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NCGA : Neighborhood Cultivation Genetic Algorithm for Multi-Objective Optimization Problems

NCGA : Neighborhood Cultivation Genetic Algorithm for Multi-Objective Optimization Problems. ○ Shinya Watanabe Tomoyuki Hiroyasu Mitsunori Miki. Intelligent Systems Design Laboratory ， Doshisha University ， Kyoto Japan. Multi-objective Optimization Problems.

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NCGA : Neighborhood Cultivation Genetic Algorithm for Multi-Objective Optimization Problems

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  1. NCGA : Neighborhood Cultivation Genetic Algorithm for Multi-Objective Optimization Problems ○ Shinya Watanabe Tomoyuki Hiroyasu Mitsunori Miki Intelligent Systems Design Laboratory， Doshisha University，Kyoto Japan Doshisha Univ., Kyoto Japan

  2. Multi-objective Optimization Problems ●Multi-objective Optimization Problems (MOPs) In the optimization problems, when there are several objective functions, the problems are called multi-objective or multi-criterion problems. Design variables X={x1, x2, …. , xn} Feasible region (x) f 2 Objective function Pareto optimal solutions F={f1(x), f2(x), … , fm(x)} Constraints f Gi(x)<0 ( i = 1, 2, … , k) (x) 1 Doshisha Univ., Kyoto Japan

  3. EMO • EMO Evolutionary Multi-criterion Optimization • MOPs solved by Evolutionary algorithms Typical method on EMO • VEGA:Schaffer (1985) • MOGA :Fonseca (1993) • DRMOGA :Hiroyasu, Miki, Watanabe (2000) • SPEA2 :Zitzler (2001) • NPGA2 :Erickson, Mayer, Horn (2001) • NSGA-II :Deb, Goel (2001) Doshisha Univ., Kyoto Japan

  4. Neighborhood Cultivation GA (NCGA) • NCGA : Neighborhood Cultivation GA The features of NCGA • The neighborhood crossover. • Archive of excellent solutions. • A Method which cuts down reserved excellent solutions. • Use of the reserved excellent solutions for searching solutions. • Unification mechanism of the values of each objective. Doshisha Univ., Kyoto Japan

  5. f2(x) f1(x) Neighborhood Cultivation GA (NCGA) • A neighborhood crossover • In MOPs GA, the searching area is wide and the searching area of each individual is different. If the distance between two selected parents is so large, the crossover may have no effect for local search. Doshisha Univ., Kyoto Japan

  6. f2(x) f1(x) Neighborhood Cultivation GA (NCGA) • A neighborhood crossover • Two parents in the crossover are chosen from the top of the sorted individuals. • One of the objectives is changed at each generation. • The sorting of a population includes a little probabilistic change. In order not to make the same couple, Doshisha Univ., Kyoto Japan

  7. Neighborhood Cultivation GA (NCGA) • The differences from the recent major algorithms like SPEA2 and NSGA-II. • NCGA has the neighborhood crossover mechanism. • NCGA has only one selection in one generation. • Many methods have two types of selection (the environment selection and the mating selection). But, NCGA has the environment selection only. Doshisha Univ., Kyoto Japan

  8. Comparison method • Sampling of the Pareto frontier Lines of Intersection (ILI) (Knowles and Corne 2000) = 5/12=0.42 = 7/12=0.58 Doshisha Univ., Kyoto Japan

  9. Applied models and Parameters Applied models GA Operator • SPEA2 • NSGA-II • NCGA • non-NCGA • (NCGA except neighborhood crossover ) • Crossover • One point crossover • Mutation • Bit flip Parameters population size 100 250 1.0 crossover rate mutation rate 0.01 250 2000 terminal condition number of trials 30 Doshisha Univ., Kyoto Japan

  10. Test Problems • Discontinuous Function • Fdiscon (Deb’00) Doshisha Univ., Kyoto Japan

  11. Pareto solutions of Fdiscon Doshisha Univ., Kyoto Japan

  12. Comparison resultof Fdiscon (ILI) Doshisha Univ., Kyoto Japan

  13. Test Problems • Continuous Function • KUR Doshisha Univ., Kyoto Japan

  14. Pareto solutions of KUR Doshisha Univ., Kyoto Japan

  15. Comparison resultof KUR (ILI) Doshisha Univ., Kyoto Japan

  16. Test Problems • Combination problem • KP 750-2 Objectives Constraints pi,j = profit of item j according to knapsack i wi,j = weight of item j according to knapsack i ci,= capacity of knapsack i Doshisha Univ., Kyoto Japan

  17. Pareto solutions of KP750-2 Doshisha Univ., Kyoto Japan

  18. Comparison resultof KP750-2 (ILI) Doshisha Univ., Kyoto Japan

  19. Conclusion • We proposed a new model for Multi-objective GAs. • NCGA:NeighborhoodCultivationGA • Effective method for multi objective GA • The neighborhood crossover • Archive of excellent solutions. • A Method which cuts down reserved excellent solutions. • Use of the reserved excellent solutions for searching solutions. • Unification mechanism of the values of each objective. Doshisha Univ., Kyoto Japan

  20. Conclusion • NCGA was applied to some test functions and the results were compared to the other methods; such as SPEA2, NSGA-II and non-NCGA. • In almost test functions, NCGA derives the good results. • Comparing NCGA to NCGA without neighborhood crossover, NCGA is obviously superior to in all problems. NCGA is an effective algorithm for multi-objective problems. Doshisha Univ., Kyoto Japan

  21. Test Problems • Continuous Function • ZDT4 Doshisha Univ., Kyoto Japan

  22. Pareto solutions of ZDT4 Doshisha Univ., Kyoto Japan

  23. Comparison resultof ZDT4 (ILI) Doshisha Univ., Kyoto Japan

  24. ILIof KP750-2 Doshisha Univ., Kyoto Japan

  25. URL of reference • About EMO • http://www.lania.mx/~ccoello/EMOO/EMOObib.html • About 0/1 Knapsack problem • http://www.tik.ee.ethz.ch/~zitzler/ • NCGA source program • http://mikilab.doshisha.ac.jp/dia/research/mop_ga/archive/ • My e-mail address • sin@mikilab.doshisha.ac.jp Doshisha Univ., Kyoto Japan

  26. 0.333 0.666 (x) 2 f Method A Method B Performance Measure • The Ratio of Non-dominated Individuals (RNI) is derived from two types of Pareto solutions. Method A (x) 2 f f (x) 1 Method B (x) 2 f f (x) 1 f (x) 1 Doshisha Univ., Kyoto Japan

  27. EMO • The following topics are the mechanisms that the recent GA approaches have. • Archive of the excellent solutions • Cut down (sharing) method of the reserved excellent solutions • An appropriate assign of fitness • Reflection to search solutions mechanism of the reserved excellent solutions • Unification mechanism of values of each objective Doshisha Univ., Kyoto Japan

  28. Performance Assessment Measures • The Ratio of Non-dominated Individuals :RNI • The Performance measure perform to compare two type of Pareto solutions. • Two types of pareto solutions derived by difference methods are compared. • Cover Rate Index • Diversity of the Pareto optimum. • Error • The distance between the real pareto front and derived solutions. • Various rate • Diversity of the pareto optimum individuals. Doshisha Univ., Kyoto Japan

  29. Cluster System Spec. of Cluster(16 nodes) Processor Pentium Ⅲ(Coppermine) Clock 600MHz # Processors 1 × 16 Main memory 256Mbytes × 16 Network Fast Ethernet (100Mbps) Communication TCP/IP, MPICH 1.2.1 OS Linux 2.4 Compiler gcc 2.95.4 Doshisha Univ., Kyoto Japan

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