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Self-adjusting population sizes for non-elitist evolutionary algorithms: why success rates matter

Published: 26 June 2021 Publication History

Abstract

Recent theoretical studies have shown that self-adjusting mechanisms can provably outperform the best static parameters in evolutionary algorithms on discrete problems. However, the majority of these studies concerned elitist algorithms and we do not have a clear answer on whether the same mechanisms can be applied for non-elitist algorithms.
We study one of the best-known parameter control mechanisms, the one-fifth success rule, to control the offspring population size λ in the non-elitist (1, λ) EA. It is known that the (1, λ) EA has a sharp threshold with respect to the choice of λ where the runtime on OneMax changes from polynomial to exponential time. Hence, it is not clear whether parameter control mechanisms are able to find and maintain suitable values of λ.
We show that the answer crucially depends on the success rate s (i. e. a one-(s + 1)-th success rule). We prove that, if the success rate is appropriately small, the self-adjusting (1, λ) EA optimises OneMax in O(n) expected generations and O(n log n) expected evaluations. A small success rate is crucial: we also show that if the success rate is too large, the algorithm has an exponential runtime on OneMax.

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    cover image ACM Conferences
    GECCO '21: Proceedings of the Genetic and Evolutionary Computation Conference
    June 2021
    1219 pages
    ISBN:9781450383509
    DOI:10.1145/3449639
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    Publication History

    Published: 26 June 2021

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    Author Tags

    1. drift analysis
    2. evolutionary algorithms
    3. non-elitism
    4. parameter control
    5. runtime analysis
    6. theory

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    • Consejo Nacional de Ciencia y Tecnología

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    Overall Acceptance Rate 1,669 of 4,410 submissions, 38%

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    Cited By

    View all
    • (2024)A Gentle Introduction to Theory (for Non-Theoreticians)Proceedings of the Genetic and Evolutionary Computation Conference Companion10.1145/3638530.3648402(800-829)Online publication date: 14-Jul-2024
    • (2024)Empirical Evaluation of Evolutionary Algorithms with Power-Law Ranking SelectionIntelligent Information Processing XII10.1007/978-3-031-57808-3_16(217-232)Online publication date: 6-Apr-2024
    • (2023)A Gentle Introduction to Theory (for Non-Theoreticians)Proceedings of the Companion Conference on Genetic and Evolutionary Computation10.1145/3583133.3595042(946-975)Online publication date: 15-Jul-2023
    • (2023)Self-adaptation Can Help Evolutionary Algorithms Track Dynamic OptimaProceedings of the Genetic and Evolutionary Computation Conference10.1145/3583131.3590494(1619-1627)Online publication date: 15-Jul-2023
    • (2023)Comma Selection Outperforms Plus Selection on OneMax with Randomly Planted OptimaProceedings of the Genetic and Evolutionary Computation Conference10.1145/3583131.3590488(1602-1610)Online publication date: 15-Jul-2023
    • (2023)Self-adjusting Population Sizes for Non-elitist Evolutionary Algorithms: Why Success Rates MatterAlgorithmica10.1007/s00453-023-01153-986:2(526-565)Online publication date: 24-Jul-2023
    • (2022)A gentle introduction to theory (for non-theoreticians)Proceedings of the Genetic and Evolutionary Computation Conference Companion10.1145/3520304.3533628(890-921)Online publication date: 9-Jul-2022
    • (2022)More Precise Runtime Analyses of Non-elitist Evolutionary Algorithms in Uncertain EnvironmentsAlgorithmica10.1007/s00453-022-01044-586:2(396-441)Online publication date: 2-Oct-2022
    • (2022)Self-adaptation via Multi-objectivisation: An Empirical StudyParallel Problem Solving from Nature – PPSN XVII10.1007/978-3-031-14714-2_22(308-323)Online publication date: 10-Sep-2022

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