Simple genetic algorithms on populations of $l$-binary words usually become iterative systems on $2^l$ 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.<br> 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:<br> 1. We exhibit a Markov chain with states in $\Re^l$ that approximates the system behavior.<br> 2. We estimate the steady state distribution of the Markov chain.
Analysis of a Genetic Model with Finite Populations
POSENATO, Roberto
2005-01-01
Abstract
Simple genetic algorithms on populations of $l$-binary words usually become iterative systems on $2^l$ 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 $\Re^l$ that approximates the system behavior.
2. We estimate the steady state distribution of the Markov chain.
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