Mutation Strength Adaptation of the (μ/μ_I, λ)-ES for Large Population Sizes on the Sphere Function

Abstract

The mutation strength adaptation properties of a multi-recombinative (/_I, )-ES are studied for isotropic mutations. To this end, standard implementations of cumulative step-size adaptation (CSA) and mutative self-adaptation (SA) are investigated experimentally and theoretically by assuming large population sizes () 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 -adaptation variants behave as and N are varied. Standard CSA-variants show notably different adaptation properties and progress rates on the sphere, becoming slower or faster as or N are varied. This is shown by investigating common choices for the cumulation and damping parameters. Standard 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 SA with log-normal and normal mutation sampling are elaborated.

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