Asymptotical Convergence Rates of Simple Evolutionary Algorithms under Factorizing Mutation Distributions

Abstract

The standard choice for mutating an individual of an evolutionary algorithm with continuous variables is the normal distribution. It is shown that there is a broad class of alternative mutation distributions offering local convergence rates being asymptotical equal to the convergence rates achieved with normally distributed mutations. Such mutation distributions must be factorizing and the absolute fourth moments must be finite. Under these conditions an asymptotical theory of the convergence rates of simple evolutionary algorithms can be established for the entire class of distributions.