Generalizations of intermediate recombination in evolution strategies

In this paper two different generalizations of intermediate recombination in evolution strategies are investigated. Both generalizations allow for recombining an arbitrary number of ρ parents. However, the so-called ρ/ρ-mechanism averages all ρ parents, while the so-called ρ/2-mechanism repeatedly (for each object variable anew) selects two out of ρ parents and averages the corresponding object variables to create an offspring individual. Results presented for the spherical function demonstrate that these two operators can cause a significantly different behavior concerning the convergence velocity of the algorithm. Both operators are applied to a number of different objective functions (including separable and non-separable, unimodal and multimodal, regular and irregular topologies), and the impact of the number of parents ρ is investigated. The results illustrate that important differences in the results are not consistent with the canonical topology classification of objective functions, but can be explained to some extent by the “genetic repair” hypothesis of Beyer in combination with a reasoning about the success region