We study the $(1:s+1)$ success rule for controlling the population size of the $(1,\lambda)$-EA. It was shown by Hevia Fajardo and Sudholt that this parameter control mechanism can run into problems for large $s$ if the fitness landscape is too easy. They conjectured that this problem is worst for the OneMax benchmark, since in some well-established sense OneMax is known to be the easiest fitness landscape. In this paper we disprove this conjecture and show that OneMax is not the easiest fitness landscape with respect to finding improving steps. As a consequence, we show that there exists $s$ and $\varepsilon$ such that the self-adjusting $(1,\lambda)$-EA with $(1:s+1)$-rule optimizes OneMax efficiently when started with $\varepsilon n$ zero-bits, but does not find the optimum in polynomial time on Dynamic BinVal. Hence, we show that there are landscapes where the problem of the $(1:s+1)$-rule for controlling the population size of the $(1, \lambda)$-EA is more severe than for OneMax.

翻译：我们研究了用于控制$(1,\lambda)$-EA种群规模的$(1:s+1)$成功规则。Hevia Fajardo与Sudholt曾指出，当适应度景观过于简单时，该参数控制机制在大$s$取值下可能出现问题。他们推测该问题在OneMax基准函数上最为严重，因为从已建立的严格意义上看，OneMax被认为是最简单的适应度景观。本文否证了这一猜想，表明在寻找改进步长方面，OneMax并非最简单的适应度景观。进而我们证明：存在特定$s$与$\varepsilon$取值，使得采用$(1:s+1)$规则的自适应$(1,\lambda)$-EA在初始种群含$\varepsilon n$个零比特时能高效优化OneMax，但在Dynamic BinVal问题上无法在多项式时间内找到最优解。因此我们证明，存在某些适应度景观使得$(1:s+1)$规则控制$(1,\lambda)$-EA种群规模时产生的问题比OneMax更加严重。