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A Markov Chain Analysis of Genetic Algorithms: Large Deviation Principle Approach

Part of: Probabilistic methods, simulation and stochastic differential equations

Published online by Cambridge University Press:  14 July 2016

Joe Suzuki
Joe Suzuki*
Affiliation:
Osaka University
*
∗Postal address: Department of Mathematics, Osaka University, Toyonaka, Osaka 560-0043, Japan. Email address: suzuki@math.sci.osaka-u.ac.jp
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Abstract

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In this paper we prove that the stationary distribution of populations in genetic algorithms focuses on the uniform population with the highest fitness value as the selective pressure goes to ∞ and the mutation probability goes to 0. The obtained sufficient condition is based on the work of Albuquerque and Mazza (2000), who, following Cerf (1998), applied the large deviation principle approach (Freidlin-Wentzell theory) to the Markov chain of genetic algorithms. The sufficient condition is more general than that of Albuquerque and Mazza, and covers a set of parameters which were not found by Cerf.

Keywords

Genetic algorithmMarkov chainlarge deviation principleevolutionary algorithmFreidlin-Wentzell

MSC classification

Secondary: 65C40: Computational Markov chains 65C50: Other computational problems in probability
Type
Research Article
Information
Journal of Applied Probability , Volume 47 , Issue 4 , December 2010 , pp. 967 - 975
Copyright
Copyright © Applied Probability Trust 2010 

References

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