All Constant Mutation Rates for the $(1+1)$ Evolutionary Algorithm
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866910204230107136 |
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| author | Kelley, Andrew James |
| author_facet | Kelley, Andrew James |
| contents | For every mutation rate $p \in (0, 1)$, and for all $\varepsilon > 0$, there is a fitness function $f : \{0,1\}^n \to \mathbb{R}$ with a unique maximum for which the optimal mutation rate for the $(1+1)$ evolutionary algorithm on $f$ is in $(p-\varepsilon, p+\varepsilon)$. In other words, the set of optimal mutation rates for the $(1+1)$ EA is dense in the interval $[0, 1]$. To show that, this paper introduces DistantSteppingStones, a fitness function which consists of large plateaus separated by large fitness valleys. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_18989 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | All Constant Mutation Rates for the $(1+1)$ Evolutionary Algorithm Kelley, Andrew James Neural and Evolutionary Computing For every mutation rate $p \in (0, 1)$, and for all $\varepsilon > 0$, there is a fitness function $f : \{0,1\}^n \to \mathbb{R}$ with a unique maximum for which the optimal mutation rate for the $(1+1)$ evolutionary algorithm on $f$ is in $(p-\varepsilon, p+\varepsilon)$. In other words, the set of optimal mutation rates for the $(1+1)$ EA is dense in the interval $[0, 1]$. To show that, this paper introduces DistantSteppingStones, a fitness function which consists of large plateaus separated by large fitness valleys. |
| title | All Constant Mutation Rates for the $(1+1)$ Evolutionary Algorithm |
| topic | Neural and Evolutionary Computing |
| url | https://arxiv.org/abs/2602.18989 |