Multidimensional mutations in evolutionary algorithms based on real-valued representation

This work is focused on the fact that the most probable distance of mutated points in multi-dimensional Gaussian and Cauchy mutations is not in a close neighborhood of the origin, but at a certain distance from it. In the case of the Gaussian mutation, this distance is proportional to the norm of the standard deviation vector and increases with the landscape dimension. This may cause a decrease in the sensitivity of the evolutionary algorithm to narrow peaks when the landscape dimension increases, but, simultaneously, it strengthens the exploration property of the algorithm. Moreover, the influence of the reference frame orientation on the effectiveness of the non-spherical multi-dimensional Cauchy mutation is analyzed using simulation experiments. Four multi-dimensional mutations (Gaussian, modified Gaussian, non-spherical and spherical Cauchy mutations) are applied to two classes of evolutionary algorithms based on real-valued representation, i.e. Galar's evolutionary search with soft selection and evolutionary programming. A comparative analysis is provided for convergence to the local optimum, sensitivity to narrow peaks, saddle crossing and symmetry problems.