2015/06/30 by Raphaël Cerf, Cerf, Raphaël
Biochemistry, Genetics and Molecular Biology · Computer Science · #Evolution and Genetic Dynamics #Evolutionary Algorithms and Applications #FOS: Computer and information sciences #FOS: Mathematics #Metaheuristic Optimization Algorithms Research #Neural and Evolutionary Computing (cs.NE) #Probability (math.PR)
paper · pdf · doi:10.48550/arxiv.1506.09081
openalex publication_date 2015/06/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce a new parameter to discuss the behavior of a genetic algorithm.\nThis parameter is the mean number of exact copies of the best fit chromosomes\nfrom one generation to the next. We argue that the genetic algorithm should\noperate efficiently when this parameter is slightly larger than 1. We\nconsider the case of the simple genetic algorithm with the roulette--wheel\nselection mechanism. We denote by \ℓ the length of the chromosomes, by m\nthe population size, by pC the crossover probability and by pM the\nmutation probability. We start the genetic algorithm with an initial population\nwhose maximal fitness is equal to f0^* and whose mean fitness is equal to\n\f0. We show that, in the limit of large populations, the\ndynamics of the genetic algorithm depends in a critical way on the parameter\n\π ,= ,\(f0^*/\f0\) (1-pC)(1-pM)^\ℓ ,. Our\nresults suggest that the mutation and crossover probabilities should be tuned\nso that, at each generation, \maximal fitness \× (1-pC)\n(1-pM)^\ℓ > \mean fitness.\n