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Tomoyuki HIROYASU Mitsunori MIKI Sinya WATANABE

Distributed Genetic Algorithms with a New Sharing Approach in Multiobjective Optimization Problems. Tomoyuki HIROYASU Mitsunori MIKI Sinya WATANABE. Doshisha University Kyoto, Japan. 1. Introduction. Introduction (No.1). Multiobjective Optimization Problems. Genetic Algorithms.

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Tomoyuki HIROYASU Mitsunori MIKI Sinya WATANABE

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  1. Distributed Genetic Algorithms with a New Sharing Approach in Multiobjective Optimization Problems Tomoyuki HIROYASU Mitsunori MIKI Sinya WATANABE Doshisha University Kyoto, Japan

  2. 1. Introduction

  3. Introduction (No.1) Multiobjective Optimization Problems Genetic Algorithms The Pareto optimum solutions Need a lot of iterations Many objects Need a large memory Real world problem Parallel Processing

  4. Introduction (No.2) High performance Commodity hardware Low cost PC Clusters

  5. Introduction (No.3) Evaluation fitness Makinen, et. al.，Parallel CFD96, (1996) Crossover, selection Rowe, et. al.，2NWGA, (1996) Population Hiyane, No. 9 Automatic system symposium(1997) Distributed Genetic Algorithms

  6. Introduction (No. 4) Distributed Genetic Algorithms Hiyane (1997) concluded that DGAs are the powerful tool for MOPs. The diversity of solutions becomes low Sharing to total population

  7. Aim of this study Introduced simple algorithms of Distributed Genetic Algorithm with sharing for total population Preliminary study of parallel genetic algorithms Effects of sharing in distributed genetic algorithms Single processor

  8. 2. Distributed Genetic Algorithms with Sharing

  9. Genetic operations in each island Genetic operations in each island island Divide population into sub populations Migration interval Migration rate Migration Distributed Genetic Algorithms

  10. gather populations from islands Genetic operations in each island divide population into islands migration F1 F1 F2 Total sharing F2 Total sharing Divide population into islands Distributed Genetic Algorithms with Sharing

  11. Evaluation methods The number of solutions Error Cover rate of solutions Coefficient of variation

  12. Evaluation method (Error)

  13. Min Max F1 F2 Evaluation method (Cover rate)

  14. F1 F2 Evaluation method (Coefficient of variation) 1) Count the number of solutions in the certain radius for each solution 2) Derive the coefficient of variation of the numbers 3) Derive the average 4) It shows the diversity of the solutions ( 1.0 is the best)

  15. 3. Numerical Examples

  16. Test Function Objective function Constraints In this study, we used 4 objectives.

  17. Test functions 2 objectives 3 objectives

  18. Coding Design variables　→　real values keep good heredity phenotype　ｘ x={1.23, 34.2, 4.23, 8.29} = genotypeX X={1.23, 34.2, 4.23, 8.29}

  19. Parameters parameter value initial population size 1000 crossover rate 1.0 mutation rate 0.0 migration rate 0.1 migration interval 2 island number 10

  20. Effect of distribution number of coefficient of variation calculation cover generations solutions error ratio time [sec] 2.46 1 island 1980 0.191 0.856 6 194.9 3.10 10 islands 2690 0.196 0.853 6 34.3 Terminal condition = function call (1000)

  21. number of solutions cover ratio calculation time [sec] coefficient of variation generations error DGA 3888 0.171 0.855 4.11 8.7 91.0 DGA with sharing 10.1 3079 0.153 0.855 3.10 563.1 function call number of solutions cover ratio coefficient of variation error generations 18998 DGA 3422 0.182 0.856 3.65 7.8 DGA with sharing 1581 0.226 0.847 2.15 3.0 4985 Termination condition= number of function call Termination condition= calculation time

  22. Errors 0.12 0.11 0.1 0.09 Error 0.08 0.07 0.06 DGA 0.05 DGA with sharing 0.000 0.025 0.050 0.075 0.100 0.125 Sleep time

  23. Cover ratio 0.950 0.925 0.900 Cover ratio 0.875 DGA DGA with sharing 0.850 0.000 0.025 0.050 0.075 0.100 0.125 Sleep time

  24. Hybrid sharing method total sharing divide population into small islands gather populations from islands genetic operation in each island sharing in each island migration

  25. Results of hybrid method coefficient of variation number of solutions cover ratio Calculation Time [sec] generations error DGA 3888 0.171 0.855 4.11 8.7 91.0 DGA with sharing 3079 0.153 0.855 10.1 563.1 3.10 Hybrid sharing 2922 0.183 0.858 2.43 10.0 275.5

  26. 4. Conclusions

  27. DGA with sharing to total population Conclusions Distributed genetic algorithm is good method for parallel processing but it reduces the diversity of solutions. To increase the diversity of solutions, the sharing is necessary even in distributed genetic algorithm. The proposed approach increase the diversity and the accuracy of solutions The proposed approach is especially useful when it takes much time to evaluate objective functions Another approach where the sharing is performed in islands and in total population is proposed and this approach reduces the calculation time and makes some increase in the diversity while the accuracy of the solutions is decreased.

  28. Conclusions (future work) Applying to another test functions Larger problems, something from real applications Parallel processing Sorting in parallel

  29. G Crossover

  30. c1 c2 c3 Constraints Feasible region p1

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