Oliveto, P.S., Sudholt, D. orcid.org/0000-0001-6020-1646 and Witt, C. (2020) A tight lower bound on the expected runtime of standard steady state genetic algorithms. In: GECCO '20: Proceedings of the 2020 Genetic and Evolutionary Computation Conference. GECCO '20: Genetic and Evolutionary Computation Conference, 08-12 Jul 2020, Online conference. ACM Digital Library , pp. 1323-1331. ISBN 9781450371285
Abstract
Recent progress in the runtime analysis of evolutionary algorithms (EAs) has allowed the derivation of upper bounds on the expected runtime of standard steady-state GAs. These upper bounds have shown speed-ups of the GAs using crossover and mutation over the same algorithms that only use mutation operators (i.e., steady-state EAs) both for standard unimodal (i.e., OneMax) and multimodal (i.e., Jump) benchmark functions. These upper bounds suggest that populations are beneficial to the GA as well as higher mutation rates than the default 1/n rate. However, making rigorous claims was not possible because matching lower bounds were not available. Proving lower bounds on crossover-based EAs is a notoriously difficult task as it is hard to capture the progress that a diverse population can make. We use a potential function approach to prove a tight lower bound on the expected runtime of the (2 + 1) GA for OneMax for all mutation rates c/n with c < 1.422. This provides the last piece of the puzzle that completes the proof that larger population sizes improve the performance of the standard steady-state GA for OneMax for various mutation rates, and it proves that the optimal mutation rate for the (2 + 1) GA on OneMax is [EQUATION].
Metadata
Item Type: | Proceedings Paper |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2020 The Authors. This is an author-produced version of a paper subsequently published in GECCO '20: Proceedings of the 2020 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) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 27 Apr 2020 09:58 |
Last Modified: | 22 Oct 2021 13:05 |
Status: | Published |
Publisher: | ACM Digital Library |
Refereed: | Yes |
Identification Number: | 10.1145/3377930.3390212 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:159915 |