Hevia Fajardo, M.A. and Sudholt, D. orcid.org/0000-0001-6020-1646 (2020) On the choice of the parameter control mechanism in the (1+(λ, λ)) genetic algorithm. In: GECCO 2020: Proceedings of the Genetic and Evolutionary Computation Conference. GECCO 2020 : Genetic and Evolutionary Computation Conference, 08-12 Jul 2020, Cancún, Mexico. ACM Digital Library , pp. 832-840. ISBN 9781450371285
Abstract
The self-adjusting (1 + (λ, λ)) GA is the best known genetic algorithm for problems with a good fitness-distance correlation as in OneMax. It uses a parameter control mechanism for the parameter λ that governs the mutation strength and the number of offspring. However, on multimodal problems, the parameter control mechanism tends to increase λ uncontrollably.
We study this problem and possible solutions to it using rigorous runtime analysis for the standard Jumpk benchmark problem class. The original algorithm behaves like a (1+n) EA whenever the maximum value λ = n is reached. This is ineffective for problems where large jumps are required. Capping λ at smaller values is beneficial for such problems. Finally, resetting λ to 1 allows the parameter to cycle through the parameter space. We show that this strategy is effective for all Jumpk problems: the (1 + (λ, λ)) GA performs as well as the (1 + 1) EA with the optimal mutation rate and fast evolutionary algorithms, apart from a small polynomial overhead.
Along the way, we present new general methods for bounding the runtime of the (1 + (λ, λ)) GA that allows to translate existing runtime bounds from the (1 + 1) EA to the self-adjusting (1 + (λ, λ)) GA. Our methods are easy to use and give upper bounds for novel classes of functions.
Metadata
Item Type: | Proceedings Paper |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2020 Copyright held by the owner/author(s). Publication rights licensed to the Association for Computing Machinery. This is an author-produced version of a paper subsequently published in GECCO '20: Proceedings of the 2020 Genetic and Evolutionary Computation Conference. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Parameter control; runtime analysis; theory |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Engineering (Sheffield) > Department of Computer Science (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 27 Apr 2020 10:12 |
Last Modified: | 15 Oct 2020 11:27 |
Status: | Published |
Publisher: | ACM Digital Library |
Refereed: | Yes |
Identification Number: | 10.1145/3377930.3390200 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:159916 |