Oliveto, P.S., Paixão, T., Pérez Heredia, J. et al. (2 more authors) (2018) How to escape local optima in black box optimisation: when non-elitism outperforms elitism. Algorithmica, 80 (5). pp. 1604-1633. ISSN 0178-4617
Abstract
Escaping local optima is one of the major obstacles to function optimisation. Using the metaphor of a fitness landscape, local optima correspond to hills separated by fitness valleys that have to be overcome. We define a class of fitness valleys of tunable difficulty by considering their length, representing the Hamming path between the two optima and their depth, the drop in fitness. For this function class we present a runtime comparison between stochastic search algorithms using different search strategies. The ((Formula presented.)) EA is a simple and well-studied evolutionary algorithm that has to jump across the valley to a point of higher fitness because it does not accept worsening moves (elitism). In contrast, the Metropolis algorithm and the Strong Selection Weak Mutation (SSWM) algorithm, a famous process in population genetics, are both able to cross the fitness valley by accepting worsening moves. We show that the runtime of the ((Formula presented.)) EA depends critically on the length of the valley while the runtimes of the non-elitist algorithms depend crucially on the depth of the valley. Moreover, we show that both SSWM and Metropolis can also efficiently optimise a rugged function consisting of consecutive valleys.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © The Author(s) 2017. 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: | Evolutionary algorithms; Runtime analysis; Population genetics; Strong selection weak mutation regime; Metropolis algorithm; Simulated annealing; Black box optimisation |
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 European Cooperation in Science and Technology CA15140 |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 06 Oct 2017 11:49 |
Last Modified: | 08 Nov 2023 15:41 |
Status: | Published |
Publisher: | Springer Verlag |
Refereed: | Yes |
Identification Number: | 10.1007/s00453-017-0369-2 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:122143 |