Source: J. Appl. Probab. Volume 47, Number 4
(2010), 967-975.
In this paper we prove that the stationary distribution of populations in
genetic algorithms focuses on the uniform population with the highest fitness
value as the selective pressure goes to ∞ and the mutation probability
goes to 0. The obtained sufficient condition is based on the work of
Albuquerque and Mazza (2000), who, following Cerf (1998), applied the large
deviation principle approach (Freidlin-Wentzell theory) to the Markov chain of
genetic algorithms. The sufficient condition is more general than that of
Albuquerque and Mazza, and covers a set of parameters which were not found by
Cerf.
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