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

  • Raphaël Cerf (a1)

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) is greater than the mean fitness.

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

References

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

  • Raphaël Cerf (a1)

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