Sharp asymptotic results for simplified mutation-selection algorithms

• 成果类型: Article
• 署名作者: Bérard, J; Bienvenüe, A
• 署名单位: Universite Claude Bernard Lyon 1; Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA)
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• 发表日期: 2003
• 页码: 1534-1568
• 关键词: genetic algorithms; CONVERGENCE; EVOLUTION

摘要

We study the asymptotic behavior of a mutation-selection genetic algorithm on the integers with finite population of size p greater than or equal to 1. The mutation is defined by the steps of a simple random walk and the fitness function is linear. We prove that the normalized population satisfies an invariance principle, that a large-deviations principle holds and that the relative positions converge in law. After n steps, the population is asymptotically around rootn times the position at time 1 of a Bessel process of dimension 2p - 1.