A further result on the Markov chain model of genetic algorithms and its application to a simulated annealing-like strategy

Authors:
J. Suzuki
Affiliations:
Dept. of Math., Osaka Univ.
Venue:
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Year:
1998

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Abstract

This paper shows a theoretical property on the Markov chain of genetic algorithms: the stationary distribution focuses on the uniform population with the optimal solution as mutation and crossover probabilities go to zero and some selective pressure defined in this paper goes to infinity. Moreover, as a result, a sufficient condition for ergodicity is derived when a simulated annealing-like strategy is considered. Additionally, the uniform crossover counterpart of the Vose-Liepins formula is derived using the Markov chain model