Evolutionary algorithms with adaptive lévy mutations

An evolutionary programming algorithm with adaptive mutation operators based on Lévy probability distribution is studied. Lévy stable distribution has an infinite second moment. Because of this, Lévy mutation is more likely to generate an offspring that is farther away from its parent than Gaussian mutation, which is often used in evolutionary algorithms. Such likelihood depends on a parameter α in the distribution. Based on this, we propose an adaptive Lévy mutation in which four different candidate offspring are generated by each parent, according to α = 1.0, 1.3, 1.7, and 2.0, and the best one is chosen as the offspring for the next generation. The proposed algorithm was applied to several multivariate function optimization problems. We showed empirically that the performance of the proposed algorithm was better than that of classical evolutionary algorithms using Gaussian mutation.