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DCMOGA : D istributed C ooperation model of M ulti- O bjective G enetic A lgorithm

DCMOGA : D istributed C ooperation model of M ulti- O bjective G enetic A lgorithm. Tamaki Okuda ● Tomoyuki Hiroyasu Mitsunori Miki Shinya Watanabe Doshisha University, Kyoto Japan. Multi-objective Optimization Problems.

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DCMOGA : D istributed C ooperation model of M ulti- O bjective G enetic A lgorithm

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  1. DCMOGA:Distributed Cooperation model of Multi-Objective Genetic Algorithm Tamaki Okuda ● Tomoyuki Hiroyasu Mitsunori Miki Shinya Watanabe Doshisha University, 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 } Objective function F = { f1(x), f2(x), … , fm(x) } Constrains Gi(x) < 0 ( i = 1, 2, … , k ) f1(x): Maximum f2(x): Maximum Pareto-optimal front Non-Dominated solutions Feasible region

  3. EMOs: Evolutionary Multi-criterion Optimization Typical method on EMOs: • VEGA : Schaffer (1985) • MOGA : Fonseca (1993) • SPEA2 : Zitzler (2001) • NPGA2 : Erickson, Mayer, Horn (2001) • NSGA-II : Deb (2001) Good non-dominated solutions: • Minimal distance to the Pareto-optimal front • Uniform distribution • Maximum spreading >> Proposed a new model of EMOs. This model searches for non-dominated solutions, which are widespread and closed to pareto-optimal front, and can make the existing algorithms more efficient.

  4. DCMOGA DCMOGA:Distributed Cooperation model of Multi-Objective GA DC-scheme for MOGA The features of DC-scheme: • N+1 sub populations (when N objects) 1 group: searches for pareto optimum by MOGA N groups: searches for optimum by SOGA (Single Objective GA) • Cooperative search Exchanged between each group Adjustment of each sub population size

  5. N+1 groups (sub populations) MOGA group:The Pareto-optimal solutions are searched by MOGA SOGA groups:The optimum of ith objective function is searched by SOGA.

  6. Cooperative search (1) Exchange of the solutions: Exchange the best solutions between the MOGA group and each SOGA group.

  7. Cooperative search (2) Adjustment of each sub population size: • Some individuals move to other group. • This adjustment is according to the function values of best solution in each group. • Each sub population size changes, but the whole population size don’t change. >> The difference between search ability of each group is reduce

  8. The algorithm of DC-scheme >> N objective function • all individuals are initialized. • all individuals are divided into N+1 groups. • In the MOGA group, thepareto optimal solutions are searched, and in each SOGA group the optimum is searched. • After some iterations, exchange the solutions between MOGA group and SOGA. • The exchanged solutions are compared, and sub each population size is adjusted. • The terminal condition is checked, >> 2 objective functions

  9. Combined MOGA and SOGA method DCMOGA:Distributed Cooperation model of MOGADC-scheme >>Combined MOGA and SOGA DC-scheme can combine any MOGA and SOGA. Used algorithms: SOGA: DGA MOGA: MOGA (Fonseca) SPEA2 (Zitzler) NSGA-II (Deb)

  10. profit of item j according to knapsack i weight of item j according to knapsack i capacity of knapsack i Test Problem: KP750-m 0/1 Knapsack Problem(750items, m knapsacks)-Combination problems Objectives: Constraints:

  11. Test Problem: KUR KUR(2 objective function, 100 design variables )- Continuous- Multi-modal

  12. Test Problem: ZDT4 ZDT4( 2 objective function, 10 design variables )- Continuous- Multi-modal

  13. Performance Metrics Function(C) Coverage of two sets: C A: front1 B: front2 C(A,B) = 1/5 = 0.2 C(B,A) = 2/4 = 0.5

  14. Applied models and Parameters Applied models • MOGA / DCMOGA • SPEA2 / DCSPEA2 • NSGA-II / DCNSGA-II Parameters GA operator Crossover: 2 points crossover Mutation:bit flip

  15. Results: KP750-3 DCMOGA MOGA << with DC-scheme is more widespread << without DC-scheme is closer to Pareto optimum

  16. Results: KP750-3 DCSPEA2 SPEA2 << with DC-scheme is more widespread

  17. Results: KP750-3 DCNSGA-II NSGA-II << with DC-scheme is more widespread << without DC-scheme is closer to Pareto optimum

  18. Results: KP750-3 The Coverage of two sets << Without DC superior than with DC << With DC superior than without DC << Without DC superior than with DC >> both results are almost the same.

  19. Results: KUR DCMOGA MOGA DCSPEA2 SPEA2

  20. Results: KUR DCNSGA-II NSGA-II << With DC superior than without DC << With DC superior than without DC << With DC superior than without DC >> With DC-scheme is superior

  21. Results: ZDT4

  22. Results: ZDT4 << With DC superior than without DC << With DC superior than without DC << With DC superior than without DC >> With DC-scheme is superior

  23. Conclusion We proposed a new model of EMOs. • DCMOGA (DC-scheme):Distributed Cooperation model of MOGA Compared the algorithms combined with DC-scheme against algorithm without DC-scheme. • The algorithms combined DC-scheme derives the efficient results. • DC-scheme can be combined any other EMOs, and the algorithm is more efficient algorithm than without DC-scheme. >> DC-scheme is efficient scheme for EMOs.

  24. Performance Metrics RNI: Ratio of Non-dominated Individualsderived from 2 types of non-dominated solutions Set A: front1 Set A: 3/5 = 0.6 Set B: 2/5 = 0.4 Set B: front2

  25. Results: ZDT6

  26. Results: ZDT6

  27. Results: KP750-2

  28. Results: KP750-2

  29. Performance Metrics: Coverage(D) Coverage difference of two sets: D

  30. The improved MOGA MOGA is proposed by Fonseca Improved MOGA: MOGA added to the Sharing and using pareto archive.

  31. SOGA and MOGA DC-scheme are compared SOGA and MOGA >> SOGA and MOGASOGA: 300 generation x 2MOGA: 400

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