From 106ccbcef62a6d5d1565ee5387593ccd08e3bc8e Mon Sep 17 00:00:00 2001 From: Matheus Santana Lima Date: Thu, 13 May 2021 18:00:40 -0300 Subject: [PATCH 1/2] Quantitative Algorithm for solving the TSP problem --- python/qa/Makefile | 6 + python/qa/README.md | 109 ++++ python/qa/SA-Benchmark.py | 301 +++++++++++ python/qa/TSP-Quantitative-Algorithm.py | 259 +++++++++ python/qa/a280.tsp | 287 ++++++++++ python/qa/license | 674 ++++++++++++++++++++++++ python/qa/output/qa_.best_cost.txt | 50 ++ python/qa/output/qa_.init_cost.txt | 50 ++ python/qa/output/qa_.time2run.txt | 50 ++ python/qa/output/sa_.best_cost.txt | 50 ++ python/qa/output/sa_.time2run.txt | 50 ++ python/qa/run.sh | 13 + python/qa/small_test5.tsp | 12 + 13 files changed, 1911 insertions(+) create mode 100644 python/qa/Makefile create mode 100644 python/qa/README.md create mode 100644 python/qa/SA-Benchmark.py create mode 100644 python/qa/TSP-Quantitative-Algorithm.py create mode 100644 python/qa/a280.tsp create mode 100644 python/qa/license create mode 100644 python/qa/output/qa_.best_cost.txt create mode 100644 python/qa/output/qa_.init_cost.txt create mode 100644 python/qa/output/qa_.time2run.txt create mode 100644 python/qa/output/sa_.best_cost.txt create mode 100644 python/qa/output/sa_.time2run.txt create mode 100755 python/qa/run.sh create mode 100644 python/qa/small_test5.tsp diff --git a/python/qa/Makefile b/python/qa/Makefile new file mode 100644 index 0000000..c2e880c --- /dev/null +++ b/python/qa/Makefile @@ -0,0 +1,6 @@ +TSP_FILE_PATH=a280.tsp +TSP_FILE_PATH=small_test5.tsp + + +all: + python TSP-simulated-annealing.py $(TSP_FILE_PATH) \ No newline at end of file diff --git a/python/qa/README.md b/python/qa/README.md new file mode 100644 index 0000000..4feec6d --- /dev/null +++ b/python/qa/README.md @@ -0,0 +1,109 @@ +Matheus Lima (Computer Science, Federal University of Sao Carlos, Brazil) + +(1) To run: + +$ ./run.sh + +(2) To change the path of the TSP data file: change the path in the Makefile. + + +# Quantitative Algorithm to solve the TSP problem + +The proposed Quantitative Algorithm is based on elements of Information Theory and Kolmogorov Complexity. The algorithm is described in more details in the paper "Information theory inspired optimization algorithm for efficient service orchestration in distributed systems" [https://doi.org/10.1371/journal.pone.0242285] + +It's method is based on the assumption that the output of a given utility function such as the euclidean distance can be modeled by a probabilistic density function defined by a log-normal distribution. Therefore the entropy can be calculated and the level of state-output uncertainty about the best candidate string can be measured by the Shannon entropy function. The amount of information encoded by each sequence of a random candidate solution is defined by the Kolmogorov complexity with a mean and standard deviation. There is shared information between the total cost distance (utility function) and the solution encoded in the string that forms any random valid candidate. + +This meta heuristics method proposed an alternative view on the TSP problem. The salesman needs to evaluate from a random set of candidate solutions where the information "at hand" could lead to the optimal solution with a given probability of Success and Failure. The salesman's needs to "place a bet" wherever any solution will find the best optimal solution. Unless there is inside information the salesmans is not able to know the candidate solution route that will find the optimal value with higher certainty. If the right candidate is chosen it will generate the path to the best optimal global value, but if it chooses the wrong path the salesmans will be destined to find only a local optima result such as in the hill climbing problem. + +This problem is similar to the Gambler's Ruin problem in statistics where a player of a game with negative expected value will eventually go broke and lose. In probability theory, the optimal bet size can be calculated by the Kelly criterion and is found by maximizing the expected value of the logarithm of wealth. This method provides the minimal amount of wealth(fractional betting) a given player must place at each bet to optimize the rate of wealth return and avoid the risk of ruin in the long-run. + +Algorithms such as Genetic Algorithm, Ant Colony and Neural Networks are based on nature inspired models that replicate the mechanics of living organisms or the decaying of a dependent temperature function (gradient) of metals such as Simulated Annealing to optimize the computational requirements imposed by the NP complexity. The Quantitative Algorithms defined here is a stochastic process that simulates the amount of entropy in a Bernoulli process and is the smallest encoded program that solves the TSP and halt, for a given degree of freedom and a turing-shannon machine. The proposed method does not depends on heuristics that are biased towards a given encoded schema and is therefore more efficient as it requires less code operations and string permutations to produce near-optimal results with the same or better quality per unit of computing running time than other finite-traditional algorithms. + +Similarly to the Manhattan meta-heuristics in Simulated Annealing, the Quantitative Algorithm accepts solutions with worst quality occasionally with a decaying probability schema. For each iteration the probability of success is decreased by a given parameter rate. The Kelly fraction is then used to measure the amount of useful encoded information for the simulated function state. The ratio of quality improvement is defined as the expected returned cost optimization value for a sample distribution. In the TSP problem this is the average reduction in cost distance variable (from an array of candidate solutions). If the solution A has cost c(A)=10 and alternative solution B has cost derived by c(B)=100 then B is 90% more expensive (worst) than random sequence A. In a sequence of costs C=[10,9,8,2,3,2,3,4] with Mean=5.125 and Standard Deviation=9.609375. + +As the QA iterates, the entropy is proportional reduced as the machine evaluates the search-space and the probability function decay in time. The candidate solutions are randomly generated by swapping two symbols in a random model sequence. Each symbols encode the euclidean coordinates in a 2D graph. The utility function is defined as the euclidean distance function between m nodes. The salesmans wants to reduce the distances for a given path as best as possible and find the shortest route. The method iterates sequentially until the maximum number of executions allowed is reached. If the alternative random solution is smaller (better) than the current best known solution then the best known state is updated with the alternative state values. However, if the alternative solution produces distances with larger distances, then the solution is only accepted according to the output binary values from the simulated kelly criterion method. If the return is True then the alternative with negative gain is temporarily accepted as the best known solution. This approach allows variability in the beginning of the execution process but gradually reduces the probability of acceptance, but still occasionally accepting worst alternatives, to avoid lock in a local minima state. + +The pseudo code is demonstrated below: + +``` +# set parameters + +prob_sucess = 1.0 +prob_loss = 1 - prob_sucess +decay_rate = 0.001 +improvement_ratio = average_solution_cost_quality_improvement / average_solution_cost_quality_loss +f_kelly = prob_sucess - ((1-prob_sucess)/improvement_ratio) + +# generate first random solution + +best_solution = generate_random_solution() +best_solution_cost = getCost(best_solution) + +# runs until max iteration parameter is reached +For i in (0..N): + + # generate new random solution + new_solution = generate_random_solution() + new_solution_cost = getCost(new_solution) + + # if found new solution; accepts; iterates... + + if new_solution_cost < best_solution_cost: + best_solution = new_solution_cost + best_solution_cost = new_solution_cost + else: + # Simulate Entropy Decay + + # get a random index number _val set by a normal distribution between 0 and 1 + _val = generate_a_value_random(0,1) + + # simulate the uncertainty level with the kelly criterion + f_kelly = prob_sucess - ((1-prob_sucess)/improvement_ratio) + + # control function: bernoulli process to avoid local minima solutions in the long run + bernoulli_sequence = generate_bernoulli_sequence(p_true=1/100) + + # if index value is less than the kelly percentage or the control function + if (_val_rnd < f_kelly) or bernoulli_sequence == 1 + + # temporarily accept candidate solution with worst quality + best_solution = new_solution_cost + best_solution_cost = new_solution_cost + + prob_sucess = 1 - decay_rate +``` + +The Quantitative Algorithm (QA) is implemented in python and the output is recorded. A simulation was deployed for a city with 280 nodes with a max of 3000 iterations. The performance was compared to a benchmark heuristics defined by the Simulated Annealing algorithm (SA). The trial size is n=100 split between QA=50 and SA=50, for a two-tailed t-test for 2 independent means. The average initial solution cost is 34012.854. The average best cost for QA=30036.7 and SA=31344.41 and standard deviation QA=631.6520 and SA=410.536. Therefore QA results have a improvement rate of 4.353% than the benchmark SA algorithm. + +The 50 best-candidate solutions produced by QA compared to the 50 near-optimal solutions in the control (benchmark) group SA demonstrated significantly better cost with smaller total route distance in a 2D graph, the t-value is 12.27454. The p-value is < .00001. The result is significant at p < .05. + +# Scores Calculations + +## Quantitative Algorithm +``` +N1: 50 +df1 = N - 1 = 50 - 1 = 49 +M1: 30036.7 +SS1: 19550233.73 +s21 = SS1/(N - 1) = 19550233.73/(50-1) = 398984.36 +``` + +## Simulated Annealing +``` +N2: 50 +df2 = N - 1 = 50 - 1 = 49 +M2: 31344.41 +SS2: 8258472.24 +s22 = SS2/(N - 1) = 8258472.24/(50-1) = 168540.25 +``` + +## T-value Calculation +``` +s2p = ((df1/(df1 + df2)) * s21) + ((df2/(df2 + df2)) * s22) = ((49/98) * 398984.36) + ((49/98) * 168540.25) = 283762.31 + +s2M1 = s2p/N1 = 283762.31/50 = 5675.25 +s2M2 = s2p/N2 = 283762.31/50 = 5675.25 + +t = (M1 - M2)/√(s2M1 + s2M2) = -1307.71/√11350.49 = -12.27 + +``` \ No newline at end of file diff --git a/python/qa/SA-Benchmark.py b/python/qa/SA-Benchmark.py new file mode 100644 index 0000000..13bfb58 --- /dev/null +++ b/python/qa/SA-Benchmark.py @@ -0,0 +1,301 @@ +############################################################################### +# Mike Feilbach +# University of Texas at Austin +# CS 345, Spring 2016 +# Prof. Rellermeyer +############################################################################### + +import sys +import math +import random +import copy + + +DEBUG_SET = True + + +def debug(label, _str, stop=False, key="none_", write_to_file=True): + if DEBUG_SET == True: + print(key + label, _str) + + if write_to_file == True: + filename = "./output/"+key+"."+label+".txt" + filename = filename.replace(" ", "") + f = open(filename, "a") + f.write(str(_str)+"\n") + f.close() + + if stop == True: + input() + else: + print() + + + + +############################################################################### +# Each Node represents a pyhsical location in the TSP problem. +############################################################################### +class Node: + + def __init__(self, name, x_coord, y_coord): + self.name = name + self.x_coord = x_coord + self.y_coord = y_coord + + def getName(self): + return self.name + + def getXCoordinate(self): + return self.x_coord + + def getYCoordinate(self): + return self.y_coord + + def __repr__(self): + return '[' + self.name + ', ' + str(self.x_coord) + ', ' + str(self.y_coord) + ']\n' + + +############################################################################### +# Returns the Edclidean distance between two Nodes. +############################################################################### +def distanceBetween(NodeA, NodeB): + + return math.sqrt(((NodeB.getXCoordinate() - NodeA.getXCoordinate()) ** 2) + + ((NodeB.getYCoordinate() - NodeA.getYCoordinate()) ** 2)) + + +############################################################################### +# Parses the a280.tsp file (the TSP input file). Returns a list of Nodes, +# where each Node represents a location in the file. +############################################################################### +def parseTSPFile(TSPfileName): + + file = open(TSPfileName, 'r') + + # List of Nodes to return. + listOfNodes = [] + + # Parse line by line. + for line in file: + splitList = line.split(); + + # If we received three digits, it is a location in the TSP file. + if all(item.isdigit() for item in splitList): + if len(splitList) == 3: + + # Make a node out of this location. + listOfNodes.append(Node(splitList[0], float(splitList[1]), float(splitList[2]))) + + return listOfNodes + + +############################################################################### +# Returns the distance of this tour. The tour goes from the first Node +# in the list to the second Node, to the third Node,..., to the last Node, and +# back to the first Node. +############################################################################### +def tourDistance(listOfNodes): + + distance = 0; + + # Get the distance from Node 1 to Node 2,... to Node N, where N is + # the last node in the list. + for i in range(0, len(listOfNodes) - 1): + + distance = distance + distanceBetween(listOfNodes[i], listOfNodes[i + 1]) + + + # Get the distance from Node N back to Node 1. + # Note: no error checking here, beacuse the input file is assumed to have + # locations in it. + distance += distanceBetween(listOfNodes[len(listOfNodes) - 1], listOfNodes[0]) + + return distance + + +############################################################################### +# Generates a neighboring tour, given a current tour. For now, this will +# simply swap two locations on the tour. For example, [1, 2, 3, 4] might go to +# [1, 4, 3, 2]. +############################################################################### +def getNeighborTour(listOfNodes): + + newList = copy.deepcopy(listOfNodes) + + # Generate two random numbers corresponding to two elements in this + # list of Nodes (in this tour). + random1 = random.randint(0, len(listOfNodes) - 1) + random2 = random.randint(0, len(listOfNodes) - 1) + + newList[random1], newList[random2] = newList[random2], newList[random1] + + return newList + + +############################################################################### +# Exponential coin flip, as defined in the simulated annealing algorithm +# at: https://www.seas.gwu.edu/~simhaweb/champalg/tsp/tsp.html +############################################################################### +def exponentialCoinFlip(currState, neighborState, currTemperature): + + probabilityToFlip = math.exp((-1 * (tourDistance(neighborState) - tourDistance(currState))) / currTemperature) + + uniformRandom = random.random() + + if (uniformRandom < probabilityToFlip): + return True + else: + return False + + +############################################################################### +# Given an initial tour, initial temp, number of iterations, and cooling rate, +# performed simulated annealing on the tour and returns the final solution +# tour. +############################################################################### +def performSimulatedAnnealing(listOfNodes, startingTemp, numIterations, coolingRate): + + # Do not modify the argument. + s = copy.deepcopy(listOfNodes) + + # Create a random initial state. + for i in range (0, 500): + s = getNeighborTour(s) + + # This is the initial cost. + print ("INITIAL COST: ", tourDistance(s)) + + # The best tour yet is the initial one to start. + # Must deep copy to kill the reference. + minTour = copy.deepcopy(s) + minCost = tourDistance(s) + + temperature = startingTemp + + for i in range (0, numIterations): + + # Get a random neighboring tour. + # Note: this does not modify s and returns a new list. + newS = getNeighborTour(s) + + if (tourDistance(newS) < tourDistance(s)): + + # The neighboring tour is better. Jump to it. + s = copy.deepcopy(newS) + + # See if it is the best so far. + if (tourDistance(newS) < minCost): + minCost = tourDistance(newS) + minTour = copy.deepcopy(newS) + + #print "Updated min tour: old dist: ", minCost, "new dist: ", tourDistance(newS), "iterations left: ", (numIterations - i) + + elif exponentialCoinFlip(s, newS, temperature): + + # Jump to the neighbor, even though it's worse. + s = copy.deepcopy(newS) + + # Decrease temperature. + temperature = temperature * coolingRate + + return minTour + + +def main(): + + # Check for TSP input file. + if len(sys.argv) < 2: + print ("No input file given.") + sys.exit(1) + + # Parse the TSP input file. Get a list of Nodes, where each Node + # represents a location in the TSP problem within the file. + #print "Parsing file: ", sys.argv[1] + listOfNodes = parseTSPFile(sys.argv[1]) + + + ######################################################### + # Example experiment with: + # initial temperature: 200,000 + # number of iterations: 40,000 + # cooling rate: .999 + ######################################################### + from timeit import default_timer + + start = default_timer() # start time of running 2opt + + # Get a solution to TSP via the simulated annealing algorithm. #40000 + solutionList = performSimulatedAnnealing(listOfNodes, 200000, 3000, .999) + debug("best_cost", tourDistance( + solutionList), stop=False, key="sa_") + + end = default_timer() # end time of running 2opt + time = str(end - start) + + debug("time2run", time, stop=False, key="sa_") + + ######################################## + # Experimental data below. + ######################################## + + # 8359 + #solutionList = performSimulatedAnnealing(listOfNodes, 200000, 40000, .99) + #print tourDistance(solutionList) + + # 8720 + #solutionList = performSimulatedAnnealing(listOfNodes, 100000, 40000, .999) + #print tourDistance(solutionList) + + # 7843 + #solutionList = performSimulatedAnnealing(listOfNodes, 100000, 40000, .99) + #print tourDistance(solutionList) + + # 8458 + #solutionList = performSimulatedAnnealing(listOfNodes, 10000, 40000, .99) + #print tourDistance(solutionList) + + # 8326 + #solutionList = performSimulatedAnnealing(listOfNodes, 50000, 40000, .99) + #print tourDistance(solutionList) + + # 8897 + #solutionList = performSimulatedAnnealing(listOfNodes, 5000, 40000, .99) + #print tourDistance(solutionList) + + # 8456 + #solutionList = performSimulatedAnnealing(listOfNodes, 10000, 60000, .99) + #print tourDistance(solutionList) + + # Not good. + #solutionList = performSimulatedAnnealing(listOfNodes, 200000, 40000, .9999) + #print tourDistance(solutionList) + + # 7422 + #solutionList = performSimulatedAnnealing(listOfNodes, 200000, 80000, .999) + #print tourDistance(solutionList) + + # 8638 + #solutionList = performSimulatedAnnealing(listOfNodes, 10000, 40000, .99) + #print tourDistance(solutionList) + + # Not good. + #solutionList = performSimulatedAnnealing(listOfNodes, 10000, 10000, .99) + #print tourDistance(solutionList) + + # Not good. + #solutionList = performSimulatedAnnealing(listOfNodes, 200000, 10000, .99) + #print tourDistance(solutionList) + + # Very not good. + #solutionList = performSimulatedAnnealing(listOfNodes, 100000, 80000, .9999) + #print tourDistance(solutionList) + + +if __name__ == '__main__': + main() + + + + + diff --git a/python/qa/TSP-Quantitative-Algorithm.py b/python/qa/TSP-Quantitative-Algorithm.py new file mode 100644 index 0000000..695a6b9 --- /dev/null +++ b/python/qa/TSP-Quantitative-Algorithm.py @@ -0,0 +1,259 @@ +############################################################################### +# Matheus Lima +# Universidade Federal de Sao Carlos, Brazil +# 2021 +############################################################################### + +import sys +import math +import random +import copy + + +DEBUG_SET = True + +def debug(label, _str, stop=False, key="none_", write_to_file=True): + if DEBUG_SET == True: + print(key + label, _str) + + if write_to_file == True: + filename = "./output/"+key+"."+label+".txt" + filename = filename.replace(" ", "") + f = open(filename, "a") + f.write(str(_str)+"\n") + f.close() + + if stop == True: + input() + else: + print() + + +############################################################################### +# Each Node represents a pyhsical location in the TSP problem. +############################################################################### +class Node: + + def __init__(self, name, x_coord, y_coord): + self.name = name + self.x_coord = x_coord + self.y_coord = y_coord + + def getName(self): + return self.name + + def getXCoordinate(self): + return self.x_coord + + def getYCoordinate(self): + return self.y_coord + + def __repr__(self): + return '[' + self.name + ', ' + str(self.x_coord) + ', ' + str(self.y_coord) + ']\n' + + +############################################################################### +# Returns the Edclidean distance between two Nodes. +############################################################################### +def distanceBetween(NodeA, NodeB): + + return math.sqrt(((NodeB.getXCoordinate() - NodeA.getXCoordinate()) ** 2) + + ((NodeB.getYCoordinate() - NodeA.getYCoordinate()) ** 2)) + + +############################################################################### +# Parses the a280.tsp file (the TSP input file). Returns a list of Nodes, +# where each Node represents a location in the file. +############################################################################### +def parseTSPFile(TSPfileName): + + file = open(TSPfileName, 'r') + + # List of Nodes to return. + listOfNodes = [] + + # Parse line by line. + for line in file: + splitList = line.split(); + + # If we received three digits, it is a location in the TSP file. + if all(item.isdigit() for item in splitList): + if len(splitList) == 3: + + # Make a node out of this location. + listOfNodes.append(Node(splitList[0], float(splitList[1]), float(splitList[2]))) + + return listOfNodes + + +############################################################################### +# Returns the distance of this tour. The tour goes from the first Node +# in the list to the second Node, to the third Node,..., to the last Node, and +# back to the first Node. +############################################################################### +def tourDistance(listOfNodes): + + distance = 0; + + # Get the distance from Node 1 to Node 2,... to Node N, where N is + # the last node in the list. + for i in range(0, len(listOfNodes) - 1): + + distance = distance + distanceBetween(listOfNodes[i], listOfNodes[i + 1]) + + + # Get the distance from Node N back to Node 1. + # Note: no error checking here, beacuse the input file is assumed to have + # locations in it. + distance += distanceBetween(listOfNodes[len(listOfNodes) - 1], listOfNodes[0]) + + return distance + + +############################################################################### +# Generates a neighboring tour, given a current tour. For now, this will +# simply swap two locations on the tour. For example, [1, 2, 3, 4] might go to +# [1, 4, 3, 2]. +############################################################################### +def getNeighborTour(listOfNodes): + + newList = copy.deepcopy(listOfNodes) + + # Generate two random numbers corresponding to two elements in this + # list of Nodes (in this tour). + random1 = random.randint(0, len(listOfNodes) - 1) + random2 = random.randint(0, len(listOfNodes) - 1) + + newList[random1], newList[random2] = newList[random2], newList[random1] + + return newList + + +decay_rate = 0.0001 +p_win = 0.999 + + +############################################################################### +# Bernoulli-Shannon-Kelly coin flip +############################################################################### +def KellyBernoulliCoinFlip(b=None): + global decay_rate + global p_win + + if b is None: + b = random.uniform(0.01, 2) + + f_k = (p_win * (b + 1) - 1) / b + + p_win = p_win - decay_rate + + uniformRandom = random.random() + + bernoulli_trial = random.choices( + population=[0, 1], weights=[0.999, 0.001], k=1)[0] + + + if (uniformRandom < f_k or bernoulli_trial == 1): + return True + else: + return False + +############################################################################### +# Given an initial tour, number of iterations, and cooling rate, +# performed quantitative method on the tour and returns the final solution +# tour. +############################################################################### +def runQuantitativeAlgorithm(listOfNodes,numIterations):#(listOfNodes, startingTemp, numIterations, coolingRate): + + # Do not modify the argument. + s = copy.deepcopy(listOfNodes) + + + # Create a random initial state. + for i in range (0, 500): + s = getNeighborTour(s) + + # This is the initial cost. + print ("INITIAL COST: ", tourDistance(s)) + + + + debug("init_cost", + tourDistance(s), stop=False, key="qa_") + + # The best tour yet is the initial one to start. + # Must deep copy to kill the reference. + minTour = copy.deepcopy(s) + minCost = tourDistance(s) + + + for i in range (0, numIterations): + + # Get a random neighboring tour. + # Note: this does not modify s and returns a new list. + newS = getNeighborTour(s) + + if (tourDistance(newS) < tourDistance(s)): + + # The neighboring tour is better. Jump to it. + s = copy.deepcopy(newS) + + # See if it is the best so far. + if (tourDistance(newS) < minCost): + minCost = tourDistance(newS) + minTour = copy.deepcopy(newS) + + #print "Updated min tour: old dist: ", minCost, "new dist: ", tourDistance(newS), "iterations left: ", (numIterations - i) + + elif KellyBernoulliCoinFlip(): + + # Jump to the neighbor, even though it's worse. + s = copy.deepcopy(newS) + + + return minTour + +def main(): + + # Check for TSP input file. + if len(sys.argv) < 2: + print ("No input file given.") + sys.exit(1) + + # Parse the TSP input file. Get a list of Nodes, where each Node + # represents a location in the TSP problem within the file. + #print "Parsing file: ", sys.argv[1] + listOfNodes = parseTSPFile(sys.argv[1]) + + + ######################################################### + # Example experiment with: + # initial temperature: 200,000 + # number of iterations: 40,000 + # cooling rate: .999 + ######################################################### + from timeit import default_timer + + start = default_timer() # start time of running 2opt + + # Get a solution to TSP via the simulated annealing algorithm. + solutionList = runQuantitativeAlgorithm(listOfNodes, 3000)#200)#40000) + #print ('Solution tour distance: ', tourDistance(solutionList)) + + + debug("best_cost", tourDistance( + solutionList), stop=False, key="qa_") + + end = default_timer() # end time of running 2opt + time = str(end - start) + + debug("time2run", time, stop=False, key="qa_") + + +if __name__ == '__main__': + main() + + + + + diff --git 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Interpretation of Sections 15 and 16. + + If the disclaimer of warranty and limitation of liability provided +above cannot be given local legal effect according to their terms, +reviewing courts shall apply local law that most closely approximates +an absolute waiver of all civil liability in connection with the +Program, unless a warranty or assumption of liability accompanies a +copy of the Program in return for a fee. + + END OF TERMS AND CONDITIONS + + How to Apply These Terms to Your New Programs + + If you develop a new program, and you want it to be of the greatest +possible use to the public, the best way to achieve this is to make it +free software which everyone can redistribute and change under these terms. + + To do so, attach the following notices to the program. It is safest +to attach them to the start of each source file to most effectively +state the exclusion of warranty; and each file should have at least +the "copyright" line and a pointer to where the full notice is found. + + + Copyright (C) + + This program is free software: you can redistribute it and/or modify + it under the terms of the GNU General Public License as published by + the Free Software Foundation, either version 3 of the License, or + (at your option) any later version. + + This program is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + GNU General Public License for more details. + + You should have received a copy of the GNU General Public License + along with this program. If not, see . + +Also add information on how to contact you by electronic and paper mail. + + If the program does terminal interaction, make it output a short +notice like this when it starts in an interactive mode: + + Copyright (C) + This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'. + This is free software, and you are welcome to redistribute it + under certain conditions; type `show c' for details. + +The hypothetical commands `show w' and `show c' should show the appropriate +parts of the General Public License. Of course, your program's commands +might be different; for a GUI interface, you would use an "about box". + + You should also get your employer (if you work as a programmer) or school, +if any, to sign a "copyright disclaimer" for the program, if necessary. +For more information on this, and how to apply and follow the GNU GPL, see +. + + The GNU General Public License does not permit incorporating your program +into proprietary programs. If your program is a subroutine library, you +may consider it more useful to permit linking proprietary applications with +the library. If this is what you want to do, use the GNU Lesser General +Public License instead of this License. But first, please read +. diff --git a/python/qa/output/qa_.best_cost.txt b/python/qa/output/qa_.best_cost.txt new file mode 100644 index 0000000..d52fa36 --- /dev/null +++ b/python/qa/output/qa_.best_cost.txt @@ -0,0 +1,50 @@ +30163.543476043018 +30949.78665060476 +29420.84935114648 +30768.665012942423 +29496.450870674926 +29824.09370984302 +29874.209692821096 +30030.527470654102 +30187.970328160183 +29795.632101544787 +30827.11391706286 +29733.200895918195 +30030.494159049722 +29531.246177016958 +29739.455782860798 +30160.77923166716 +30898.259074763555 +30098.78664128437 +29659.862323267756 +29507.112350776482 +31188.715198793983 +30519.932379941652 +28854.606973559672 +30132.88443632628 +28489.140295153637 +28543.332512216493 +29548.805595170652 +30370.987383963533 +29340.560641821972 +29539.032532368536 +30619.990698490707 +30840.750338862937 +30102.416104738546 +30156.80400884809 +31023.62140300963 +30437.52500319538 +29382.832419212886 +30003.628398515975 +30064.475394380093 +31225.866070073185 +30449.932415200983 +29331.696164819172 +30358.092349540926 +30221.990953733275 +30922.486282192374 +30044.581086380815 +29216.461241459732 +30394.766681639874 +29984.54553098131 +29826.40619942106 diff --git a/python/qa/output/qa_.init_cost.txt b/python/qa/output/qa_.init_cost.txt new file mode 100644 index 0000000..d18c58e --- /dev/null +++ b/python/qa/output/qa_.init_cost.txt @@ -0,0 +1,50 @@ +34194.68372980124 +33431.9676077416 +34786.69815367768 +33783.26168011337 +33313.06410389703 +34164.40181494389 +34453.4317401747 +34896.45537967534 +33124.82568138141 +33394.77638500375 +33284.563414137214 +34541.765140858355 +33653.7735900642 +35021.0858051746 +33362.704966055375 +34877.227560316096 +33197.02813233481 +34733.19390111885 +32944.200502742315 +33426.3220139514 +33961.34242257984 +33964.01742008202 +34128.56011742351 +34764.252891364726 +36091.27899580692 +34456.38920827304 +33644.05973755443 +33264.930735894995 +35694.0788685195 +33284.32005007158 +32654.599933465885 +33590.25481753937 +34951.05857406727 +33297.44906958739 +34079.53166202095 +35326.67740015148 +33818.138211756595 +34036.06109404577 +34658.80430954343 +34229.36856551649 +33876.88868066849 +33321.05369740455 +33234.544113221345 +33847.58159994721 +33874.643029905565 +33099.851185492764 +35715.03202500672 +33886.16136900272 +34028.22127799258 +33278.135542643075 diff --git a/python/qa/output/qa_.time2run.txt b/python/qa/output/qa_.time2run.txt new file mode 100644 index 0000000..2a88d5e --- /dev/null +++ b/python/qa/output/qa_.time2run.txt @@ -0,0 +1,50 @@ +75.430273521 +69.566485512 +110.512449751 +80.25524759299999 +63.80803703 +59.917447318 +72.244816317 +63.474441039 +38.563258894 +42.792255258 +38.977335788999994 +39.101684916 +43.78343533699999 +39.108557843999996 +39.626630665 +38.556154323 +40.826598992 +39.402826514 +52.502685895999996 +58.389733934 +38.934944447 +38.772560481999996 +38.663629631 +40.616287876 +39.074382623000005 +39.281629616000004 +39.527038682 +45.365838094999994 +57.071454436 +37.680859510999994 +44.440149109 +38.274543117 +40.536364473 +38.786052011 +39.254296477 +40.037572597 +39.265467231 +44.057724993 +39.070739512 +38.854788493 +42.110182533 +42.89941305 +39.670196622 +38.826654661 +38.626987287999995 +38.972673335 +40.281367026 +54.916568171 +53.463396057 +60.797467702999995 diff --git a/python/qa/output/sa_.best_cost.txt b/python/qa/output/sa_.best_cost.txt new file mode 100644 index 0000000..42203aa --- /dev/null +++ b/python/qa/output/sa_.best_cost.txt @@ -0,0 +1,50 @@ +31077.467303778263 +31012.98573421236 +31542.72452659442 +30909.99714886679 +31285.79746194061 +31888.62746301445 +31109.07795860244 +30254.503570047134 +31629.506466421662 +31463.399134295778 +31120.790547675017 +31285.303726680642 +30945.891390979585 +31598.775889107408 +30755.042407671175 +30797.567992927045 +31995.54829451096 +31384.352957376348 +31662.714242836817 +31967.33669072789 +31648.90607469655 +31196.254163757356 +30954.861866178304 +31089.8085882273 +31571.71216218461 +31479.659634387357 +30655.839516819466 +31620.317061113583 +31215.36083426841 +31929.18671246766 +31252.243495090443 +31187.07472678203 +31185.671345589126 +31493.369528496987 +32220.897825187585 +30989.87689624139 +31167.7767080113 +31704.09610800141 +31467.2601978059 +31598.966801258455 +31046.808382588122 +31474.19571190715 +31513.16701994126 +30963.35064193664 +30865.36656324189 +32068.500645703793 +31051.775544037373 +31138.422729374186 +32101.737893017886 +31680.67476232697 diff --git a/python/qa/output/sa_.time2run.txt b/python/qa/output/sa_.time2run.txt new file mode 100644 index 0000000..a6e6922 --- /dev/null +++ b/python/qa/output/sa_.time2run.txt @@ -0,0 +1,50 @@ +68.264213931 +103.756445855 +77.024009327 +80.013437244 +66.764871529 +66.02418550899999 +65.214235318 +72.591842372 +47.252777524 +45.620155743000005 +41.3020911 +42.751176294 +42.552084586 +43.295485532 +43.009826225000005 +44.379079845 +42.905693534 +56.014993486 +50.700587591 +42.000668926 +42.142702548 +42.788445826 +45.885694413 +43.038300590999995 +43.09513786 +43.310758922 +47.352510512 +50.471787892 +42.758540171 +44.364144786 +43.017392883 +42.859604354 +43.460816079999994 +46.526634296 +43.213584376 +42.248035290000004 +43.077233786 +41.892931233 +43.176754299 +50.323515277999995 +42.412856207000004 +43.304248535 +44.404204097 +43.267950818 +47.749539723999995 +42.763760962 +82.081866941 +87.215238056 +58.525173471 +50.779978303 diff --git a/python/qa/run.sh b/python/qa/run.sh new file mode 100755 index 0000000..ce8e1fe --- /dev/null +++ b/python/qa/run.sh @@ -0,0 +1,13 @@ +#!/usr/bin/env bash + +rm -rf ./output/* +for ((i=1;i<=50;i++)); do + + + + python3.9 ./TSP-Quantitative-Algorithm.py a280.tsp ; + python3 ./SA-Benchmark.py a280.tsp + + +echo "=====" +done \ No newline at end of file diff --git a/python/qa/small_test5.tsp b/python/qa/small_test5.tsp new file mode 100644 index 0000000..a10977a --- /dev/null +++ b/python/qa/small_test5.tsp @@ -0,0 +1,12 @@ +NAME : a280 +COMMENT : drilling problem (Ludwig) +TYPE : TSP +DIMENSION: 5 +EDGE_WEIGHT_TYPE : EUC_2D +NODE_COORD_SECTION + 1 288 149 + 2 288 129 + 3 270 133 + 4 256 141 + 5 256 157 +EOF From 13e841fb0789986ff3acf54876fe787ad2528c86 Mon Sep 17 00:00:00 2001 From: Matheus Santana Lima Date: Mon, 17 May 2021 20:57:52 -0300 Subject: [PATCH 2/2] Improving code description to simulation trial sampling and renaming file run.sh to run-simulation.trial.sh --- python/qa/README.md | 9 +-------- python/qa/run-simulation-trial.sh | 20 ++++++++++++++++++++ python/qa/run.sh | 13 ------------- 3 files changed, 21 insertions(+), 21 deletions(-) create mode 100755 python/qa/run-simulation-trial.sh delete mode 100755 python/qa/run.sh diff --git a/python/qa/README.md b/python/qa/README.md index 4feec6d..387c506 100644 --- a/python/qa/README.md +++ b/python/qa/README.md @@ -1,11 +1,4 @@ -Matheus Lima (Computer Science, Federal University of Sao Carlos, Brazil) - -(1) To run: - -$ ./run.sh - -(2) To change the path of the TSP data file: change the path in the Makefile. - +Matheus Lima (Computer Science, Federal University of Sao Carlos, Brazil # Quantitative Algorithm to solve the TSP problem diff --git a/python/qa/run-simulation-trial.sh b/python/qa/run-simulation-trial.sh new file mode 100755 index 0000000..6d2dbc4 --- /dev/null +++ b/python/qa/run-simulation-trial.sh @@ -0,0 +1,20 @@ +#!/usr/bin/env bash + +# The goal of this script is to simplify the collection and the generation of the trial sample data (with n=50 population size). +# The n=50 is arbitrarily set, as the minimum recommendation for the t-test is a sample size larger than 30. + +# The code writes the algorithm output variables (i.e. values for the best solution cost, total execution time and the initial solution distance) for each completed execution in a text file. +# Those values were them analyzed using a statistical test (details in the README.md file). The script provides an automated method to deploy the proposed method QA and the benchmark SA. The data set that can be quantified by statistical modeling. + + +rm -rf ./output/* +for ((i=1;i<=50;i++)); do + + + + python3.9 ./TSP-Quantitative-Algorithm.py a280.tsp ; + python3 ./SA-Benchmark.py a280.tsp + + +echo "=====" +done \ No newline at end of file diff --git a/python/qa/run.sh b/python/qa/run.sh deleted file mode 100755 index ce8e1fe..0000000 --- a/python/qa/run.sh +++ /dev/null @@ -1,13 +0,0 @@ -#!/usr/bin/env bash - -rm -rf ./output/* -for ((i=1;i<=50;i++)); do - - - - python3.9 ./TSP-Quantitative-Algorithm.py a280.tsp ; - python3 ./SA-Benchmark.py a280.tsp - - -echo "=====" -done \ No newline at end of file