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) Genetic Algorithms Multiobjective Optimization Problems Need a lot of iterations Need a large memory Real world problem Many objects The Pareto optimum solutions Parallel Processing

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

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

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

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

2. Distributed Genetic Algorithms with Sharing

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

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

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

Evaluation method (Error)

F1 F2 Evaluation method (Cover rate) MinMax

Evaluation method (Coefficient of variation) F1 F2 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)

3. Numerical Examples

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

Test functions 2 objectives 3 objectives

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

Parameters initial population size crossover rate mutation rate migration rate migration interval island number parametervalue

Effect of distribution 1 island 10 islands number of solutionserror cover ratio generations calculation time [sec] coefficient of variation Terminal condition = function call (1000)

DGA DGA with sharing number of solutions error cover ratio coefficient of variation generations function call DGA DGA with sharing number of solutions error cover ratio coefficient of variation generations calculation time [sec] Termination condition= number of function call Termination condition= calculation time

Errors Error Sleep time DGA with sharing DGA

Cover ratio Cover ratio Sleep time DGA with sharing DGA

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

Results of hybrid method DGA DGA with sharing number of solutions error cover ratio coefficient of variation generations Calculation Time [sec] Hybrid sharing

4. Conclusions

Conclusions The proposed approach is especially useful when it takes much time to evaluate objective functions 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. DGA with sharing to total population The proposed approach increase the diversity and the accuracy of solutions 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.

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

Crossover G

Constraints c2 p1 c1 c3 Feasible region