USUAL_CONSTRAINTS::Dict

Dictionary that contains all the usual constraints defined in Constraint.jl. It is based on XCSP3-core specifications available at https://arxiv.org/abs/2009.00514

Adding a new constraint is as simple as defining a new function with the same name as the constraint and using the @usual macro to define it. The macro will take care of adding the new constraint to the USUAL_CONSTRAINTS dictionary.

Example

julia
@usual concept_all_different(x; vals=nothing) = xcsp_all_different(list=x, except=vals)

source

Constraints.describe Function
julia
describe(constraints::Dict{Symbol,Constraint}=USUAL_CONSTRAINTS; width=150)

Return a pretty table with the description of the constraints in constraints.

Arguments

  • constraints::Dict{Symbol,Constraint}: dictionary of constraints to describe. Default is USUAL_CONSTRAINTS.

  • width::Int: width of the table.

Example

julia
describe()

source

Constraints.constraints_parameters Function
julia
constraints_parameters(C=USUAL_CONSTRAINTS)

Return a pretty table with the parameters of the constraints in C.

Arguments

  • C::Dict{Symbol,Constraint}: dictionary of constraints. Default is USUAL_CONSTRAINTS.

Example

julia
constraints_parameters()

source

Constraints.constraints_descriptions Function
julia
constraints_descriptions(C=USUAL_CONSTRAINTS)

Return a pretty table with the descriptions of the constraints in C.

Arguments

  • C::Dict{Symbol,Constraint}: dictionary of constraints. Default is USUAL_CONSTRAINTS.

Example

julia
constraints_descriptions()

source

- + \ No newline at end of file diff --git a/dev/cp/00_intro.html b/dev/cp/00_intro.html index 277ae85..a764819 100644 --- a/dev/cp/00_intro.html +++ b/dev/cp/00_intro.html @@ -8,9 +8,9 @@ - + - + @@ -18,7 +18,7 @@
Julia Constraints

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Welcome to Julia Constraints ​

An introductory post/chapter that provides an overview of the JuliaConstraint organization, its mission, and what readers can expect to learn from the content. Highlight the importance of Constraint Programming (CP) and optimization in solving real-world problems.

- + \ No newline at end of file diff --git a/dev/cp/10_cp101.html b/dev/cp/10_cp101.html index bd34f2e..24f027c 100644 --- a/dev/cp/10_cp101.html +++ b/dev/cp/10_cp101.html @@ -8,9 +8,9 @@ - + - + @@ -18,7 +18,7 @@
Julia Constraints

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Constraint Programming 101 ​

What is Constraint Programming? ​

  • Define CP and its significance in solving combinatorial problems.

Basic Concepts and Terminology ​

  • Introduce key concepts such as constraints, domains, and variables.

How CP differs from other optimization techniques ​

  • Contrast with other methods like linear programming and metaheuristics.
- + \ No newline at end of file diff --git a/dev/cp/20_opt.html b/dev/cp/20_opt.html index ab410d1..de2ef92 100644 --- a/dev/cp/20_opt.html +++ b/dev/cp/20_opt.html @@ -8,9 +8,9 @@ - + - + @@ -18,7 +18,7 @@
Julia Constraints

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Dive into Optimization ​

Understanding Optimization ​

  • Explanation of optimization, types of optimization problems (e.g., linear, nonlinear, integer programming).

Metaheuristics Overview ​

  • Introduce concepts like Genetic Algorithms, Simulated Annealing, and Tabu Search.

Mathematical Programming Basics ​

  • Cover the fundamentals of mathematical programming and its role in optimization.
- + \ No newline at end of file diff --git a/dev/cp/30_getting_started.html b/dev/cp/30_getting_started.html index df7c56c..e6a95b3 100644 --- a/dev/cp/30_getting_started.html +++ b/dev/cp/30_getting_started.html @@ -8,25 +8,25 @@ - + - + - + -
Julia Constraints

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Getting Started with Julia for CP and Optimization ​

Why Julia? ​

  • Discuss the advantages of Julia for computational science and optimization, highlighting its performance and ease of use.

Setting Up Your Julia Environment ​

We encourage users to install Julia through juliaup, a version manager for the Julia language. Please look at the official Julia language download page for further information. Once installed, Julia can be used through various editors (Visual Studio Code), notebooks (Pluto.jl), or command-line (REPL).

Although a part of the CP solvers available within the Julia ecosystem have their own interface, we encourage users to use the JuMP modeling language if possible.

Julia Constraints host several solvers(' interfaces). Due to its flexibility in modeling and solving, we will use LocalSearchSolvers.jl through its JuMP interface CBLS.jl as the basic example. Note that depending on the targeted instances, available hardware, and expectations, it is not necessarily the best choice.

All along the documentation, we will try to provide syntax examples for different setup.

julia
using LocalSearchSolvers
julia
using JuMP, CBLS
julia
# TODO: Add other solvers

Your First Julia CP Model ​

We will start with a classic puzzle game and some of its not that simple variants: the Sudoku.

(From Wikipedia) In classic Sudoku, the objective is to fill a 9 × 9 grid with digits so that each column, each row, and each of the nine 3 × 3 subgrids that compose the grid (also called "boxes", "blocks", or "regions") contains all of the digits from 1 to 9. The puzzle setter provides a partially completed grid, which for a well-posed puzzle has a single solution.

Constraint Programming follows the model-and-solve approach. We first need to model our Sudoku problem.

julia
m = JuMP.Model(CBLS.Optimizer)
julia
# TODO: Add other solvers

But what are the basis of CP models? It is quite simple:

  1. A collection X=X1,⋯,Xn of variables with each an associated domain.
julia
@variable(m, 1 ≤ X[1:9, 1:9] ≤ 9, Int)
julia
# TODO: Add other solvers
  1. A collection of predicates (called constraints) C=C1,⋯,Cn over (subsets of) X.

When modeling problems as CP, one might define and use their own predicates. However, a large collection of already defined constraints exists. One, if not the most, iconic global constraint is called AllDifferent. It ensures that all variables take distinct values.

Sudoku puzzles can be defined using only this one constraint applied to different subsets of variables.

julia
for i in 1:9
+    
Julia Constraints
Appearance
Getting Started with Julia for CP and Optimization ​
Why Julia? ​
  • Discuss the advantages of Julia for computational science and optimization, highlighting its performance and ease of use.
Setting Up Your Julia Environment ​
We encourage users to install Julia through juliaup, a version manager for the Julia language. Please look at the official Julia language download page for further information. Once installed, Julia can be used through various editors (Visual Studio Code), notebooks (Pluto.jl), or command-line (REPL).
Although a part of the CP solvers available within the Julia ecosystem have their own interface, we encourage users to use the JuMP modeling language if possible.
Julia Constraints host several solvers(' interfaces). Due to its flexibility in modeling and solving, we will use LocalSearchSolvers.jl through its JuMP interface CBLS.jl as the basic example. Note that depending on the targeted instances, available hardware, and expectations, it is not necessarily the best choice.
All along the documentation, we will try to provide syntax examples for different setup.
julia
using LocalSearchSolvers
julia
using JuMP, CBLS
julia
# TODO: Add other solvers
Your First Julia CP Model ​
We will start with a classic puzzle game and some of its not that simple variants: the Sudoku.
(From Wikipedia) In classic Sudoku, the objective is to fill a 9 × 9 grid with digits so that each column, each row, and each of the nine 3 × 3 subgrids that compose the grid (also called "boxes", "blocks", or "regions") contains all of the digits from 1 to 9. The puzzle setter provides a partially completed grid, which for a well-posed puzzle has a single solution.
Constraint Programming follows the model-and-solve approach. We first need to model our Sudoku problem.
julia
m = JuMP.Model(CBLS.Optimizer)
julia
# TODO: Add other solvers
But what are the basis of CP models? It is quite simple:
  1. A collection X=X1,⋯,Xn of variables with each an associated domain.
julia
@variable(m, 1 ≤ X[1:9, 1:9] ≤ 9, Int)
julia
# TODO: Add other solvers
  1. A collection of predicates (called constraints) C=C1,⋯,Cn over (subsets of) X.
When modeling problems as CP, one might define and use their own predicates. However, a large collection of already defined constraints exists. One, if not the most, iconic global constraint is called AllDifferent. It ensures that all variables take distinct values.
Sudoku puzzles can be defined using only this one constraint applied to different subsets of variables.
julia
for i in 1:9
         @constraint(m, X[i,:] in AllDifferent()) # rows
         @constraint(m, X[:,i] in AllDifferent()) # columns
-end
julia
# TODO: Add other solvers
The last series of AllDifferent constraint is less straight forward. We need to ensure that each 3 × 3 subgrid (block) is filled with distinct values.
julia
for i in 0:2, j in 0:2 # blocks
+end
julia
# TODO: Add other solvers
The last series of AllDifferent constraint is less straight forward. We need to ensure that each 3 × 3 subgrid (block) is filled with distinct values.
julia
for i in 0:2, j in 0:2 # blocks
     @constraint(
         m,
         vec(X[(3i+1):(3(i+1)), (3j+1):(3(j+1))]) in AllDifferent(),
     )
-end
julia
# TODO: Add other solvers
We can now simply run our solver to look for a feasible solution.
julia
optimize!(m)
Note that this is heuristic solver, we might not get a feasible solution! Let's check it out. The value function print the value of a JuMP variable. We can cast it over a collection with the value. syntax.
julia
value.(X)

-    
+end
julia
# TODO: Add other solvers

We can now simply run our solver to look for a feasible solution.

julia
optimize!(m)

Note that this is heuristic solver, we might not get a feasible solution! Let's check it out. The value function print the value of a JuMP variable. We can cast it over a collection with the value. syntax.

julia
value.(X)
+ \ No newline at end of file diff --git a/dev/cp/40_ecosystem.html b/dev/cp/40_ecosystem.html index 5c9fb88..3e8561a 100644 --- a/dev/cp/40_ecosystem.html +++ b/dev/cp/40_ecosystem.html @@ -8,9 +8,9 @@ - + - + @@ -18,7 +18,7 @@
Julia Constraints

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Exploring JuliaConstraint Packages ​

Package Overviews ​

  • Introduce each package within the JuliaConstraint organization, its purpose, and primary features.

Installation and Getting Started Guides ​

  • Provide step-by-step instructions for installing and getting started with each package.
- + \ No newline at end of file diff --git a/dev/cp/50_advanced.html b/dev/cp/50_advanced.html index 4a11a7c..11534b3 100644 --- a/dev/cp/50_advanced.html +++ b/dev/cp/50_advanced.html @@ -8,9 +8,9 @@ - + - + @@ -18,7 +18,7 @@
Julia Constraints

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Advanced Constraint Programming Techniques ​

Global Constraints and Their Uses ​

  • Dive deeper into global constraints and how they simplify complex problems.

Search Strategies and Optimization ​

  • Discuss various search strategies and their impact on solving CP problems.
- + \ No newline at end of file diff --git a/dev/cp/60_applications.html b/dev/cp/60_applications.html index 063a084..eae0f39 100644 --- a/dev/cp/60_applications.html +++ b/dev/cp/60_applications.html @@ -8,9 +8,9 @@ - + - + @@ -18,7 +18,7 @@
Julia Constraints

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Applying Optimization Methods ​

Case Studies and Real-World Applications ​

  • Showcase studies where CP and optimization have been successfully applied.

From Theory to Practice ​

  • Guide readers through the process of formulating and solving an optimization problem from a real-world scenario.
- + \ No newline at end of file diff --git a/dev/cp/70_models.html b/dev/cp/70_models.html index 4ff2e47..5dfdb31 100644 --- a/dev/cp/70_models.html +++ b/dev/cp/70_models.html @@ -8,9 +8,9 @@ - + - + @@ -18,7 +18,7 @@
Julia Constraints

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Building and Analyzing Models ​

Modeling Best Practices ​

  • Share best practices and tips for building efficient CP and optimization models.

Performance Analysis and Improvement ​

  • Teach how to analyze and improve the performance of models.
- + \ No newline at end of file diff --git a/dev/cp/80_tuto_xp.html b/dev/cp/80_tuto_xp.html index ca3d939..851cea1 100644 --- a/dev/cp/80_tuto_xp.html +++ b/dev/cp/80_tuto_xp.html @@ -8,9 +8,9 @@ - + - + @@ -18,7 +18,7 @@
Julia Constraints

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Tutorials and Experiments ​

Hands-On Tutorials ​

  • Provide step-by-step tutorials covering various topics and complexity levels.

Experimental Analysis ​

  • Discuss the importance of experimental analysis in CP and how to conduct meaningful experiments.
- + \ No newline at end of file diff --git a/dev/cp/90_contribution.html b/dev/cp/90_contribution.html index 3eaff30..a4adcda 100644 --- a/dev/cp/90_contribution.html +++ b/dev/cp/90_contribution.html @@ -8,9 +8,9 @@ - + - + @@ -18,7 +18,7 @@
Julia Constraints

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Community and Contribution ​

Joining the JuliaConstraint Community ​

  • Encourage readers to join the community, highlighting how they can contribute and collaborate.

Future Directions ​

  • Share the vision for JuliaConstraint and upcoming projects or areas of research.
- + \ No newline at end of file diff --git a/dev/hashmap.json b/dev/hashmap.json index 926d441..e30ec86 100644 --- a/dev/hashmap.json +++ b/dev/hashmap.json @@ -1 +1 @@ -{"api_00_public.md":"Cqf6QMJN","api_10_full.md":"DufIdSXa","constraints_00_intro.md":"wE3p7Yn4","constraints_10_variables_and_domains.md":"2DoRmBqU","constraints_20_constraints.md":"DmKL30J8","constraints_21_generic_constraints.md":"Cq_hAjZf","constraints_22_language_constraints.md":"CKu7YAtW","constraints_23_comparison_constraints.md":"4b0z8qtK","constraints_24_counting_summing_constraints.md":"DVkY5sTG","constraints_25_connection_constraints.md":"ajGM2nJs","constraints_26_packing_scheduling_constraints.md":"CrG8P0jZ","constraints_27_graph_constraints.md":"tZ8kDC6h","constraints_28_elementary_constraints.md":"LoJStkX7","constraints_40_constraint_models.md":"Dv2qEx3_","constraints_60_constraint_commons.md":"CfOCoBuP","constraints_61_pattern_folds.md":"xjkZia50","constraints_62_constraint_domains.md":"DMsVVEqc","constraints_63_constraints_jl.md":"WJF85byi","cp_00_intro.md":"CsgSXI99","cp_10_cp101.md":"B-tHlXuM","cp_20_opt.md":"C0pIlKYp","cp_30_getting_started.md":"QuTvdZuh","cp_40_ecosystem.md":"YmIJU8G_","cp_50_advanced.md":"CJxpgFIM","cp_60_applications.md":"CA8-f1fu","cp_70_models.md":"1-J7V95h","cp_80_tuto_xp.md":"BBnKLYxi","cp_90_contribution.md":"DOrkQHq1","index.md":"pHtYR91m","learning_00_intro.md":"CBu38Cu4","learning_10_compositional_networks.md":"D4-tXiP7","learning_11_layers.md":"C199f07V","learning_12_transformation.md":"BKCQ-7xu","learning_13_arithmetic.md":"42vK0uzX","learning_14_aggregation.md":"V0-R09TM","learning_15_comparison.md":"CUM575C4","learning_20_qubo_constraints.md":"DfeUpk7q","learning_21_qubo_encoding.md":"U06_V_uV","learning_22_qubo_learning.md":"CzSOBa1N","learning_30_constraints_translator.md":"CRGr1CIB","learning_90_constraint_learning.md":"YM6S0n3n","perf_00_perf_checker.md":"BMTPCZnU","perf_10_tutorial.md":"C4bm3h6K","perf_20_perf_interface.md":"Cfce352q","perf_30_benchmark_ext.md":"CzInbrh4","perf_40_chairmarks_ext.md":"h8pfB9sA","perf_90_api.md":"0OTlDWyk","solvers_00_intro.md":"s1tbOTQV","solvers_10_cbls.md":"BCa7hnj8","solvers_40_constraint_explorer.md":"CjuNUjfR","solvers_50_local_search_solvers.md":"CnhmzQ0z","solvers_80_meta_strategist.md":"Cv_QCe0I"} +{"api_00_public.md":"Cqf6QMJN","api_10_full.md":"DufIdSXa","constraints_00_intro.md":"wE3p7Yn4","constraints_10_variables_and_domains.md":"BmMtN-L8","constraints_20_constraints.md":"DmKL30J8","constraints_21_generic_constraints.md":"DIVWDhM8","constraints_22_language_constraints.md":"CKu7YAtW","constraints_23_comparison_constraints.md":"6Pt2XSoe","constraints_24_counting_summing_constraints.md":"XccROfRE","constraints_25_connection_constraints.md":"CrGkCkeo","constraints_26_packing_scheduling_constraints.md":"C0OPa6mw","constraints_27_graph_constraints.md":"tZ8kDC6h","constraints_28_elementary_constraints.md":"LoJStkX7","constraints_40_constraint_models.md":"Dv2qEx3_","constraints_60_constraint_commons.md":"CfOCoBuP","constraints_61_pattern_folds.md":"xjkZia50","constraints_62_constraint_domains.md":"DMsVVEqc","constraints_63_constraints_jl.md":"WJF85byi","cp_00_intro.md":"CsgSXI99","cp_10_cp101.md":"B-tHlXuM","cp_20_opt.md":"C0pIlKYp","cp_30_getting_started.md":"B_EkJgkt","cp_40_ecosystem.md":"YmIJU8G_","cp_50_advanced.md":"CJxpgFIM","cp_60_applications.md":"CA8-f1fu","cp_70_models.md":"1-J7V95h","cp_80_tuto_xp.md":"BBnKLYxi","cp_90_contribution.md":"DOrkQHq1","index.md":"pHtYR91m","learning_00_intro.md":"CBu38Cu4","learning_10_compositional_networks.md":"D4-tXiP7","learning_11_layers.md":"C199f07V","learning_12_transformation.md":"BKCQ-7xu","learning_13_arithmetic.md":"42vK0uzX","learning_14_aggregation.md":"V0-R09TM","learning_15_comparison.md":"CUM575C4","learning_20_qubo_constraints.md":"DfeUpk7q","learning_21_qubo_encoding.md":"U06_V_uV","learning_22_qubo_learning.md":"CzSOBa1N","learning_30_constraints_translator.md":"CRGr1CIB","learning_90_constraint_learning.md":"YM6S0n3n","perf_00_perf_checker.md":"BMTPCZnU","perf_10_tutorial.md":"C4bm3h6K","perf_20_perf_interface.md":"Cfce352q","perf_30_benchmark_ext.md":"CzInbrh4","perf_40_chairmarks_ext.md":"h8pfB9sA","perf_90_api.md":"0OTlDWyk","solvers_00_intro.md":"s1tbOTQV","solvers_10_cbls.md":"CdQMlrVz","solvers_40_constraint_explorer.md":"DrX4zrKv","solvers_50_local_search_solvers.md":"CnhmzQ0z","solvers_80_meta_strategist.md":"Cv_QCe0I"} diff --git a/dev/index.html b/dev/index.html index 542c8ef..5582e1a 100644 --- a/dev/index.html +++ b/dev/index.html @@ -8,9 +8,9 @@ - + - + @@ -18,7 +18,7 @@
Julia Constraints

Appearance

Julia Constraints

Model Smoothly Decide Wisely

A Toolkit for Constraint Programming

Model, Learn, and Solve!
View on Github
JuliaConstraints
JuMP.jl

JuMP.jl

Model optimization problems via JuMP.jl!

PerfChecker.jl

PerfChecker.jl

Cross-version performance checking tool

Pluto.jl

Pluto.jl

Simple, reactive programming environment via Julia notebooks

What is Julia Constraints?

The Julia Constraints organization serves as a hub for resources to create, understand, and solve optimization through the lens of Constraint Programming. Our goal is to make Constraint Programming accessible and efficient for users at all levels of expertise, by providing a comprehensive suite of tools.

Most tools integrate seamlessly with JuMP, a popular Julia package for mathematical optimization.

Ecosystem overview

Core Packages

The foundation of common packages that provide essential features for constraint programming ensures that users possess the fundamental tools required for their projects.

  • ConstraintCommons.jl is designed to make constraint programming solutions in Julia interoperable. It provides shared structures, abstract types, functions, and generic methods used by both basic feature packages and learning-oriented packages.
  • ConstraintDomains.jl focuses on the definition and manipulation of variable domains, which are used to solve constraint programming problems. This package provides the infrastructure needed to specify both discrete and continuous domains, allowing a wide range of constraint programming applications.
  • Constraints.jl is a key component, specifically designed to facilitate the definition, manipulation, and application of constraints in constraint programming. This package is central to handling both standard and complex constraints, making it an indispensable tool for developers and researchers working in CP.
  • ConstraintModels.jl is a package for Julia Constraints' solvers that stores Constraint Programming models.

Learning and Translation Tools

A collection that bridges the gap between the ease of modeling and computational efficacy. These tools learn from constraints or convert natural language problems into constraint programming solutions, requiring minimal input from the user beyond the model itself.

  • CompositionalNetworks.jl provides interpretable compositional networks (ICN), a combinatorial variant of neural networks that allows the user to obtain interpretable results, unlike regular artificial neural networks.
  • QUBOConstraints.jl is a package that can (automatically) learn QUBO matrices from optimization constraints.
  • ConstraintsTranslator.jl is a tool for converting problems expressed in natural language into optimization models.
  • ConstraintLearning.jl is a common interface that integrates the various components outlined above.

Solvers

We offer a variety of solvers, from native Julia solvers to interfaces with JuMP for external CP solvers, to cater to various problem-solving needs.

  • LocalSearchSolvers.jl is a Julia native framework to (semi-)automatically build Constraint-based Local Search solvers. It serves as a basic for the experimental design or core and learning oriented packages in Julia Constraints.
  • CBLS.jl a MOI/JuMP interface for the above framework!
  • CPLEXCP.jl a Julia interface for CPLEX CP Optimizer.
  • Chuffed.jl a wrapper for the constraint-programming solver Chuffed to Julia.
  • JaCoP.jl a Julia interface for the JaCoP constraint-programming solver.
  • ConstraintExplorer.jl a MOI/JuMP interface to explore search spaces modeled as CP.

JuMP extras

Constraint Programming is slowly making steps into the main JuMP components. However, some extra resources are available as

Meta-solving

MetaStrategist.jl is a meta-solving package in its formative stages, which aims to harness the strengths of CP and JuMP. Its goal is to formulate tailored strategies that take into consideration the unique hardware and software resources at hand, offering a new horizon in problem-solving efficiency and adaptability. Stay tuned!

Performance related tools

We've made a tool for cross-version performance checking that ensures the high efficiency and reliability of our solutions. By facilitating clear and simple performance evaluations, PerfChecker.jl enhances both development and maintenance, contributing to the overall health and progress of Julia (Constraints)'s growing library of resources.

Contributors Page

Acknowledgments

The Julia Constraints community would not be where it is today without the collective efforts of many talented individuals and organizations. We extend our heartfelt thanks to:

  • IIJ Research Lab: The driving force behind more than half of this project!
  • JuMP-dev Community: For their extensive contributions to the development of our packages.
  • Individual Contributors: Numerous developers and researchers who have dedicated their time and skills to enhance our tools.
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Julia Constraints

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Learning about Constraints ​

About learning constraints related matters.

Parameters ​

<!– To be moved –>

One major challenge of learning the features of constraints is exploring the domains of parameters. To tackle this issue, we provide some way to generate parameters from variables' domains.

ConstraintDomains.BoolParameterDomain Type
julia
BoolParameterDomain <: AbstractDomain

A domain to store boolean values. It is used to generate random parameters.

source

ConstraintDomains.DimParameterDomain Type
julia
DimParameterDomain <: AbstractDomain

A domain to store dimensions. It is used to generate random parameters.

source

ConstraintDomains.IdParameterDomain Type
julia
IdParameterDomain <: AbstractDomain

A domain to store ids. It is used to generate random parameters.

source

ConstraintDomains.FakeAutomaton Type
julia
FakeAutomaton{T} <: ConstraintCommons.AbstractAutomaton

A structure to generate pseudo automaton enough for parameter exploration.

source

ConstraintCommons.accept Function
julia
accept(a::Union{Automaton, MDD}, w)

Return true if a accepts the word w and false otherwise.

source

julia
ConstraintCommons.accept(fa::FakeAutomaton, word)

Implement the accept methods for FakeAutomaton.

source

ConstraintDomains.fake_automaton Function
julia
fake_automaton(d)

Construct a FakeAutomaton.

source

ConstraintDomains.LanguageParameterDomain Type
julia
LanguageParameterDomain <: AbstractDomain

A domain to store languages. It is used to generate random parameters.

source

ConstraintDomains.OpParameterDomain Type
julia
OpParameterDomain{T} <: AbstractDomain

A domain to store operators. It is used to generate random parameters.

source

ConstraintDomains.PairVarsParameterDomain Type
julia
PairVarsParameterDomain{T} <: AbstractDomain

A domain to store values paired with variables. It is used to generate random parameters.

source

ConstraintDomains.ValParameterDomain Type
julia
ValParameterDomain{T} <: AbstractDomain

A domain to store one value. It is used to generate random parameters.

source

ConstraintDomains.ValsParameterDomain Type
julia
ValsParameterDomain{T} <: AbstractDomain

A domain to store values. It is used to generate random parameters.

source

Base.rand Function
julia
Base.rand(::Vector{IntervalsFold})

Extend the Base.rand function to Vector{IntervalsFold}.

source

julia
rand(pf<:PatternFold)

Returns a random value of pf as if it was unfolded.

source

julia
Base.rand(::Vector{AbstractVectorFold})
 Extend the `Base.rand` function to `Vector{AbstractVectorFold}`.

source

julia
Base.rand(d::Union{Vector{D},Set{D}, D}) where {D<:AbstractDomain}

Extends Base.rand to (a collection of) domains.

source

julia
Base.rand(itv::Intervals)
 Base.rand(itv::Intervals, i)

Return a random value from itv, specifically from the ith interval if i is specified.

source

julia
Base.rand(d::D) where D <: DiscreteDomain

Draw randomly a point in d.

source

julia
Base.rand(fa::FakeAutomaton)

Extends Base.rand. Currently simply returns fa.

source

ConstraintDomains.generate_parameters Function
julia
generate_parameters(d<:AbstractDomain, param)

Generates random parameters based on the domain d and the kind of parameters param.

source

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Julia Constraints

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CompositionalNetworks.jl ​

Documentation for CompositionalNetworks.jl.

Utilities ​

CompositionalNetworks.map_tr! Function
julia
map_tr!(f, x, X, param)

Return an anonymous function that applies f to all elements of x and store the result in X, with a parameter param (which is set to nothing for function with no parameter).

source

CompositionalNetworks.lazy Function
julia
lazy(funcs::Function...)

Generate methods extended to a vector instead of one of its components. A function f should have the following signature: f(i::Int, x::V).

source

CompositionalNetworks.lazy_param Function
julia
lazy_param(funcs::Function...)

Generate methods extended to a vector instead of one of its components. A function f should have the following signature: f(i::Int, x::V; param).

source

CompositionalNetworks.as_bitvector Function
julia
as_bitvector(n::Int, max_n::Int = n)

Convert an Int to a BitVector of minimal size (relatively to max_n).

source

CompositionalNetworks.as_int Function
julia
as_int(v::AbstractVector)

Convert a BitVector into an Int.

source

CompositionalNetworks.reduce_symbols Function
julia
reduce_symbols(symbols, sep)

Produce a formatted string that separates the symbols by sep. Used internally for show_composition.

source

CompositionalNetworks.tr_in Function
julia
tr_in(tr, X, x, param)

Application of an operation from the transformation layer. Used to generate more efficient code for all compositions.

source

Metrics ​

CompositionalNetworks.hamming Function
julia
hamming(x, X)

Compute the hamming distance of x over a collection of solutions X, i.e. the minimal number of variables to switch in xto reach a solution.

source

CompositionalNetworks.minkowski Function
julia
minkowski(x, X, p)

source

CompositionalNetworks.manhattan Function
julia
manhattan(x, X)

source

CompositionalNetworks.weights_bias Function
julia
weights_bias(x)

A metric that bias x towards operations with a lower bit. Do not affect the main metric.

source

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Assert if a pair of layer/icn and weights compose a viable pattern. If no weights are given with an icn, it will check the current internal value.

source

CompositionalNetworks.generate_inclusive_operations Function
julia
generate_inclusive_operations(predicate, bits)
 generate_exclusive_operation(max_op_number)

Generates the operations (weights) of a layer with inclusive/exclusive operations.

source

CompositionalNetworks.generate_exclusive_operation Function
julia
generate_exclusive_operation(max_op_number)

Generates the operations (weights) of a layer with exclusive operations.

source

CompositionalNetworks.generate_weights Function
julia
generate_weights(layers)
 generate_weights(icn)

Generate the weights of a collection of layers or of an ICN.

source

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source

CompositionalNetworks.transformation_layer Function
julia
transformation_layer(param = Vector{Symbol}())

Generate the layer of transformations functions of the ICN. Iff param value is non empty, also includes all the related parametric transformations.

source

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Arithmetic Layer ​

Some text to describe the arithmetic layer within usual ICNs.

List of arithmetic operations ​

CompositionalNetworks.ar_sum Function
julia
ar_sum(x)

Reduce k = length(x) vectors through sum to a single vector.

source

CompositionalNetworks.ar_prod Function
julia
ar_prod(x)

Reduce k = length(x) vectors through product to a single vector.

source

Layer generation ​

CompositionalNetworks.arithmetic_layer Function
julia
arithmetic_layer()

Generate the layer of arithmetic operations of the ICN. The operations are mutually exclusive, that is only one will be selected.

source

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Julia Constraints

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Aggregation Layer ​

Some text to describe the aggragation layer within usual ICNs.

List of aggregations ​

CompositionalNetworks.ag_sum Function
julia
ag_sum(x)

Aggregate through + a vector into a single scalar.

source

CompositionalNetworks.ag_count_positive Function
julia
ag_count_positive(x)

Count the number of strictly positive elements of x.

source

Layer generation ​

CompositionalNetworks.aggregation_layer Function
julia
aggregation_layer()

Generate the layer of aggregations of the ICN. The operations are mutually exclusive, that is only one will be selected.

source

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Julia Constraints

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Comparison Layer ​

Some text to describe the comparison layer within usual ICNs.

List of comparisons ​

List the possible parameters and how it affects the comparison.

Non-parametric ​

CompositionalNetworks.co_identity Function
julia
co_identity(x)

Identity function. Already defined in Julia as identity, specialized for scalars in the comparison layer.

source

CompositionalNetworks.co_euclidean Function
julia
co_euclidean(x; dom_size)

Compute an euclidean norm with domain size dom_size of a scalar.

source

CompositionalNetworks.co_abs_diff_var_vars Function
julia
co_abs_diff_var_vars(x; nvars)

Return the absolute difference between x and the number of variables nvars.

source

CompositionalNetworks.co_var_minus_vars Function
julia
co_var_minus_vars(x; nvars)

Return the difference x - nvars if positive, 0.0 otherwise, where nvars denotes the numbers of variables.

source

CompositionalNetworks.co_vars_minus_var Function
julia
co_vars_minus_var(x; nvars)

Return the difference nvars - x if positive, 0.0 otherwise, where nvars denotes the numbers of variables.

source

Param: :val ​

CompositionalNetworks.co_abs_diff_var_val Function
julia
co_abs_diff_var_val(x; val)

Return the absolute difference between x and val.

source

CompositionalNetworks.co_var_minus_val Function
julia
co_var_minus_val(x; val)

Return the difference x - val if positive, 0.0 otherwise.

source

CompositionalNetworks.co_val_minus_var Function
julia
co_val_minus_var(x; val)

Return the difference val - x if positive, 0.0 otherwise.

source

CompositionalNetworks.co_euclidean_val Function
julia
co_euclidean_val(x; val, dom_size)

Compute an euclidean norm with domain size dom_size, weighted by val, of a scalar.

source

Layer generation ​

CompositionalNetworks.make_comparisons Function
julia
make_comparisons(param::Symbol)

Generate the comparison functions for the given parameter.

source

CompositionalNetworks.comparison_layer Function
julia
comparison_layer(param = false)

Generate the layer of transformations functions of the ICN. Iff param value is set, also includes all the parametric comparison with that value. The operations are mutually exclusive, that is only one will be selected.

source

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Introduction to QUBOConstraints.jl ​

Introduction to QUBOConstraints.jl.

Basic features ​

QUBOConstraints.QUBO_base Function
julia
QUBO_base(n, weight = 1)

A basic QUBO matrix to ensure that binarized variables keep a valid encoding.

source

QUBOConstraints.QUBO_linear_sum Function
julia
QUBO_linear_sum(n, σ)

One valid QUBO matrix given n variables and parameter σ for the linear sum constraint.

source

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Encoding for QUBO programs ​

QUBOConstraints.is_valid Function
julia
is_valid(x, encoding::Symbol = :none)

Check if x has a valid format for encoding.

For instance, if encoding == :one_hot, at most one bit of x can be set to 1.

source

QUBOConstraints.binarize Function
julia
binarize(x[, domain]; binarization = :one_hot)

Binarize x following the binarization encoding. If x is a vector (instead of a number per say), domain is optional.

source

QUBOConstraints.debinarize Function
julia
debinarize(x[, domain]; binarization = :one_hot)

Transform a binary vector into a number or a set of number. If domain is not given, it will compute a default value based on binarization and x.

source

- + \ No newline at end of file diff --git a/dev/learning/22_qubo_learning.html b/dev/learning/22_qubo_learning.html index 64d3c16..668f8f0 100644 --- a/dev/learning/22_qubo_learning.html +++ b/dev/learning/22_qubo_learning.html @@ -8,9 +8,9 @@ - + - + @@ -136,7 +136,7 @@ ) return train(X, penalty, to_domains(X, dom_stuff); optimizer, X_test) end - + \ No newline at end of file diff --git a/dev/learning/30_constraints_translator.html b/dev/learning/30_constraints_translator.html index f09129c..901efdd 100644 --- a/dev/learning/30_constraints_translator.html +++ b/dev/learning/30_constraints_translator.html @@ -8,9 +8,9 @@ - + - + @@ -18,7 +18,7 @@
Julia Constraints

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ConstraintsTranslator.jl ​

Documentation for ConstraintsTranslator.jl.

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Julia Constraints

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ConstraintLearning.jl ​

Documentation for ConstraintLearning.jl.

ConstraintLearning.ICNConfig Type
julia
struct ICNConfig{O <: ICNOptimizer}

A structure to hold the metric and optimizer configurations used in learning the weights of an ICN.

source

ConstraintLearning.ICNConfig Method
julia
ICNConfig(; metric = :hamming, optimizer = ICNGeneticOptimizer())

Constructor for ICNConfig. Defaults to hamming metric using a genetic algorithm.

source

ConstraintLearning.ICNGeneticOptimizer Method
julia
ICNGeneticOptimizer(; kargs...)

Default constructor to learn an ICN through a Genetic Algorithm. Default kargs TBW.

source

ConstraintLearning.ICNLocalSearchOptimizer Type
julia
ICNLocalSearchOptimizer(options = LocalSearchSolvers.Options())

Default constructor to learn an ICN through a CBLS solver.

source

ConstraintLearning.ICNOptimizer Type
julia
const ICNOptimizer = CompositionalNetworks.AbstractOptimizer

An abstract type for optmizers defined to learn ICNs.

source

ConstraintLearning.QUBOGradientOptimizer Method
julia
QUBOGradientOptimizer(; kargs...)

A QUBO optimizer based on gradient descent. Defaults TBW

source

ConstraintLearning.QUBOOptimizer Type
julia
const QUBOOptimizer = QUBOConstraints.AbstractOptimizer

An abstract type for optimizers used to learn QUBO matrices from constraints.

source

CompositionalNetworks.optimize! Method
julia
CompositionalNetworks.optimize!(icn, solutions, non_sltns, dom_size, metric, optimizer::ICNGeneticOptimizer; parameters...)

Extends the optimize! method to ICNGeneticOptimizer.

source

CompositionalNetworks.optimize! Method
julia
CompositionalNetworks.optimize!(icn, solutions, non_sltns, dom_size, metric, optimizer::ICNLocalSearchOptimizer; parameters...)

Extends the optimize! method to ICNLocalSearchOptimizer.

source

ConstraintLearning._optimize! Method
julia
_optimize!(icn, X, X_sols; metric = hamming, pop_size = 200)

Optimize and set the weights of an ICN with a given set of configuration X and solutions X_sols.

source

ConstraintLearning.domain_size Method
julia
domain_size(ds::Number)

Extends the domain_size function when ds is number (for dispatch purposes).

source

ConstraintLearning.generate_population Method
julia
generate_population(icn, pop_size

Generate a pôpulation of weights (individuals) for the genetic algorithm weighting icn.

source

ConstraintLearning.icn Method
julia
icn(X,X̅; kargs..., parameters...)

TBW

source

ConstraintLearning.loss Method
julia
loss(x, y, Q)

Loss of the prediction given by Q, a training set y, and a given configuration x.

source

ConstraintLearning.make_df Method
julia
make_df(X, Q, penalty, binarization, domains)

DataFrame arrangement to output some basic evaluation of a matrix Q.

source

ConstraintLearning.make_set_penalty Method
julia
make_set_penalty(X, X̅, args...; kargs)

Return a penalty function when the training set is already split into a pair of solutions X and non solutions X̅.

source

ConstraintLearning.make_training_sets Method
julia
make_training_sets(X, penalty, args...)

Return a pair of solutions and non solutions sets based on X and penalty.

source

ConstraintLearning.mutually_exclusive Method
julia
mutually_exclusive(layer, w)

Constraint ensuring that w encode exclusive operations in layer.

source

ConstraintLearning.no_empty_layer Method
julia
no_empty_layer(x; X = nothing)

Constraint ensuring that at least one operation is selected.

source

ConstraintLearning.optimize! Method
julia
optimize!(icn, X, X_sols, global_iter, local_iter; metric=hamming, popSize=100)

Optimize and set the weights of an ICN with a given set of configuration X and solutions X_sols. The best weights among global_iter will be set.

source

ConstraintLearning.parameter_specific_operations Method
julia
parameter_specific_operations(x; X = nothing)

Constraint ensuring that at least one operation related to parameters is selected if the error function to be learned is parametric.

source

ConstraintLearning.predict Method
julia
predict(x, Q)

Return the predictions given by Q for a given configuration x.

source

ConstraintLearning.preliminaries Method
julia
preliminaries(args)

Preliminaries to the training process in a QUBOGradientOptimizer run.

source

ConstraintLearning.qubo Function
julia
qubo(X,X̅; kargs..., parameters...)

TBW

source

ConstraintLearning.sub_eltype Method
julia
sub_eltype(X)

Return the element type of of the first element of a collection.

source

ConstraintLearning.train! Method
julia
train!(Q, X, penalty, η, precision, X_test, oversampling, binarization, domains)

Training inner method.

source

ConstraintLearning.train Method
julia
train(X, penalty[, d]; optimizer = QUBOGradientOptimizer(), X_test = X)

Learn a QUBO matrix on training set X for a constraint defined by penalty with optional domain information d. By default, it uses a QUBOGradientOptimizer and X as a testing set.

source

ConstraintLearning.δ Method
julia
δ(X[, Y]; discrete = true)

Compute the extrema over a collection X``or a pair of collection(X, Y)`.

source

- + \ No newline at end of file diff --git a/dev/perf/00_perf_checker.html b/dev/perf/00_perf_checker.html index ce83950..8fe3d9d 100644 --- a/dev/perf/00_perf_checker.html +++ b/dev/perf/00_perf_checker.html @@ -8,9 +8,9 @@ - + - + @@ -30,7 +30,7 @@ # Visualization of the results using Makie checkres_to_scatterlines(results)

The config dictionary can take many options, depending on the backend.

Some of the commonly used options are:

  • :PATH => The path where to the default environment of julia when creating a new process.

  • :pkgs => A list of versions to test performance for. Its defined as the Tuple, (name::String, option::Symbol, versions::Vector{VersionNumber}, last_or_first::Bool) Can be given as follows:

    • name is the name of the package.

    • option is one of the 5 symbols:

      • :patches: last patch or first patch of a version

      • :breaking: last breaking or next breaking version

      • :major: previous or next major version

      • :minor: previous or next minor version

      • :custom: custom version numbers (provide any boolean value for last_or_first in this case as it doesn't matter)

    • versions: The input for the provided option

    • last_or_first: Input for the provided option

  • :tags => A list of tags (a vector of symbols) to easily tag performance tests.

  • :devops => Giving a custom input to Pkg.develop. Intended to be used to test performance of a local development branch of a pacakge with previous versions. Often can be used as simply as :devops => "MyPackageName"

  • :threads => An integer to select the number of threads to start Julia with.

Checkout the documentation of the other backends for more default options and the default values.

- + \ No newline at end of file diff --git a/dev/perf/10_tutorial.html b/dev/perf/10_tutorial.html index d7286a1..69b0c36 100644 --- a/dev/perf/10_tutorial.html +++ b/dev/perf/10_tutorial.html @@ -8,9 +8,9 @@ - + - + @@ -57,7 +57,7 @@ c2 = checkres_to_boxplots(x, Val(:chairmark); kwarg) save(joinpath(@__DIR__, "visuals", "chair_boxplots_$kwarg.png"), c2) end

d here is the configuration dictionary. x stores the results from performance testing

The code below the macro call is for plotting and storing the plots. It creates the visuals folder and stores the following plots in the folder:

Boxplots from Chairmarks for allocations:

chair_boxplots

Boxplots from Chairmarks for times:

chair_times

Evolution of different metrics across versions according to Chairmarks:

chair_evolution - + \ No newline at end of file diff --git a/dev/perf/20_perf_interface.html b/dev/perf/20_perf_interface.html index 98ef481..4710c9f 100644 --- a/dev/perf/20_perf_interface.html +++ b/dev/perf/20_perf_interface.html @@ -8,9 +8,9 @@ - + - + @@ -44,7 +44,7 @@ allocs = [chair.samples[i].allocs for i in 1:l] return Table(times = times, gctimes = gctimes, bytes = bytes, allocs = allocs) end

There are also other functions that can be overloaded, mostly related to plotting but these are the basic functions to extend PerfChecker for a custom backend.

- + \ No newline at end of file diff --git a/dev/perf/30_benchmark_ext.html b/dev/perf/30_benchmark_ext.html index 8f5f22d..008510f 100644 --- a/dev/perf/30_benchmark_ext.html +++ b/dev/perf/30_benchmark_ext.html @@ -8,9 +8,9 @@ - + - + @@ -35,7 +35,7 @@ :gcsample => BenchmarkTools.DEFAULT_PARAMETERS.gcsample :time_tolerance => BenchmarkTools.DEFAULT_PARAMETERS.time_tolerance :memory_tolerance => BenchmarkTools.DEFAULT_PARAMETERS.memory_tolerance - + \ No newline at end of file diff --git a/dev/perf/40_chairmarks_ext.html b/dev/perf/40_chairmarks_ext.html index 53c5aff..6b921ee 100644 --- a/dev/perf/40_chairmarks_ext.html +++ b/dev/perf/40_chairmarks_ext.html @@ -8,9 +8,9 @@ - + - + @@ -31,7 +31,7 @@ :seconds => 1, :samples => nothing :gc => true - + \ No newline at end of file diff --git a/dev/perf/90_api.html b/dev/perf/90_api.html index f87ea5c..99fef8a 100644 --- a/dev/perf/90_api.html +++ b/dev/perf/90_api.html @@ -8,9 +8,9 @@ - + - + @@ -26,7 +26,7 @@ v"0.1.1" v"0.1.3" v"0.1.2"

source

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Julia Constraints

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- + \ No newline at end of file diff --git a/dev/solvers/10_cbls.html b/dev/solvers/10_cbls.html index f145624..5a89609 100644 --- a/dev/solvers/10_cbls.html +++ b/dev/solvers/10_cbls.html @@ -8,11 +8,11 @@ - + - + - + @@ -24,8 +24,8 @@ @objective(model, ScalarFunction(f)) # Generic use -@objective(model, ScalarFunction(f, X))

source

CBLS.Sum Type

Global constraint ensuring that the sum of the variables in x satisfies a given condition.

source

CBLS.Supports Type

Global constraint ensuring that the tuple x matches a configuration listed within the support set pair_vars. This constraint is derived from the extension model, specifying that x must be one of the explicitly defined supported configurations: x ∈ pair_vars. It is utilized to directly declare the tuples that are valid and should be included in the solution space.

julia
@constraint(model, X in Supports(; pair_vars))

source

Base.copy Method
julia
Base.copy(set::MOIError) = begin

DOCSTRING

source

Base.copy Method
julia
Base.copy(set::MOIIntention)

Copy an intention set.

Arguments

  • set::MOIIntention: The intention set to be copied.

Returns

  • MOIIntention: A copy of the intention set.

source

Base.copy Method
julia
Base.copy(set::DiscreteSet)

Copy a discrete set.

Arguments

  • set::DiscreteSet: The discrete set to be copied.

Returns

  • DiscreteSet: A copy of the discrete set.

source

Base.copy Method
julia
Base.copy(op::F) where {F <: Function}

Copy a function.

Arguments

  • op::F: The function to be copied.

Returns

  • F: The copied function.

source

Base.copy Method
julia
Base.copy(::Nothing)

Copy a Nothing value.

Arguments

  • ::Nothing: The Nothing value to be copied.

Returns

  • Nothing: The copied Nothing value.

source

JuMP.build_variable Method
julia
JuMP.build_variable(::Function, info::JuMP.VariableInfo, set::T) where T <: MOI.AbstractScalarSet

Create a variable constrained by a scalar set.

Arguments

  • info::JuMP.VariableInfo: Information about the variable to be created.

  • set::T where T <: MOI.AbstractScalarSet: The set defining the constraints on the variable.

Returns

  • JuMP.VariableConstrainedOnCreation: A variable constrained by the specified set.

source

JuMP.moi_set Method
julia
JuMP.moi_set(set::Intention, dim::Int) -> MOIIntention

Convert an Intention set to a MOIIntention set.

Arguments

  • set::Intention: The intention set to be converted.

  • dim::Int: The dimension of the vector set.

Returns

  • MOIIntention: The converted MOIIntention set.

source

JuMP.moi_set Method
julia
JuMP.moi_set(set::Predicate, dim::Int) -> MOIIntention

Convert a Predicate set to a MOIIntention set.

Arguments

  • set::Predicate: The predicate set to be converted.

  • dim::Int: The dimension of the vector set.

Returns

  • MOIIntention: The converted MOIIntention set.

source

MathOptInterface.add_constraint Method
julia
MOI.add_constraint(optimizer::Optimizer, vars::MOI.VectorOfVariables, set::MOIError)

DOCSTRING

Arguments:

  • optimizer: DESCRIPTION

  • vars: DESCRIPTION

  • set: DESCRIPTION

source

MathOptInterface.add_constraint Method
julia
MOI.add_constraint(optimizer::Optimizer, vars::MOI.VectorOfVariables, set::MOIIntention{F}) where {F <: Function}

Add an intention constraint to the optimizer.

Arguments

  • optimizer::Optimizer: The optimizer instance.

  • vars::MOI.VectorOfVariables: The variables for the constraint.

  • set::MOIIntention{F}: The intention set defining the constraint.

Returns

  • CI{VOV, MOIIntention{F}}: The constraint index.

source

MathOptInterface.add_constraint Method
julia
MOI.add_constraint(optimizer::Optimizer, v::VI, set::DiscreteSet{T}) where T <: Number

DOCSTRING

Arguments:

  • optimizer: DESCRIPTION

  • v: DESCRIPTION

  • set: DESCRIPTION

source

MathOptInterface.add_variable Method
julia
MOI.add_variable(model::Optimizer) = begin

DOCSTRING

source

MathOptInterface.copy_to Method
julia
MOI.copy_to(model::Optimizer, src::MOI.ModelLike)

Copy the source model to the optimizer.

Arguments

  • model::Optimizer: The optimizer instance.

  • src::MOI.ModelLike: The source model to be copied.

Returns

  • Nothing

source

MathOptInterface.empty! Method
julia
MOI.empty!(opt)

Empty the optimizer.

Arguments

  • opt::Optimizer: The optimizer instance.

Returns

  • Nothing

source

MathOptInterface.get Method
julia
MOI.get(::Optimizer, ::MOI.SolverName)

Get the name of the solver.

Arguments

  • ::Optimizer: The optimizer instance.

Returns

  • String: The name of the solver.

source

MathOptInterface.get Method
julia
Moi.get(::Optimizer, ::MOI.SolverVersion)

Get the version of the solver, here LocalSearchSolvers.jl.

source

MathOptInterface.is_empty Method
julia
MOI.is_empty(model::Optimizer)

Check if the model is empty.

Arguments

  • model::Optimizer: The optimizer instance.

Returns

  • Bool: True if the model is empty, false otherwise.

source

MathOptInterface.is_valid Method
julia
MOI.is_valid(optimizer::Optimizer, index::CI{VI, MOI.Integer})

Check if an index is valid for the optimizer.

Arguments

  • optimizer::Optimizer: The optimizer instance.

  • index::CI{VI, MOI.Integer}: The index to be checked.

Returns

  • Bool: True if the index is valid, false otherwise.

source

MathOptInterface.optimize! Method
julia
MOI.optimize!(model::Optimizer)

Optimize the model using the optimizer.

Arguments

  • model::Optimizer: The optimizer instance.

Returns

  • Nothing

source

MathOptInterface.set Function
julia
MOI.set(::Optimizer, ::MOI.Silent, bool = true)

Set the verbosity of the solver.

Arguments

  • ::Optimizer: The optimizer instance.

  • ::MOI.Silent: The silent option for the solver.

  • bool::Bool: Whether to set the solver to silent mode.

Returns

  • Nothing

source

MathOptInterface.set Method
julia
MOI.set(model::Optimizer, p::MOI.RawOptimizerAttribute, value)

Set a RawOptimizerAttribute to value

source

MathOptInterface.set Method
julia
MOI.set(model::Optimizer, ::MOI.TimeLimitSec, value::Union{Nothing,Float64})

Set the time limit

source

MathOptInterface.supports_constraint Method
julia
MOI.supports_constraint(::Optimizer, ::Type{VOV}, ::Type{MOIError}) = begin

DOCSTRING

Arguments:

  • ``: DESCRIPTION

  • ``: DESCRIPTION

  • ``: DESCRIPTION

source

MathOptInterface.supports_constraint Method
julia
MOI.supports_constraint(::Optimizer, ::Type{VOV}, ::Type{MOIIntention{F}}) where {F <: Function}

Check if the optimizer supports a given intention constraint.

Arguments

  • ::Optimizer: The optimizer instance.

  • ::Type{VOV}: The type of the variable.

  • ::Type{MOIIntention{F}}: The type of the intention.

Returns

  • Bool: True if the optimizer supports the constraint, false otherwise.

source

MathOptInterface.supports_incremental_interface Method
julia
MOI.supports_incremental_interface(::Optimizer)

Check if the optimizer supports incremental interface.

Arguments

  • ::Optimizer: The optimizer instance.

Returns

  • Bool: True if the optimizer supports incremental interface, false otherwise.

source

- +@objective(model, ScalarFunction(f, X))

source

CBLS.Sum Type

Global constraint ensuring that the sum of the variables in x satisfies a given condition.

source

CBLS.Supports Type

Global constraint ensuring that the tuple x matches a configuration listed within the support set pair_vars. This constraint is derived from the extension model, specifying that x must be one of the explicitly defined supported configurations: x ∈ pair_vars. It is utilized to directly declare the tuples that are valid and should be included in the solution space.

julia
@constraint(model, X in Supports(; pair_vars))

source

Base.copy Method
julia
Base.copy(set::DiscreteSet)

Copy a discrete set.

Arguments

  • set::DiscreteSet: The discrete set to be copied.

Returns

  • DiscreteSet: A copy of the discrete set.

source

Base.copy Method
julia
Base.copy(set::MOIError) = begin

DOCSTRING

source

Base.copy Method
julia
Base.copy(set::MOIIntention)

Copy an intention set.

Arguments

  • set::MOIIntention: The intention set to be copied.

Returns

  • MOIIntention: A copy of the intention set.

source

Base.copy Method
julia
Base.copy(op::F) where {F <: Function}

Copy a function.

Arguments

  • op::F: The function to be copied.

Returns

  • F: The copied function.

source

Base.copy Method
julia
Base.copy(::Nothing)

Copy a Nothing value.

Arguments

  • ::Nothing: The Nothing value to be copied.

Returns

  • Nothing: The copied Nothing value.

source

JuMP.build_variable Method
julia
JuMP.build_variable(::Function, info::JuMP.VariableInfo, set::T) where T <: MOI.AbstractScalarSet

Create a variable constrained by a scalar set.

Arguments

  • info::JuMP.VariableInfo: Information about the variable to be created.

  • set::T where T <: MOI.AbstractScalarSet: The set defining the constraints on the variable.

Returns

  • JuMP.VariableConstrainedOnCreation: A variable constrained by the specified set.

source

JuMP.moi_set Method
julia
JuMP.moi_set(set::Intention, dim::Int) -> MOIIntention

Convert an Intention set to a MOIIntention set.

Arguments

  • set::Intention: The intention set to be converted.

  • dim::Int: The dimension of the vector set.

Returns

  • MOIIntention: The converted MOIIntention set.

source

JuMP.moi_set Method
julia
JuMP.moi_set(set::Predicate, dim::Int) -> MOIIntention

Convert a Predicate set to a MOIIntention set.

Arguments

  • set::Predicate: The predicate set to be converted.

  • dim::Int: The dimension of the vector set.

Returns

  • MOIIntention: The converted MOIIntention set.

source

MathOptInterface.add_constraint Method
julia
MOI.add_constraint(optimizer::Optimizer, vars::MOI.VectorOfVariables, set::MOIError)

DOCSTRING

Arguments:

  • optimizer: DESCRIPTION

  • vars: DESCRIPTION

  • set: DESCRIPTION

source

MathOptInterface.add_constraint Method
julia
MOI.add_constraint(optimizer::Optimizer, vars::MOI.VectorOfVariables, set::MOIIntention{F}) where {F <: Function}

Add an intention constraint to the optimizer.

Arguments

  • optimizer::Optimizer: The optimizer instance.

  • vars::MOI.VectorOfVariables: The variables for the constraint.

  • set::MOIIntention{F}: The intention set defining the constraint.

Returns

  • CI{VOV, MOIIntention{F}}: The constraint index.

source

MathOptInterface.add_constraint Method
julia
MOI.add_constraint(optimizer::Optimizer, v::VI, set::DiscreteSet{T}) where T <: Number

DOCSTRING

Arguments:

  • optimizer: DESCRIPTION

  • v: DESCRIPTION

  • set: DESCRIPTION

source

MathOptInterface.add_variable Method
julia
MOI.add_variable(model::Optimizer) = begin

DOCSTRING

source

MathOptInterface.copy_to Method
julia
MOI.copy_to(model::Optimizer, src::MOI.ModelLike)

Copy the source model to the optimizer.

Arguments

  • model::Optimizer: The optimizer instance.

  • src::MOI.ModelLike: The source model to be copied.

Returns

  • Nothing

source

MathOptInterface.empty! Method
julia
MOI.empty!(opt)

Empty the optimizer.

Arguments

  • opt::Optimizer: The optimizer instance.

Returns

  • Nothing

source

MathOptInterface.get Method
julia
MOI.get(::Optimizer, ::MOI.SolverName)

Get the name of the solver.

Arguments

  • ::Optimizer: The optimizer instance.

Returns

  • String: The name of the solver.

source

MathOptInterface.get Method
julia
Moi.get(::Optimizer, ::MOI.SolverVersion)

Get the version of the solver, here LocalSearchSolvers.jl.

source

MathOptInterface.is_empty Method
julia
MOI.is_empty(model::Optimizer)

Check if the model is empty.

Arguments

  • model::Optimizer: The optimizer instance.

Returns

  • Bool: True if the model is empty, false otherwise.

source

MathOptInterface.is_valid Method
julia
MOI.is_valid(optimizer::Optimizer, index::CI{VI, MOI.Integer})

Check if an index is valid for the optimizer.

Arguments

  • optimizer::Optimizer: The optimizer instance.

  • index::CI{VI, MOI.Integer}: The index to be checked.

Returns

  • Bool: True if the index is valid, false otherwise.

source

MathOptInterface.optimize! Method
julia
MOI.optimize!(model::Optimizer)

Optimize the model using the optimizer.

Arguments

  • model::Optimizer: The optimizer instance.

Returns

  • Nothing

source

MathOptInterface.set Function
julia
MOI.set(::Optimizer, ::MOI.Silent, bool = true)

Set the verbosity of the solver.

Arguments

  • ::Optimizer: The optimizer instance.

  • ::MOI.Silent: The silent option for the solver.

  • bool::Bool: Whether to set the solver to silent mode.

Returns

  • Nothing

source

MathOptInterface.set Method
julia
MOI.set(model::Optimizer, p::MOI.RawOptimizerAttribute, value)

Set a RawOptimizerAttribute to value

source

MathOptInterface.set Method
julia
MOI.set(model::Optimizer, ::MOI.TimeLimitSec, value::Union{Nothing,Float64})

Set the time limit

source

MathOptInterface.supports_constraint Method
julia
MOI.supports_constraint(::Optimizer, ::Type{VOV}, ::Type{MOIError}) = begin

DOCSTRING

Arguments:

  • ``: DESCRIPTION

  • ``: DESCRIPTION

  • ``: DESCRIPTION

source

MathOptInterface.supports_constraint Method
julia
MOI.supports_constraint(::Optimizer, ::Type{VOV}, ::Type{MOIIntention{F}}) where {F <: Function}

Check if the optimizer supports a given intention constraint.

Arguments

  • ::Optimizer: The optimizer instance.

  • ::Type{VOV}: The type of the variable.

  • ::Type{MOIIntention{F}}: The type of the intention.

Returns

  • Bool: True if the optimizer supports the constraint, false otherwise.

source

MathOptInterface.supports_incremental_interface Method
julia
MOI.supports_incremental_interface(::Optimizer)

Check if the optimizer supports incremental interface.

Arguments

  • ::Optimizer: The optimizer instance.

Returns

  • Bool: True if the optimizer supports incremental interface, false otherwise.

source

+ \ No newline at end of file diff --git a/dev/solvers/40_constraint_explorer.html b/dev/solvers/40_constraint_explorer.html index 7897bdc..728da98 100644 --- a/dev/solvers/40_constraint_explorer.html +++ b/dev/solvers/40_constraint_explorer.html @@ -8,17 +8,17 @@ - + - + - + -
Julia Constraints

Appearance

ConstraintExplorer.jl ​

Documentation for ConstraintExplorer.jl.

- +
Julia Constraints

Appearance

ConstraintExplorer.jl ​

Documentation for ConstraintExplorer.jl.

ConstraintExplorer.MOIInstantiation Type
julia
MOIInstantiation{T <: Number, V <: Vector{T}} <: MOI.AbstractVectorSet

DOCSTRING

source

ConstraintExplorer.MOISupports Type
julia
MOISupports{T <: Number, V <: Vector{Vector{T}}} <: MOI.AbstractVectorSet

DOCSTRING

source

+ \ No newline at end of file diff --git a/dev/solvers/50_local_search_solvers.html b/dev/solvers/50_local_search_solvers.html index 09ef7aa..136330a 100644 --- a/dev/solvers/50_local_search_solvers.html +++ b/dev/solvers/50_local_search_solvers.html @@ -8,9 +8,9 @@ - + - + @@ -53,7 +53,7 @@ variable(domain::AbstractDomain, name::AbstractString) where D <: AbstractDomain

Construct a variable with discrete domain. See the domain method for other options.

julia
d = domain([1,2,3,4], types = :indices)
 x1 = variable(d, "x1")
 x2 = variable([-89,56,28], "x2", domain = :indices)

source

- + \ No newline at end of file diff --git a/dev/solvers/80_meta_strategist.html b/dev/solvers/80_meta_strategist.html index 3a0fae3..3c757f7 100644 --- a/dev/solvers/80_meta_strategist.html +++ b/dev/solvers/80_meta_strategist.html @@ -8,9 +8,9 @@ - + - + @@ -18,7 +18,7 @@
Julia Constraints

Appearance

MetaStrategist.jl ​

Documentation for MetaStrategist.jl.

- + \ No newline at end of file