Step Length Adaptation on Ridge Functions

Step length adaptation is central to evolutionary algorithms in real-valued search spaces. This paper contrasts several step length adaptation algorithms for evolution strategies on a family of ridge functions. The algorithms considered are cumulative step length adaptation, a variant of mutative self-adaptation, two-point adaptation, and hierarchically organized strategies. In all cases, analytical results are derived that yield insights into scaling properties of the algorithms. The influence of noise on adaptation behavior is investigated. Similarities and differences between the adaptation strategies are discussed.