Covantes Osuna, E. and Sudholt, D. orcid.org/0000-0001-6020-1646 (2020) Runtime analysis of crowding mechanisms for multimodal optimisation. IEEE Transactions on Evolutionary Computation, 24 (3). pp. 581-592. ISSN 1089-778X
Abstract
Many real-world optimisation problems lead to multimodal domains and require the identification of multiple optima. Crowding methods have been developed to maintain population diversity, to investigate many peaks in parallel and to reduce genetic drift. We present the first rigorous runtime analyses of probabilistic crowding and generalised crowding, embedded in a (mu+1)EA. In probabilistic crowding the offspring compete with their parent in a fitness-proportional selection. Generalised crowding decreases the fitness of the inferior solution by a scaling factor during selection. We consider the bimodal function TwoMax and introduce a novel and natural notion for functions with bounded gradients. For a broad range of such functions we prove that probabilistic crowding needs exponential time with overwhelming probability to find solutions significantly closer to any global optimum than those found by random search. Even when the fitness function is scaled exponentially, probabilistic crowding still fails badly. Only if the exponential's base is linear in the problem size, probabilistic crowding becomes efficient on TwoMax. A similar threshold behaviour holds for generalised crowding on TwoMax with respect to the scaling factor. Our theoretical results are accompanied by experiments for TwoMax showing that the threshold behaviours also apply to the best fitness found.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2019 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works. Reproduced in accordance with the publisher's self-archiving policy. |
Keywords: | Crowding methods; runtime analysis; probabilistic crowding; generalised crowding; theory |
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) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 14 Jun 2019 11:41 |
Last Modified: | 07 Dec 2021 10:35 |
Status: | Published |
Publisher: | Institute of Electrical and Electronics Engineers |
Refereed: | Yes |
Identification Number: | 10.1109/TEVC.2019.2914606 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:147333 |