Lengler, J., Sudholt, D. orcid.org/0000-0001-6020-1646 and Witt, C. (2018) Medium step sizes are harmful for the compact genetic algorithm. In: Aquirre, H., (ed.) Proceedings of the Genetic and Evolutionary Computation Conference (GECCO 2018). Genetic and Evolutionary Computation Conference (GECCO 2018), 15-19 Jul 2018, Kyoto, Japan. ACM , pp. 1499-1506. ISBN 978-1-4503-5618-3
Abstract
We study the intricate dynamics of the Compact Genetic Algorithm (cGA) on OneMax, and how its performance depends on the step size 1/K, that determines how quickly decisions about promising bit values are fixed in the probabilistic model. It is known that cGA and UMDA, a related algorithm, run in expected time O(n logn) when the step size is just small enough (K = Θ( √ n logn)) to avoid wrong decisions being fixed. UMDA also shows the same performance in a very different regime (equivalent to K = Θ(logn) in the cGA) with much larger steps sizes, but for very different reasons: many wrong decisions are fixed initially, but then reverted efficiently. We show that step sizes in between these two optimal regimes are harmful as they yield larger runtimes: we prove a lower bound of Ω(K 1/3n+n logn) for the cGA on OneMax for K = O( √ n/log2 n). For K = Ω(log3 n) the runtime increases with growing K before dropping again to O(K √ n + n logn) for K = Ω( √ n logn). This suggests that the expected runtime for cGA is a bimodal function inK with two very different optimal regions and worse performance in between.
Metadata
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Copyright, Publisher and Additional Information: | © 2018 The Authors. This is an author produced version of a paper subsequently published in Proceedings of the Genetic and Evolutionary Computation Conference (GECCO 2018). Uploaded in accordance with the publisher's self-archiving policy. | ||||
Keywords: | Estimation-of-distribution algorithms; compact genetic algorithm; evolutionary algorithms; running time analysis; theory | ||||
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Institution: | The University of Sheffield | ||||
Academic Units: | The University of Sheffield > Faculty of Engineering (Sheffield) > Department of Computer Science (Sheffield) | ||||
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Depositing User: | Symplectic Sheffield | ||||
Date Deposited: | 16 May 2018 13:22 | ||||
Last Modified: | 22 Nov 2018 11:29 | ||||
Published Version: | https://doi.org/10.1145/3205455.3205576 | ||||
Status: | Published | ||||
Publisher: | ACM | ||||
Refereed: | Yes | ||||
Identification Number: | https://doi.org/10.1145/3205455.3205576 |