All Mutation Rates $c/n$ for the $(1+1)$ Evolutionary Algorithm

arXiv:2602.23573v1 Announce Type: new
Abstract: 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.