分散遺伝的アルゴリズムの巡回セールスマン問題への適用

33 2000 08 Distributed Genetic Algorithm Applied to Traveling Salesman Problems Takanori MIZUTAAbstract: This paper proposes a new method of genetic algorithms for discrete optimizationproblems. We examine the performence of DGA and the proposed method for a typical discreteoptimization problem, the traveling salesman problem. The features of the proposed method are 2points. The first is DGA without migration (isolated DGA: iDGA) and the second is a crossoverfor the entire population (Centralized Multiple Crossover: CMX). The experiments showed thatthe proposed method shows better performance than conventional DGA.1 (Distributed Genetic Algorithms:DGA) DGA GA(, SGA) 1) (TravelingSalesman Problem: TSP) DGA 2 TSP DGA DGA SGA 51 (eil51) 2) (EXX) 3) 2-change 400, 0.8, 0.4/L() 0.5 5 4 16 Fig. 1 DGA SGA DGA () TSP Fig. 1Distance600 eil51500SGADGA4DGA16428Optimum4000 500 1000Generations51 TSP SGA DGA SGA SGA,DGA TSP3 DGA DGA (isolated DGA :iDGA) (Centralized Multiple Crossover: CMX)CMX iDGA DGA 1

Distance500475450eil511time10times100times500times428 Optimum425500 600 700 800 900 1000GenerationsDistance550 eil51300Gens500Gens700Gens800Gens500DGA16450428 Optimum4250 500 1000GenerationsFig. 2 CMX CMX CMX CMX 1 1) CMX 2)CMX 3) CMX 4) CMX 4 4 51 (eil51)100 (kroA100)150 (ch150) 2) SGA, DGA, 0.8 0.4/L 10 5 5.1 CMX 1 Fig. 2 CMX 400 16 CMX 100 CMX 100 Fig. 2 CMX CMX 500 51 700 iDGA CMX 5.2 CMX CMX DGA CMX CMX DistanceDistance500 eil514754501time2timesDGA32428 Optimum425500 600 700 800 900 1000Generations50000 kroA100 20000 ch1501time5times2times20times4000020times30timesDGA32 15000DGA32300002128220000500 600 700 800 900 1000GenerationsFig. 3Distance1000065285000500 600 700 800 900 1000GenerationsDGA 10 CMX 800 32 51 1 CMX DGACMX 2 100 2 DGA CMX DGA 3 DGA 6 DGA TSP DGA 1) GA (1999)2) “TSPLIB 95”, http://softlib.rice.edu/softlib/tsplib/,19953) , Vol.31, No.5, pp.598-605 (19952