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The quasispecies regime for the simple genetic algorithm with roulette wheel selection

Part of: Markov processes

Published online by Cambridge University Press:  08 September 2017

Raphaël Cerf
Raphaël Cerf*
Affiliation:
École Normale Supérieure
*
* Postal address: Département de Mathématiques et Applications, École Normale Supérieure, 45 rue d'Ulm, 75005 Paris, France. Email address: raphael.cerf@gmail.com
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Abstract

We introduce a new parameter to discuss the behavior of a genetic algorithm. This parameter is the mean number of exact copies of the best-fit chromosomes from one generation to the next. We believe that the genetic algorithm operates best when this parameter is slightly larger than 1 and we prove two results supporting this belief. We consider the case of the simple genetic algorithm with the roulette wheel selection mechanism. We denote by ℓ the length of the chromosomes, m the population size, p C the crossover probability, and p M the mutation probability. Our results suggest that the mutation and crossover probabilities should be tuned so that, at each generation, the maximal fitness multiplied by (1 - p C)(1 - p M)ℓ is greater than the mean fitness.

Keywords

Genetic algorithmquasispeciesstochastic optimization

MSC classification

Primary: 60J20: Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.)
Secondary: 92D15: Problems related to evolution

Information

Type
Research Article
Information
Advances in Applied Probability , Volume 49 , Issue 3 , September 2017 , pp. 903 - 926
Copyright
Copyright © Applied Probability Trust 2017 

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