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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, pC the crossover probability, and pM 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 - pC)(1 - pM)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
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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