DagSemProc.06061.5.pdf
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How fast does the stationary distribution of the Markov chain modelling EAs concentrate on the homogeneous populations for small mutation rate?
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Dagstuhl Seminar Proceedings, Volume 6061
Series: Dagstuhl Seminar Proceedings (DagSemProc) - License:
Creative Commons Attribution 4.0 International license
- Publication Date: 2006-07-07
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Boris S. Mitavskiy and Jonathan E. Rowe. How fast does the stationary distribution of the Markov chain modelling EAs concentrate on the homogeneous populations for small mutation rate?. In Theory of Evolutionary Algorithms. Dagstuhl Seminar Proceedings, Volume 6061, pp. 1-9, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2006)
https://doi.org/10.4230/DagSemProc.06061.5
Abstract
The state space of the Markov chain modelling an evolutionary algorithm is quite large especially if the population space and the search space are large. I shell introduce an appropriate notion of "coarse graining" for such Markov chains. Indeed, from the mathematical point of view, this can be called a quotient of a Markov chain by an equivalence relation over the state space. The newly obtained Markov chain has a significantly smaller state space and it's stationary distribution is "coherent" with the initial large chain. Although the transition probabilities of the coarse-grained Markov chain are defined in terms of the stationary distribution of the original big chain, in some cases it is possible to deduce interesting information about the stationary distribution of the original chain in terms of the quatient chain. I will demonstrate how this method works. I shell also present some simple results and open questions.
Subject Classification
Keywords
- Markov chains
- Evolutionary algorithms
- coarse graining quotients of irreducible Markov chains
- concentration on the uniform populations
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