世代交代モデル， 母集団分割効果の検討 - 知的システムデザイン研究室

54 2002 10 A Discussion on Real Number Vector Representation, Generation Alternation Modelsand Effect by Division of Population of Genetic Algorithm Takahiro FUKUNAGAAbstract:Recently, many Genetic Algorithm (GA) schemes have been developed to find the good results.Among them, Real-coded Genetic Algorithm, Generation Alternation Model, and Island Model arefocused. In this paper, we discuss the performance of real-coded GA with MGG and island model.The examined model is applied to some test functions to verify the effectiveness of each scheme.The numerical result shows that real-coded GA with multiple sub populations provides the highersearch ability than that with a single population.1 GA 123 3 GA 3 GA 1 MGG GA 2 GA Fig. 1 GA GA GA 1) 3 Minimal Generation Gap (MGG) 2) MGG 2 1 MGG x2Objective Functionx 1(18, 5)Gene Type of Bit-string1 0 0 1 0 0 0 1 0 1x1 x218 5Gene Type of Real-codedFig. 1 Real value codingFig. 2 MGG Selection for ReproductionSelection for SurvivalGeneratePopulationFig. 2 Minimal Generation Gap4 MGG MGG UNDX MGG UNDX+MGG 1) 1

GA UNDX+MGG GA Fig. 3 Minimal Generation Gap4.2 MGG MGG 200 (1) .Repetition of CrossoverSubpopulationSubpopulationMigrationSubpopulationSubpopulationFig. 3 Distributed Real-coded GA with MGG#Children = 200/#Islands (1) 2 Table1 Fig. 5 4.1 MGG 2 Rastrigin Griewank 30000 1) 200 Table 1 Fig. 4 20 Table 1 Paremeters : 1 300 1, 2, 5, 10 / 200 / 20UNDXUNDX parameter α = 0.5 β = 0.35 0.0 0.5 51x10 31x10 31x10 21x10 21x10 11x10 1Evaluation Value1x10 01x10 -11x10 -21x10 -31x10 -41x10 -5Number of Islands13510Evaluation Value1x10 01x10 -11x10 -21x10 -31x10 -41x10 -5Number of Islands135101x10 -61x10 -61x10 -70 1x10 6 2x10 6 3x10 6 4x10 6 5x10 6 6x10 61x10 -70 1x10 6 2x10 6 3x10 6 4x10 6 5x10 6 6x10 6(a) Rastrigin(20dim)(b) Griewank(20dim)Number of EvaluationsNumber of Evaluations(a) Rastrigin(20dim)(b) Griewank(20dim)Fig. 4History of the evaluation valueFig. 5History of the evaluation valueFig. 4 MGG GA 1 [] GA MGG []*[] MGG Fig. 5 MGG 4.3 4.2 MGG 5 2

GA30000 20 Table 2 GA GA 1 30 Table 2 Paremeters : 2 GA GA30050 1, 2, 5, 10 / 201 30 UNDX 2 100 / UNDX parameter α=0.5 β=0.35 0.0 0.0017 0.5 5Table 3 #OPT 1 AVG UNDX GA2X2 2points-crossover GAGA 1.0E-104.4 Table 3 Rosenbrocck Rosenbrock 2 GA UNDX Ridge Ridge GA BLX-α UNDX 4) Ridge 4.5 Table 3 1 number of runs in which the algorithm succeeded in findingthe global optimum GA GA Rastrigtin Rotated Rastrigin GA5 1 MGGMGG 5 • MGG MGG GA GA 1 • MGG GA MGG UNDX • MGG GA 3) MGG • GA GA3

Table 3Summary of resultsNumber of IslandsFunctions Crossover 1 2 5 10(dimensions)#OPTAVG#OPTAVG#OPTAVG#OPTAVGRastrigin UNDX 17 2,822,700 18 1,478,100 17 666,900 19 472,100(20dim) 2X 20 2,888,300 20 1,742,900 20 1,578,700 20 869,300Griewank UNDX 20 1,857,700 20 1,102,100 20 585,300 20 397,300(20dim) 2X 15 3,120,500 11 1,901,100 8 979,900 13 734,500Rosenbrock UNDX 20 1,275,260 20 952,650 20 1,069,450 19 2,548,850(20dim) 2X 0 - 0 - 0 - 0 -Ridge UNDX 20 784,650 20 530,650 20 381,050 20 375,650(20dim) 2X 0 - 0 - 0 - 0 -Rotated Rastrigin UNDX 19 2,761,500 20 1,423,300 20 708,900 19 524,300(20dim) 2X 0 - 0 - 0 - 0 -MGG GA MGG 2 UNDX 6 Schwefel UNDX 4) 2 • GA GA TSCToridal Search Space Conversion 5) • GA GA GA 1) Isao Ono and Shigenobu Kobayashi : A Real CodedGenetic Algorithm for Function Optimization UsingUnimodal Normal Distributed Crossover , Proc. 7thInternational Conference on Genetic Algorithms ,Vol.16 , No.1 , pp246-253 , 19972) : , , Vol.12 , No.9 , pp734-744 , 19973) Eshleman,L.J and Schaffer,J.D : Real-Coded GeneticAlgorithms and Interval-Schemata , Foundationsof Genetic Algorithms , Vol.2, pp187-202 ,19934) Ono,I. , Yamamura,M. and Kobayashi,S. : ARobust Real-coded Genetic Algorithm using UnimodalNormal Distribution Crossover Augmentedby Uniform Crossover: Effects of self-Adaptation ofCrossover Probabilities , in Proceedings of the Geneticand Evolutionary Computation Conference,pp496-503 , 19995) : GA Toridal Search Space Conversion , , Vol.16 , No.3 , pp333-343, 20014