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

Published online by Cambridge University Press:  08 September 2017

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

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) is greater than the mean fitness.

Type
Research Article
Copyright
Copyright © Applied Probability Trust 2017 

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