Corus, D. and Oliveto, P.S. (2019) On the benefits of populations on the exploitation speed of standard steady-state genetic algorithms. In: GECCO '19 Proceedings of the Genetic and Evolutionary Computation Conference. GECCO '19, 13-17 Jul 2019, Prague, Czech Republic. ACM , pp. 1452-1460. ISBN 978-1-4503-6111-8
Abstract
It is generally accepted that populations are useful for the global exploration of multi-modal optimisation problems. Indeed, several theoretical results are available showing such advantages over single-trajectory search heuristics. In this paper we provide evidence that evolving populations via crossover and mutation may also benefit the optimisation time for hillclimbing unimodal functions. In particular, we prove bounds on the expected runtime of the standard (µ+1) GA for OneMax that are lower than its unary black box complexity and decrease in the leading constant with the population size up to [MATH HERE]. Our analysis suggests that the optimal mutation strategy is to flip two bits most of the time. To achieve the results we provide two interesting contributions to the theory of randomised search heuristics: 1) A novel application of drift analysis which compares absorption times of different Markov chains without defining an explicit potential function. 2) The inversion of fundamental matrices to calculate the absorption times of the Markov chains. The latter strategy was previously proposed in the literature but to the best of our knowledge this is the first time is has been used to show non-trivial bounds on expected runtimes.
Metadata
Item Type: | Proceedings Paper |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2019 The Authors. This is an author-produced version of a paper accepted for publication in GECCO '19 Proceedings of the Genetic and Evolutionary Computation Conference. Uploaded in accordance with the publisher's self-archiving policy. |
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 (EPSRC) EP/M004252/1 |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 10 Apr 2019 15:29 |
Last Modified: | 04 Oct 2019 08:33 |
Status: | Published |
Publisher: | ACM |
Refereed: | Yes |
Identification Number: | 10.1145/3321707.3321783 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:144388 |