Sudholt, D. orcid.org/0000-0001-6020-1646 and Witt, C. (2019) On the choice of the update strength in estimation-of-distribution algorithms and ant colony optimization. Algorithmica, 81 (4). pp. 1450-1489. ISSN 0178-4617
Abstract
Probabilistic model-building Genetic Algorithms (PMBGAs) are a class of metaheuristics that evolve probability distributions favoring optimal solutions in the underlying search space by repeatedly sampling from the distribution and updating it according to promising samples. We provide a rigorous runtime analysis concerning the update strength, a vital parameter in PMBGAs such as the step size 1 / K in the so-called compact Genetic Algorithm (cGA) and the evaporation factor ρ in ant colony optimizers (ACO). While a large update strength is desirable for exploitation, there is a general trade-off: too strong updates can lead to unstable behavior and possibly poor performance. We demonstrate this trade-off for the cGA and a simple ACO algorithm on the well-known OneMax function. More precisely, we obtain lower bounds on the expected runtime of Ω(Kn−−√+nlogn) and Ω(n−−√/ρ+nlogn), respectively, suggesting that the update strength should be limited to 1/K,ρ=O(1/(n−−√logn)). In fact, choosing 1/K,ρ∼1/(n−−√logn) both algorithms efficiently optimize OneMax in expected time Θ(nlogn). Our analyses provide new insights into the stochastic behavior of PMBGAs and propose new guidelines for setting the update strength in global optimization.
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Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © The Author(s) 2018. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. |
Keywords: | Ant colony optimization; Estimation-of-distribution algorithms; Genetic Algorithms; Probabilistic model-building Genetic Algorithms; Runtime analysis; Theory of randomized search heuristics |
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) |
Funding Information: | Funder Grant number EUROPEAN COMMISSION - FP6/FP7 SAGE - 138086 European Cooperation in Science and Technology CA15140 |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 11 Jul 2018 13:34 |
Last Modified: | 07 Aug 2020 12:41 |
Status: | Published |
Publisher: | Springer Verlag |
Refereed: | Yes |
Identification Number: | 10.1007/s00453-018-0480-z |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:133057 |
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