Local convergence rates of simple evolutionary algorithms with Cauchy mutations

The standard choice for mutating an individual of an evolutionary algorithm with con tinuous variables is the normal distribution however other distributions especially some versions of the multivariate Cauchy distribution have recently gained increased popularity in practical applications Here the extent to which Cauchy mutation distributions may a ect the local convergence behavior of evolutionary algorithms is analyzed The results show that the order of local convergence is identical for Gaussian and spherical Cauchy distributions whereas nonspherical Cauchy mutations lead to slower local convergence As a by product of the analysis some recommendations for the parametrization of the self adaptive step size control mechanism can be derived