All Mutation Rates $c/n$ for the $(1+1)$ Evolutionary Algorithm
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arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866915821452787712 |
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| author | Kelley, Andrew James |
| author_facet | Kelley, Andrew James |
| contents | For every real number $c \geq 1$ and for all $\varepsilon > 0$, there is a fitness function $f : \{0,1\}^n \to \mathbb{R}$ for which the optimal mutation rate for the $(1+1)$ evolutionary algorithm on $f$, denoted $p_n$, satisfies $p_n \approx c/n$ in that $|np_n - c| < \varepsilon$. In other words, the set of all $c \geq 1$ for which the mutation rate $c/n$ is optimal for the $(1+1)$ EA is dense in the interval $[1, \infty)$. To show this, a fitness function is introduced which is called HillPathJump. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_23573 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | All Mutation Rates $c/n$ for the $(1+1)$ Evolutionary Algorithm Kelley, Andrew James Neural and Evolutionary Computing For every real number $c \geq 1$ and for all $\varepsilon > 0$, there is a fitness function $f : \{0,1\}^n \to \mathbb{R}$ for which the optimal mutation rate for the $(1+1)$ evolutionary algorithm on $f$, denoted $p_n$, satisfies $p_n \approx c/n$ in that $|np_n - c| < \varepsilon$. In other words, the set of all $c \geq 1$ for which the mutation rate $c/n$ is optimal for the $(1+1)$ EA is dense in the interval $[1, \infty)$. To show this, a fitness function is introduced which is called HillPathJump. |
| title | All Mutation Rates $c/n$ for the $(1+1)$ Evolutionary Algorithm |
| topic | Neural and Evolutionary Computing |
| url | https://arxiv.org/abs/2602.23573 |