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While evolutionary algorithms are known to be very successful for a broadrange of applications, the algorithm designer is often left with manyalgorithmic choices, for example, the size of the population, the mutationrates, and the crossover rates of the algorithm. These parameters are known tohave a crucial influence on the optimization time, and thus need to be chosencarefully, a task that often requires substantial efforts. Moreover, theoptimal parameters can change during the optimization process. It is thereforeof great interest to design mechanisms that dynamically choose best-possibleparameters. An example for such an update mechanism is the one-fifth successrule for step-size adaption in evolutionary strategies. While in continuousdomains this principle is well understood also from a mathematical point ofview, no comparable theory is available for problems in discrete domains.  In this work we show that the one-fifth success rule can be effective also indiscrete settings. We regard the $(1+(\lambda,\lambda))$~GA proposed in[Doerr/Doerr/Ebel: From black-box complexity to designing new geneticalgorithms, TCS 2015]. We prove that if its population size is chosen accordingto the one-fifth success rule then the expected optimization time on\textsc{OneMax} is linear. This is better than what \emph{any} staticpopulation size $\lambda$ can achieve and is asymptotically optimal also amongall adaptive parameter choices.

Optimal Parameter Choices Through Self-Adjustment: Applying the 1/5-th Rule in Discrete Settings