Self-Adaptation of Multirecombinant Evolution Strategies on the Highly Multimodal Rastrigin Function

Abstract

The self-adaptive, multirecombinative $(\mu /\mu _{I},\lambda)$ -Evolution strategy (ES) is investigated on the highly multimodal Rastrigin test function by theoretical and experimental means. The analysis is based on the established dynamical systems approach. To this end, the self-adaptation response (SAR) function is derived in the limit of large populations, which are necessary to achieve high success rates. Furthermore, steady-state conditions on Rastrigin are discussed and compared to the sphere function. Then, a relation for the learning parameter $\tau $ is derived to tune the sampling process of the self-adaptive ES, improving its efficiency on Rastrigin. The obtained result is compared to default $\tau $ -values. Furthermore, expected runtime experiments are conducted varying $\tau $ and population parameters of the ES. Theoretical and experimental results regarding $\tau $ are compared in terms of efficiency and robustness showing good agreement.