Self-adjusting offspring population sizes outperform fixed parameters on the cliff function

Research output: Chapter in Book/Report/Conference proceedingConference contribution


In the discrete domain, self-adjusting parameters of evolutionary algorithms (EAs) has emerged as a fruitful research area with many runtime analyses showing that self-adjusting parameters can out-perform the best fixed parameters. Most existing runtime analyses focus on elitist EAs on simple problems, for which moderate performance gains were shown. Here we consider a much more challenging scenario: the multimodal function Cliff, defined as an example where a (1, λ) EA is effective, and for which the best known upper runtime bound for standard EAs is O(n25).

We prove that a (1, λ) EA self-adjusting the offspring population size λ using success-based rules optimises Cliff in O(n) expected generations and O(n log n) expected evaluations. Along the way, we prove tight upper and lower bounds on the runtime for fixed λ (up to a logarithmic factor) and identify the runtime for the best fixed λ as nη for η ≈ 3.9767 (up to sub-polynomial factors). Hence, the self-adjusting (1, λ) EA outperforms the best fixed parameter by a factor of at least n2.9767 (up to sub-polynomial factors).
Original languageEnglish
Title of host publicationFOGA '21
Subtitle of host publicationProceedings of the 16th ACM/SIGEVO Conference on Foundations of Genetic Algorithms
Place of PublicationNew York
PublisherAssociation for Computing Machinery (ACM)
Number of pages15
ISBN (Print)9781450383523
Publication statusPublished - 6 Sept 2021
EventFOGA '21: Foundations of Genetic Algorithms XVI - Virtual
Duration: 6 Sept 20218 Sept 2021

Publication series

NameFOGA: Foundations of Genetic Algorithms


ConferenceFOGA '21: Foundations of Genetic Algorithms XVI
Abbreviated titleFOGA '21


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