The one-fifth success rule is one of the best-known and most widely accepted techniques to control the parameters of evolutionary algorithms. While it is often applied in the literal sense, a common interpretation sees the one-fifth success rule as a family of success-based updated rules that are determined by an update strength F and a success rate. We analyze in this work how the performance of the (1+1) Evolutionary Algorithm on Leading Ones depends on these two hyper-parameters. Our main result shows that the best performance is obtained for small update strengths \(F=1+o(1)\) and success rate 1/e. We also prove that the running time obtained by this parameter setting is, apart from lower order terms, the same that is achieved with the best fitness-dependent mutation rate. We show similar results for the resampling variant of the (1+1) Evolutionary Algorithm, which enforces to flip at least one bit per iteration.

五分之一成功规则是控制进化算法参数的最著名和最广泛接受的技术之一。虽然它通常按字面意义应用，但常见的解释将五分之一成功规则视为一系列基于成功的更新规则，这些规则由更新强度F和成功率决定。我们在这项工作中分析了 (1+1) Evolutionary Algorithm on Leadership Ones 的性能如何取决于这两个超参数。我们的主要结果表明，在较小的更新强度\(F=1+o(1)\)和成功率 1/ e 下获得了最佳性能. 我们还证明了通过此参数设置获得的运行时间，除了低阶项外，与最佳适应度相关突变率所获得的运行时间相同。我们对 (1+1) 进化算法的重采样变体展示了类似的结果，该算法强制每次迭代至少翻转一位。