research-article

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

Authors:

Mario Alejandro Hevia Fajardo,

Dirk SudholtAuthors Info & Claims

FOGA '21: Proceedings of the 16th ACM/SIGEVO Conference on Foundations of Genetic Algorithms

Article No.: 5, Pages 1 - 15

https://doi.org/10.1145/3450218.3477306

Published: 06 September 2021 Publication History

Abstract

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 n^η 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 n^2.9767 (up to sub-polynomial factors).

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Cited By

Lengler JSchiller LSieberling OLi XHandl J(2024)Plus Strategies are Exponentially Slower for Planted Optima of Random HeightProceedings of the Genetic and Evolutionary Computation Conference10.1145/3638529.3654088(1587-1595)Online publication date: 14-Jul-2024
https://dl.acm.org/doi/10.1145/3638529.3654088
Neumann FSudholt DWitt C(2024)The Compact Genetic Algorithm Struggles on Cliff FunctionsAlgorithmica10.1007/s00453-024-01281-wOnline publication date: 17-Nov-2024
https://doi.org/10.1007/s00453-024-01281-w
Lehre PQin X(2023)Self-adaptation Can Improve the Noise-tolerance of Evolutionary AlgorithmsProceedings of the 17th ACM/SIGEVO Conference on Foundations of Genetic Algorithms10.1145/3594805.3607128(105-116)Online publication date: 30-Aug-2023
https://dl.acm.org/doi/10.1145/3594805.3607128
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Index Terms

Self-adjusting offspring population sizes outperform fixed parameters on the cliff function
1. Theory of computation
  1. Theory and algorithms for application domains
    1. Theory of randomized search heuristics

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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 ...
Self-adjusting offspring population sizes outperform fixed parameters on the cliff function
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In the discrete domain, self-adjusting parameters of evolutionary algorithms (EAs) have emerged as a fruitful research area with many runtime analyses showing that self-adjusting parameters can outperform the best fixed parameters. Most existing ...
Self-adjusting Population Sizes for Non-elitist Evolutionary Algorithms: Why Success Rates Matter
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cover image ACM Conferences

FOGA '21: Proceedings of the 16th ACM/SIGEVO Conference on Foundations of Genetic Algorithms

September 2021

130 pages

ISBN:9781450383523

DOI:10.1145/3450218

General Chair:
Steffen Finck
Vorarlberg University of Applied Sciences
,
Program Chairs:
Michael Hellwig
Vorarlberg University of Applied Sciences
,
Pietro S. Oliveto
University of Sheffield

Copyright © 2021 ACM.

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SIGEVO: ACM Special Interest Group on Genetic and Evolutionary Computation

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Published: 06 September 2021

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Consejo Nacional de Ciencia y Tecnología

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FOGA '21

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SIGEVO

FOGA '21: Foundations of Genetic Algorithms XVI

September 6 - 8, 2021

Virtual Event, Austria

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FOGA '21 Paper Acceptance Rate 10 of 21 submissions, 48%;

Overall Acceptance Rate 72 of 131 submissions, 55%

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Cited By

Lengler JSchiller LSieberling OLi XHandl J(2024)Plus Strategies are Exponentially Slower for Planted Optima of Random HeightProceedings of the Genetic and Evolutionary Computation Conference10.1145/3638529.3654088(1587-1595)Online publication date: 14-Jul-2024
https://dl.acm.org/doi/10.1145/3638529.3654088
Neumann FSudholt DWitt C(2024)The Compact Genetic Algorithm Struggles on Cliff FunctionsAlgorithmica10.1007/s00453-024-01281-wOnline publication date: 17-Nov-2024
https://doi.org/10.1007/s00453-024-01281-w
Lehre PQin X(2023)Self-adaptation Can Improve the Noise-tolerance of Evolutionary AlgorithmsProceedings of the 17th ACM/SIGEVO Conference on Foundations of Genetic Algorithms10.1145/3594805.3607128(105-116)Online publication date: 30-Aug-2023
https://dl.acm.org/doi/10.1145/3594805.3607128
Jorritsma JLengler JSudholt DSilva SPaquete L(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
https://dl.acm.org/doi/10.1145/3583131.3590488
Hevia Fajardo MSudholt D(2023)Theoretical and Empirical Analysis of Parameter Control Mechanisms in the (1 + (λ, λ)) Genetic AlgorithmACM Transactions on Evolutionary Learning and Optimization10.1145/35647552:4(1-39)Online publication date: 14-Jan-2023
https://dl.acm.org/doi/10.1145/3564755
Hevia Fajardo MSudholt D(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
https://dl.acm.org/doi/10.1007/s00453-023-01153-9
Doerr BGhannane YIbn Brahim M(2023)Runtime Analysis for Permutation-based Evolutionary AlgorithmsAlgorithmica10.1007/s00453-023-01146-886:1(90-129)Online publication date: 26-Jul-2023
https://dl.acm.org/doi/10.1007/s00453-023-01146-8
Lehre PQin X(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
https://dl.acm.org/doi/10.1007/s00453-022-01044-5
Qin XLehre P(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
https://dl.acm.org/doi/10.1007/978-3-031-14714-2_22

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