It seems very intuitive that for the maximization of the OneMax problem $Om(x):=∑i=1nxi$ the best that an elitist unary unbiased search algorithm can do is to store a best so far solution, and to modify it with the operator that yields the best possible expected progress in function value. This assumption has been implicitly used in several empirical works. In Doerr et al. (2020), it was formally proven that this approach is indeed almost optimal. In this work, we prove that drift maximization is not optimal. More precisely, we show that for most fitness levels between $n/2$ and $2n/3$ the optimal mutation strengths are larger than the drift-maximizing ones. This implies that the optimal RLS is more risk-affine than the variant maximizing the stepwise expected progress. We show similar results for the mutation rates of the classic (1$+$1) Evolutionary Algorithm (EA) and its resampling variant, the (1$+$1) EA$>0$⁠. As a result of independent interest we show that the optimal mutation strengths, unlike the drift-maximizing ones, can be even.

看起来很直观，对于 OneMax 问题的最大化 $哦米(X)：=∑一世=1nX一世$精英一元无偏搜索算法可以做的最好的事情是存储迄今为止最好的解决方案，并使用在函数值中产生最佳可能预期进展的运算符对其进行修改。这一假设已隐含地用于一些实证研究中。在 Doerr 等人中。（2020），正式证明这种方法确实几乎是最佳的。在这项工作中，我们证明漂移最大化不是最优的。更准确地说，我们表明，对于大多数健康水平之间的$n/2$ 和 $2n/3$最佳突变强度大于漂移最大化强度。这意味着最佳 RLS 比最大化逐步预期进展的变体更具风险仿射性。我们显示了经典（1$+$1）进化算法（EA）及其重采样变体，（1$+$1) EA$>0$⁠。作为独立兴趣的结果，我们表明与漂移最大化的不同，最佳突变强度可以是均匀的。