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The one-fifth success rule is one of the best-known and most widely acceptedtechniques to control the parameters of evolutionary algorithms. While it isoften applied in the literal sense, a common interpretation sees the one-fifthsuccess rule as a family of success-based updated rules that are determined byan update strength $F$ and a success rate. We analyze in this work how theperformance of the (1+1) Evolutionary Algorithm on LeadingOnes depends on thesetwo hyper-parameters. Our main result shows that the best performance isobtained for small update strengths $F=1+o(1)$ and success rate $1/e$. We alsoprove that the running time obtained by this parameter setting is, apart fromlower order terms, the same that is achieved with the best fitness-dependentmutation 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.

Self-Adjusting Mutation Rates with Provably Optimal Success Rules