ParetoEnsembles.jl - Pareto Optimal Ensemble Techniques

ParetoEnsembles.jl is a Julia package that implements the Pareto Optimal Ensemble Techniques (POETs) method for multiobjective optimization using simulated annealing with Pareto ranking.

References

• Song S, Chakrabarti A, and J. Varner (2010) Identifying ensembles of signal transduction models using Pareto Optimal Ensemble Techniques (POETs). Biotechnology Journal DOI: 10.1002/biot.201000059
• Bassen D, Vilkhovoy M, Minot M, Butcher J and J. Varner (2016) JuPOETs: A Constrained Multiobjective Optimization Approach to Estimate Biochemical Model Ensembles in the Julia Programming Language. bioArXiv doi: http://dx.doi.org/10.1101/056044

Installation

using Pkg
Pkg.add(url="https://github.com/varnerlab/ParetoEnsembles.jl")

Usage

using ParetoEnsembles

ParetoEnsembles requires four user-defined callback functions:

Function	Signature	Purpose
objective_function	(parameter_array) -> error_matrix	Evaluates fitness (returns n_objectives × 1 array)
neighbor_function	(parameter_array) -> new_parameter_array	Generates a candidate solution from the current one
acceptance_probability_function	(rank_array, temperature) -> Float64	Computes probability of accepting a new solution
cooling_function	(temperature) -> new_temperature	Decreases temperature for the annealing schedule

Running the optimizer

(error_cache, parameter_cache, rank_array) = estimate_ensemble(
    objective_function,
    neighbor_function,
    acceptance_probability_function,
    cooling_function,
    initial_parameter_array;
    rank_cutoff=4.0,
    maximum_number_of_iterations=20,
    temperature_min=0.0001,
    show_trace=true
)

Returns:

• error_cache - objective values for retained solutions (n_objectives × n_solutions)
• parameter_cache - parameter vectors for retained solutions (n_params × n_solutions)
• rank_array - Pareto rank of each retained solution (0 = Pareto optimal)

Pareto ranking

ranks = rank_function(error_cache)

Computes the Pareto rank for each column in the error cache. A rank of 0 means the solution is on the Pareto front (not dominated by any other solution).

Examples

See the sample/biochemical directory for a complete example of biochemical model parameter estimation from four conflicting training data sets. The driver is run_biochemical_test.jl, with callback functions in hcmem_lib.jl.

Test problems (Binh-Korn and Fonseca-Fleming benchmarks) are in the test/ directory.

Testing

using Pkg
Pkg.test("ParetoEnsembles")