A Markov Framework for the Simple Genetic Algorithm
نویسندگان
چکیده
This paper develops a theoretical framework based on Markov chains for the simple genetic algorithm (operators of reproduction, crossover, and mutation). We prove the existence of a unique stationary distribution for the Markov chain when mutation probability is used as a control parameter. We also show that there is a stationary distribution limit when the control parameter approaches zero. Finally, we also present a strong ergodicity bound to ensure that the nonstationary algorithm achieves the limiting distribution, and we prove that the stationary distribution limit has nonzero components corresponding to all solutions. Running title: Markov model of genetic algorithm
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