Mutation Strength Adaptation of the $(\mu/\mu_I, \lambda)$-ES for Large Population Sizes on the Sphere Function
<|reference_start|>Mutation Strength Adaptation of the $(\mu/\mu_I, \lambda)$-ES for Large Population Sizes on the Sphere Function: 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.<|reference_end|>
@article{omeradzic2024mutation,
    title={Mutation Strength Adaptation of the $(\mu/\mu_I, \lambda)$-ES for Large
  Population Sizes on the Sphere Function},
    author={Amir Omeradzic, Hans-Georg Beyer},
    journal={arXiv preprint arXiv:2408.09761},
    year={2024},
    archivePrefix={arXiv},
    eprint={2408.09761},
    primaryClass={cs.NE}
}