Toward a Theory of Evolution Strategies: On the Benefits of Sex— the (μ/μ, λ) Theory

The multirecombinant (μ/μ, λ) evolution strategy (ES) is investigated for real-valued, N-dimensional parameter spaces. The analysis includes both intermediate recombination and dominant recombination, as well. These investigations are done for the spherical model first. The problem of the optimal population size depending on the parameter space dimension N is solved. A method extending the results obtained for the spherical model to nonspherical success domains is presented. The power of sexuality is discussed and it is shown that this power does not stem mainly from the “combination” of “good properties” of the mates (building block hypothesis) but rather from genetic repair diminishing the influence of harmful mutations. The dominant recombination is analyzed by introduction of surrogate mutations leading to the concept of species. Conclusions for evolutionary algorithms (EAs), including genetic algorithms (GAs), are drawn.