Nallaperuma, S., Oliveto, P.S., Perez Heredia, J. et al. (1 more author) (2019) On the Analysis of Trajectory-Based Search Algorithms: When is it Beneficial to Reject Improvements? Algorithmica, 81 (2). pp. 858-885. ISSN 0178-4617
Abstract
We investigate popular trajectory-based algorithms inspired by biology and physics to answer a question of general significance: when is it beneficial to reject improvements? A distinguishing factor of SSWM (strong selection weak mutation), a popular model from population genetics, compared to the Metropolis algorithm (MA), is that the former can reject improvements, while the latter always accepts them. We investigate when one strategy outperforms the other. Since we prove that both algorithms converge to the same stationary distribution, we concentrate on identifying a class of functions inducing large mixing times, where the algorithms will outperform each other over a long period of time. The outcome of the analysis is the definition of a function where SSWM is efficient, while Metropolis requires at least exponential time. The identified function favours algorithms that prefer high quality improvements over smaller ones, revealing similarities in the optimisation strategies of SSWM and Metropolis respectively with best-improvement (BILS) and first-improvement (FILS) local search. We conclude the paper with a comparison of the performance of these algorithms and a (1, λ ) RLS on the identified function. The algorithm favours the steepest gradient with a probability that increases with the size of its offspring population. The results confirm that BILS excels and that the (1, λ ) RLS is efficient only for large enough population sizes.
Metadata
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: | Theory; Evolutionary algorithms; Non-elitism; Metropolis algorithm; Strong selection weak mutation regime |
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 ENGINEERING AND PHYSICAL SCIENCE RESEARCH COUNCIL (EPSRC) EP/M004252/1 |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 09 Aug 2018 10:12 |
Last Modified: | 14 Aug 2020 08:05 |
Status: | Published |
Publisher: | Springer |
Refereed: | Yes |
Identification Number: | 10.1007/s00453-018-0462-1 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:133642 |
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