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A new genetic algorithm specifically based on mutation and selection

Part of: Limit theorems Markov processes

Published online by Cambridge University Press:  01 July 2016

L. Rigal  and
L. Truffet
L. Rigal*
Affiliation:
Université de Provence
L. Truffet*
Affiliation:
Ecole des Mines de Nantes
*
∗ Postal address: Laboratoire d'Analyse, Topologie, Probabilités (LATP/UMR 6632), Université de Provence, 39 rue F. Joliot-Curie, F-13453 Marseille cedex 13, France.
∗∗ Postal address: Ecole des Mines de Nantes & IRCCYN, 4 rue Alfred Kastler, BP 20722, 44307 Nantes cedex 3, France. Email address: laurent.truffet@emn.fr
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Abstract

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In this paper we propose a new genetic algorithm specifically based on mutation and selection in order to maximize a fitness function. This mutation-selection algorithm behaves as a gradient algorithm which converges to local maxima. In order to obtain convergence to global maxima we propose a new algorithm which is built by randomly perturbing the selection operator of the gradient-like algorithm. The perturbation is controlled by only one parameter: that which allows the selection pressure to be governed. We use the Markov model of the perturbed algorithm to prove its convergence to global maxima. The arguments used in the proofs are based on Freidlin and Wentzell's (1984) theory and large deviation techniques also applied in simulated annealing. Our main results are that (i) when the population size is greater than a critical value, the control of the selection pressure ensures the convergence to the global maxima of the fitness function, and (ii) the convergence also occurs when the population is the smallest possible, i.e. 1.

Keywords

Freidlin-Wentzell theoryevolutionary algorithmstochastic optimization

MSC classification

Primary: 60F10: Large deviations
Secondary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces) 92D15: Problems related to evolution
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 39 , Issue 1 , March 2007 , pp. 141 - 161
Copyright
Copyright © Applied Probability Trust 2007 

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