並列多目的最適化進化アルゴリズムのブロックレイアウト問題への適用

Vol. 31(2000 06 ) Paralell Evolutionary Multi-Criterion Optimization for Block Layout Problems , Shinya WATANABE,Tomoyuki HiroyasuMitsunori MIKI (Intelligent Systems DesignLaboratory)Abstract: In this paper, a parallel evolutionary multi-criteria optimization algorithm: DGAand DRMOGA are applied to block layout problems.The results are compared to the results ofSGA and discussed.It is said that block layout problems are NP hard problems and there areseveral types of objectives.Therefore, it can be said that the block layout problems are suitable toevolutionary multi-criterion optimization algorithms.DRMOGA is one of the DGA models.Thismodel can derive good Pareto solutions in continuous optimization problems.However it has notapplied to discrete problems.In the numerical example, the Pareto solutions of the block layoutproblem who has 13 blocks are derived by DGA, DRMOGA and SGA.Then it is confirmed that itis difficult to derive the solutions with any model, even in one objective.It is also found that goodparallel efficiency can be derived from both DGA and DRMOGA.The results of Pareto solutionsof DGA and DRMOGA are almost same.However, DRMOGA searched wider area than that ofDGA.1 Genetic Algorithm, GA GA 1, 3, 5) GA GA PC GA DGADistributedGA2 2.1 DRMOGA DRMOGA 5) 3 1 f 2 (x)division 1 division 2 division 3MinFig. 1Pareto Optimum Solutionf 1(x)DRMOGAMax3 3.1 2 n∑ n∑f 1 = c ij d ij (1)n:i=1i≠jj=1f 2 = Total Area S (2)c ij : i j d ij : i j 1

Fig. 24216573:dead spacePacking Method (1) 3 4 2 4 13 2) SGADGADRMOGA 3 1600 DGADRMOGA 16 100 300 DGA DRMOGA 20 DGADRMOGA 3,4 1600 100 3 4 f 2 13000 f 2 f218000170001600015000140001300012000110001.00Fig. 31.05 1.10 1.15 1.20f1Results of DGAf2180001700016000150001400013000 A12000110001.00Fig. 41.05 1.10 1.15 1.20f1Results of DRMOGADRMOGA DGA DRMOGA DGA DGA DRMOGA 20 DGA 183.7 DRMOGA 185.6 SGA 726.3 DGADRMOGA 100% DRMOGA 5 GA DRMOGA DRMOGA GA1) C.M.Fonseca and P.J.Fleming. Genetic algorithmsfor multiobjective optimization: Formulation, discussionand generalization.In Proceedings of the 5th internationalcoference on genetic algorithms, pp.416–423,1993.2) R.L.Francis.Facility layout and location: An analyticalapproach.In Prentice Hall, p.179, 1992.3) . . , pp.295–300, 1997.4) Y.Shirai and N.Matsumoto.Performance evaluation ofes type genetic algorithms for solving block layout problemswith floor constraints.In PTransaction of JSME(C)65-634, pp.296–304, 1999.5) M.Miki T.Hiroyasu and S.Watanabe. Divided rangegenetic algorithms in multiobjectiv optimization problems.InProceedings of Economics and MathematicalSystems, pp.57–66, 1999.B2