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.

翻译：对于每个变异率$p \in (0, 1)$以及任意$\varepsilon > 0$，存在一个具有唯一最大值的适应度函数$f : \{0,1\}^n \to \mathbb{R}$，使得在该函数上$(1+1)$进化算法的最优变异率位于区间$(p-\varepsilon, p+\varepsilon)$内。换言之，$(1+1)$进化算法的最优变异率集合在区间$[0, 1]$中是稠密的。为证明这一结论，本文引入了DistantSteppingStones适应度函数，该函数由被大适应度低谷分隔的广阔平台组成。