Analysis on the Island Model Parallel Genetic Algorithms for the Genetic Drifts
 Tatsuya Niwa,
 Masaru Tanaka
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Abstract
In our former paper, we have investigated the relation among the mean convergence time, the population size, and the chromosome length of genetic algorithms (GAs). Our analyses of GAs make use of the Markov chain formalism based on the WrightFisher model, which is a typical and wellknown model in population genetics. The WrightFisher model is characterized by 1locus, 2alleles, fixed population size, and discrete generation. For these simple characters, it is easy to evaluate the behavior of genetic process. We have also given the mean convergence time under genetic drift. Genetic drift can be well described in the WrightFisher model, and we have determined the stationary states of the corresponding Markov chain model and the mean convergence time to reach one of these stationary states. The island model is also wellknown model in population genetics, and it is similar to one of the most typical model of parallel GAs, which require parallel computer for high performance computing. We have also derived the most effective migration rate for the island model parallel GAs with some restrictions. The obtained most effective migration rate is rather small value, i.e. one immigrant per generation, however the behaviors of the island model parallel GAs at that migration rate are not revealed yet clearly. In this paper, we discuss the mean convergence time for the island model parallel GAs from both of exact solution and numerical simulation. As expected from the WrightFisher model’s analysis, the mean convergence time of the island model parallel GAs is proportional to population size, and the coefficient is larger with smaller migration rate. Since to keep the diversity in population is important for effective performance of GAs, the convergence in population gives a bad influence for GAs. On the other hand, mutation and crossover operation prevent converging in GAs population. Because of the small migration rate makes converging force weak, it must be effective for GAs. This means that the island model parallel GAs is more efficient not only to use large population size with parallel computers, but also to keep the diversity in population, than usual GAs.
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 Title
 Analysis on the Island Model Parallel Genetic Algorithms for the Genetic Drifts
 Book Title
 Simulated Evolution and Learning
 Book Subtitle
 Second AsiaPacific Conference on Simulated Evolution and Learning, SEAL’98 Canberra, Australia, November 24–27, 1998 Selected Papers
 Pages
 pp 349356
 Copyright
 1999
 DOI
 10.1007/3540488731_45
 Print ISBN
 9783540659075
 Online ISBN
 9783540488736
 Series Title
 Lecture Notes in Computer Science
 Series Volume
 1585
 Series ISSN
 03029743
 Publisher
 Springer Berlin Heidelberg
 Copyright Holder
 SpringerVerlag Berlin Heidelberg
 Additional Links
 Topics
 Keywords

 Markov chain
 population genetics
 genetic drift
 WrightFisher model
 island model parallel genetic algorithms
 Industry Sectors
 eBook Packages
 Editors

 Bob McKay ^{(1)}
 Xin Yao ^{(1)}
 Charles S. Newton ^{(1)}
 JongHwan Kim ^{(2)}
 Takeshi Furuhashi ^{(3)}
 Editor Affiliations

 1. School of Computer Science, University College, UNSW Australian Defence Force Academy
 2. Department of Electrical Engineering Korea Advanced Institute of Science and Technology
 3. Department of Information Electronics, Nagoya University
 Authors

 Tatsuya Niwa ^{(6)}
 Masaru Tanaka ^{(6)}
 Author Affiliations

 6. Information Science Division, Electrotechnical Laboratory, 114 Umezono Tsukubashi, Ibaraki, 3058568, Japan
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