Modeling the Genetic Algorithm by a Nonhomogeneous Markov Chain: Weak and Strong Ergodicity
Viviane Simioli Medeiros Campos, André Grahl Pereira, Juan Alberto Rojas Cruz · Theory of Probability and Its Applications · 2013
Evolutionary algorithms are used to search for optimal points of functions. One of these algorithms, the canonical genetic algorithm, uses in its dynamics two parameters, namely mutation and crossover probabilities, which are kept fixed throughout the algorithm's evolution. In this paper, changes in those parameters will be allowed and the convergence of this new algorithm will be analyzed. We also present an approach to weak ergodicity of a nonhomogeneous Markov chains without using directly Dobrushin's $\delta$ coefficient.