Progress Rate Analysis of Evolution Strategies on the Rastrigin Function: First Results

A first order progress rate is derived for the intermediate multi-recombinative Evolution Strategy (μ/μ, λ)-ES on the highly multimodal Rastrigin test function. The progress is derived within a linearized model applying the method of so-called noisy order statistics. To this end, the mutation-induced variance of the Rastrigin function is determined. The obtained progress approximation is compared to simulations and yields strengths and limitations depending on mutation strength and distance to the optimizer. Furthermore, the progress is iterated using the dynamical systems approach and compared to averaged optimization runs. The property of global convergence within given approximation is discussed. As an outlook, the need of an improved first order progress rate as well as the extension to higher order progress including positional fluctuations is explained.