On the Asymptotic Behavior of Multirecombinant Evolution Strategies

. The performance of (=; )-ESs (Evolution Strategies) in the asymptotic limit for N !1 and !1 is investigated. The conjecture made by Schwefel that the maximum performance of such strategies scales like ln(=) will be proved. Furthermore, it will be shown that an optimally tuned (=; )-ES performs exactly times faster than an optimally tuned (1+1)-ES, if the hyper-sphere is taken as the fitness model (using the number of generations as the performance measure). The notion of fitness efficiency will be introduced and will be used to derive the ES time complexity. The results are compared to the non-recombinant (; )-ES. 1 Introduction The performance of Evolution Strategies (ES) can be investigated by experiments and by theoretical analysis. Both approaches have their advantages and disadvantages. Usually it is much easier to perform ES runs and present the results by graphs. This method can be applied to each fitness function F (x). However, there remains always an uncertainty as to t..