Modeling genetic algorithms with interacting particle systems

We present in this work a natural Interacting Particle System (IPS) approach formodeling and studying the asymptotic behavior of Genetic Algorithms (GAs). In thismodel, a population is seen as a distribution (or measure) on the search space, and theGenetic Algorithm as a measure valued dynamical sys...

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Autores Principales: Del Moral, P., Kallel, L., Rowe, J.
Formato: Artículo
Idioma: Español
Publicado: 2015
Acceso en línea: http://revistas.ucr.ac.cr/index.php/matematica/article/view/201
http://hdl.handle.net/10669/12841
Sumario: We present in this work a natural Interacting Particle System (IPS) approach formodeling and studying the asymptotic behavior of Genetic Algorithms (GAs). In thismodel, a population is seen as a distribution (or measure) on the search space, and theGenetic Algorithm as a measure valued dynamical system. This model allows one toapply recent convergence results from the IPS literature for studying the convergenceof genetic algorithms when the size of the population tends to infinity.We first review a number of approaches to Genetic Algorithms modeling and relatedconvergence results. We then describe a general and abstract discrete timeInteracting Particle System model for GAs, and we propose a brief review of some recentasymptotic results about the convergence of the N-IPS approximating model (offinite N-sized-population GAs) towards the IPS model (of infinite population GAs),including law of large number theorems, IL p-mean and exponential bounds as well aslarge deviations principles.Finally, the impact of modeling Genetic Algorithms with our interacting particlesystem approach is detailed on different classes of generic genetic algorithms includingmutation, cross-over and proportionate selection. We explore the connections betweenFeynman-Kac distribution flows and the simple genetic algorithm. This Feynman-Kacrepresentation of the infinite population model is then used to develop asymptoticstability and uniform convergence results with respect to the time parameter.Keywords:  Genetic algorithms, Interacting particle systems, asymptotical convergence,Feynman-Kac formula, measure valued processes.