Parallel Genetic Algorithms with Distributed-Environment Multiple Population Scheme

1. Parallel Genetic Algorithms with Distributed-Environment Multiple Population Scheme M.Miki T.Hiroyasu K.Hatanaka Doshisha University,Kyoto,Japan

2. Outline • Background • Optimization Problems • Effects of GA Parameters • Distributed GA • Distributed Environment GA • Conclusion

3. Disadvantage Crossover rate Mutation rate Effective for 1 and 2 Background 1) High Computation Cost 2) Convergence to local minimum 3) Difficult to choose proper GA parameters Parallel and Distributed Scheme

4. Problem on proper setting of GA parameters Propose a new parameter-free distributed GA Background The performance of GA heavily depends on the GA parameters Proper values of GA Parameters depend on problems Distributed Environment Scheme

5. 5KN Objective Minimization of Truss Volume Design Valuables Sectional area ofeach member 5 6 5KN Constraints 3 4 • Tensile Strength • Compressive buckling • Displacement at node 6 1 2 10-Member Truss Structural Optimization Problems

6. Design Variables Constraint on displacement Constraint on tensile stress Constraint onCompressive buckling Fitness Function Sectional area of each member (circular shape) 12Bit ×10 = 120Bits

7. MutationRate 9 Combinations applied to SPGA Experiment 9 combinations (3 mutation rates ×3 crossover rates) Comparison based on the average of 10 trials out of 12 trials omitting the highest and the lowest values 0.1/L 10/L 1/L 0.3 0.3 0.3 0.3 CrossoverRate 10/L 0.1/L 1/L 0.6 0.6 0.6 0.6 0.1/L 1/L 10/L 1.0 1.0 1.0 1.0 0.1/L 1/L 10/L L is the length of the chromosome Experiment on Proper GA Parameters Roulette selection Conservation of Elite Up to 1000 generations Pop. Size 270,2430

8. Crossover Rate Mutation Rate Fitness History in Single Population GA (SPGA)

9. Crossover Rate Mutation Rate Fitness History in Single Population GA (SPGA)

10. Mutation Rate 0.1/L Mutation Rate 1/L Mutation Rate 10/L The performance of SPGA depends heavily in the proper choice of GA parameters Proper GA Parameters of SPGA

11. MPGA MPGA SPGA Population GA GA GA GA GA GA GA GA GA GA A GA is performed in one entire population. Same GAs are performed in multiple sub population Multiple Population GA(MPGA)

12. SPGA GA GA GA GA GA MPGA Computation time Slow Fast

13. Migration Experiment Problem : Same as SPGA MPGA:9 sub populations Migration rate = 0.3 Migration interval = 50 [generations] Exchange of individuals among sub populations. Worse Better Migration in MPGA Randomly selected source and destination sub populations Migration Rate Migration interval

14. Mutation Rate 0.1/L Mutation Rate 1/L Mutation Rate 10/L Proper GA Parameters fo MPGA

15. Mutation Rate 0.1/L Mutation Rate 1/L Mutation Rate 10/L Comparison between SPGA and MPGA

16. Mutation Rate 0.1/L Mutation Rate 1/L Mutation Rate 10/L Comparison between SPGA and MPGA

17. Crossover Rate Increase in the quality of Solutions. However, proper setting of GA parameters is necessary. Mutation Rate Effect of Multiple Population

18. Crossover Rate Mutation Rate Distributed Environment GA Conventional Environment GA Experiment Problem : Same as MPGA 9 Different environments (3 mutation rates ×3 crossover rates) for evaluation Distributed Environment GA(DEGA) Same parameters are used. Different GA parameters are used.

19. 1.75 Crossover Rate Best = 1.78 Results Best = 1.74 Avg. 1.70 1. DEGA outperforms the best SPGA. 2.DEGA provides good performance even comparing to MPGA Avg. 1.58 Worst = 1.58 Pop.size = 270 Worst = 1.38 Mutation Rate Effect of DEGA

20. Conclusion (1) The multiple population GA yields better solutions than single population GA because the diversity of individuals are maintained in the multiple population GA during the evolutional process. (2) The distributed environment scheme in the multiple population GA shows a good performance compared to other conventional GA. This scheme does not need to predetermine the GA parameters,and it is very useful for many problems where the proper values of those parameters are not known.