Mutation Strength Adaptation of the $(μ/μ_I, λ)$-ES for Large Population Sizes on the Sphere Function
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866911993837912064 |
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| author | Omeradzic, Amir Beyer, Hans-Georg |
| author_facet | Omeradzic, Amir Beyer, Hans-Georg |
| contents | The mutation strength adaptation properties of a multi-recombinative $(μ/μ_I, λ)$-ES are studied for isotropic mutations. To this end, standard implementations of cumulative step-size adaptation (CSA) and mutative self-adaptation ($σ$SA) are investigated experimentally and theoretically by assuming large population sizes ($μ$) 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 $σ$-adaptation variants behave as $μ$ and $N$ are varied. Standard CSA-variants show notably different adaptation properties and progress rates on the sphere, becoming slower or faster as $μ$ or $N$ are varied. This is shown by investigating common choices for the cumulation and damping parameters. Standard $σ$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 $σ$SA with log-normal and normal mutation sampling are elaborated. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_09761 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Mutation Strength Adaptation of the $(μ/μ_I, λ)$-ES for Large Population Sizes on the Sphere Function Omeradzic, Amir Beyer, Hans-Georg Neural and Evolutionary Computing The mutation strength adaptation properties of a multi-recombinative $(μ/μ_I, λ)$-ES are studied for isotropic mutations. To this end, standard implementations of cumulative step-size adaptation (CSA) and mutative self-adaptation ($σ$SA) are investigated experimentally and theoretically by assuming large population sizes ($μ$) 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 $σ$-adaptation variants behave as $μ$ and $N$ are varied. Standard CSA-variants show notably different adaptation properties and progress rates on the sphere, becoming slower or faster as $μ$ or $N$ are varied. This is shown by investigating common choices for the cumulation and damping parameters. Standard $σ$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 $σ$SA with log-normal and normal mutation sampling are elaborated. |
| title | Mutation Strength Adaptation of the $(μ/μ_I, λ)$-ES for Large Population Sizes on the Sphere Function |
| topic | Neural and Evolutionary Computing |
| url | https://arxiv.org/abs/2408.09761 |