On the Asymptotic Behavior of Multirecombinant Evolution Strategies

The performance of (Μ/Μ, λ)-ESs (Evolution Strategies) in the asymptotic limit for N→∞ and λ→∞ is investigated. The conjecture made by Schwefel that the maximum performance of such strategies scales like Μ In(λ/Μ) will be proved. Furthermore, it will be shown that an optimally tuned Μ/Μ, λ)-ES performs exactly λ 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 (Μ, λ)-ES.