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The mutation strength adaptation properties of a multi-recombinative $(\mu/\mu_I, \lambda)$-ES are studied for isotropic mutations. To this end, standard implementations of cumulative step-size adaptation (CSA) and mutative self-adaptation ($\sigma$SA) are investigated experimentally and theoretically by assuming large population sizes ($\mu$) in relation to the search space dimensionality ($N$). The adaptation is characterized in terms of the scale-invariant mutation strength on the sphere in relation to its maximum achievable value for positive progress. %The results show how the different $\sigma$-adaptation variants behave as $\mu$ and $N$ are varied. Standard CSA-variants show notably different adaptation properties and progress rates on the sphere, becoming slower or faster as $\mu$ or $N$ are varied. This is shown by investigating common choices for the cumulation and damping parameters. Standard $\sigma$SA-variants (with default learning parameter settings) can achieve faster adaptation and larger progress rates compared to the CSA. However, it is shown how self-adaptation affects the progress rate levels negatively. Furthermore, differences regarding the adaptation and stability of $\sigma$SA with log-normal and normal mutation sampling are elaborated., Comment: Technical Report

In the context of the 2018 IEEE Congress of Evolutionary Computation, the Matrix Adaptation Evolution Strategy for constrained optimization turned out to be notably successful in the competition on constrained single objective real-parameter optimization. Across all considered instances the so-called $\epsilon$MAg-ES achieved the second rank. However, it can be considered to be the most successful participant in high dimensions. Unfortunately, the competition result does not provide any information about the modus operandi of a successful algorithm or its suitability for problems of a particular shape. To this end, the present paper is concerned with an extensive empirical analysis of the $\epsilon$MAg-ES working principles that is expected to provide insights about the performance contribution of specific algorithmic components. To avoid rankings with respect to insignificant differences within the algorithm realizations, the paper additionally introduces significance testing into the ranking process., Comment: 37 pages, includes appendices, preprint