Optimal static mutation strength distributions for the (1+λ) evolutionary algorithm on OneMax

Maxim Buzdalov, Carola Doerr

Research output: Chapter in Book/Report/Conference proceedingConference Proceeding (Non-Journal item)


Most evolutionary algorithms have parameters, which allow a great flexibility in controlling their behavior and adapting them to new problems. To achieve the best performance, it is often needed to control some of the parameters during optimization, which gave rise to various parameter control methods. In recent works, however, similar advantages have been shown, and even proven, for sampling parameter values from certain, often heavy-tailed, fixed distributions. This produced a family of algorithms currently known as "fast evolution strategies" and "fast genetic algorithms".

However, only little is known so far about the influence of these distributions on the performance of evolutionary algorithms, and about the relationships between (dynamic) parameter control and (static) parameter sampling. We contribute to the body of knowledge by presenting an algorithm that computes the optimal static distributions, which describe the mutation operator used in the well-known simple (1+λ) evolutionary algorithm on a classic benchmark problem OneMax. We show that, for large enough population sizes, such optimal distributions may be surprisingly complicated and counter-intuitive. We investigate certain properties of these distributions, and also evaluate the performance regrets of the (1 + λ) evolutionary algorithm using standard mutation operators.
Original languageEnglish
Title of host publicationGECCO '21
Subtitle of host publicationProceedings of the Genetic and Evolutionary Computation Conference
EditorsFrancisco Chicano
PublisherAssociation for Computing Machinery
Number of pages9
ISBN (Print)978-1-4503-8350-9
Publication statusPublished - 26 Jun 2021
Externally publishedYes
EventGECCO 2021 -Genetic and Evolutionary Computation Conference - Lille, France
Duration: 10 Jul 202114 Jul 2021


ConferenceGECCO 2021 -Genetic and Evolutionary Computation Conference
Period10 Jul 202114 Jul 2021


  • mutation operators
  • runtime analysis


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