Phenotypic evolution with a mutation based on symmetric alpha-stable distributions

Multidimensional Symmetric alpha-Stable (S alpha S) mutations are applied to phenotypic evolutionary algorithms. Such mutations are characterized by non-spherical symmetry for alpha<2 and the fact that the most probable distance of mutated points is not in a close neighborhood of the origin, but at a certain distance from it. It is the so-called surrounding effect (Obuchowicz, 2001b; 2003b). For alpha=2, the S alpha S mutation reduces to the Gaussian one, and in the case of alpha=1, the Cauchy mutation is obtained. The exploration and exploitation abilities of evolutionary algorithms, using S alpha S mutations for different alpha, are analyzed by a set of simulation experiments. The obtained results prove the important influence of the surrounding effect of symmetric alpha-stable mutations on both the abilities considered.