Corus, D., Lissovoi, A., Oliveto, P. et al. (1 more author) (2021) On steady-state evolutionary algorithms and selective pressure: Why inverse rank-based allocation of reproductive trials is best. ACM Transactions on Evolutionary Learning and Optimization, 1 (1). 2. ISSN 2688-299X
Abstract
We analyse the impact of the selective pressure for the global optimisation capabilities of steady-state evolutionary algorithms (EAs). For the standard bimodal benchmark function TwoMax, we rigorously prove that using uniform parent selection leads to exponential runtimes with high probability to locate both optima for the standard (+1) EA and (+1) RLS with any polynomial population sizes. However, we prove that selecting the worst individual as parent leads to efficient global optimisation with overwhelming probability for reasonable population sizes. Since always selecting the worst individual may have detrimental effects for escaping from local optima, we consider the performance of stochastic parent selection operators with low selective pressure for a function class called TruncatedTwoMax, where one slope is shorter than the other. An experimental analysis shows that the EAs equipped with inverse tournament selection, where the loser is selected for reproduction and small tournament sizes, globally optimise TwoMax efficiently and effectively escape from local optima of TruncatedTwoMax with high probability. Thus, they identify both optima efficiently while uniform (or stronger) selection fails in theory and in practice. We then show the power of inverse selection on function classes from the literature where populations are essential by providing rigorous proofs or experimental evidence that it outperforms uniform selection equipped with or without a restart strategy. We conclude the article by confirming our theoretical insights with an empirical analysis of the different selective pressures on standard benchmarks of the classical MaxSat and multidimensional knapsack problems.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2021 Association for Computing Machinery. This is an author-produced version of a paper subsequently published in ACM Transactions on Evolutionary Learning and Optimization. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | randomised search heuristics; (µ+1) EA; parent selection; diversity; TwoMax |
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 ENGINEERING AND PHYSICAL SCIENCE RESEARCH COUNCIL EP/M004252/1 |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 03 Nov 2020 16:28 |
Last Modified: | 15 Jul 2021 14:49 |
Status: | Published |
Publisher: | Association for Computing Machinery |
Refereed: | Yes |
Identification Number: | 10.1145/3427474 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:167459 |