Simple genetic algorithms on populations of l-binary words usually become iterative systems on 2l dimensional spaces when populations have size infinite. However, in a particular model (BCCG model) previously introduced, it has been shown that the iterative system works in a l-dimensional space. In this paper we propose a simplification of the BCCG model and we analyze it in the case of large but finite-size populations. In particular: 1. We exhibit a Markov chain with states in IRl that approximates the system behavior. 2. We estimate the steady state distribution of the Markov chain.
Analysis of a genetic model with finite populations / Alberto Bertoni, Paola Campadelli, Roberto Posenato - In: Advances in Natural Computation : First International Conference, ICNC 2005 : Changsha, China, August 27-29, 2005 : Proceedings, Part III / Lipo Wang, Ke Chen, Yew S. Ong. - Berlin : .Springer, 2005. - ISBN 354028320X. - pp. 235-244 (( Intervento presentato al 1. convegno International Conference on Natural Computation - ICNC 2005 tenutosi a Changsha, China nel 2005 [10.1007/11539902_28].
Analysis of a genetic model with finite populations.
A. Bertoni;P. Campadelli;
2005
Abstract
Simple genetic algorithms on populations of l-binary words usually become iterative systems on 2l dimensional spaces when populations have size infinite. However, in a particular model (BCCG model) previously introduced, it has been shown that the iterative system works in a l-dimensional space. In this paper we propose a simplification of the BCCG model and we analyze it in the case of large but finite-size populations. In particular: 1. We exhibit a Markov chain with states in IRl that approximates the system behavior. 2. We estimate the steady state distribution of the Markov chain.
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