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Consensus-based global optimization with personal best
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Totzeck, Claudia and Wolfram, Marie-Therese (2020) Consensus-based global optimization with personal best. Mathematical Biosciences and Engineering, 17 (5). pp. 6026-6044. doi:10.3934/mbe.2020320 ISSN 1547-1063.
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Official URL: https://doi.org/10.3934/mbe.2020320
Abstract
In this paper we propose a variant of a consensus-based global optimization (CBO) method that uses personal best information in order to compute the global minimum of a non-convex, locally Lipschitz continuous function. The proposed approach is motivated by the original particle swarming algorithms, in which particles adjust their position with respect to the personal best, the current global best, and some additive noise. The personal best information along an individual trajectory is included with the help of a weighted mean. This weighted mean can be computed very efficiently due to its ac-cumulative structure. It enters the dynamics via an additional drift term. We illustrate the performance with a toy example, analyze the respective memory-dependent stochastic system and compare the per-formance with the original CBO with component-wise noise for several benchmark problems. The proposed method has a higher success rate for computational experiments with a small particle number and where the initial particle distribution is disadvantageous with respect to the global minimum.
| Item Type: | Journal Article | ||||||||||||
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| Subjects: | Q Science > QA Mathematics | ||||||||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||||||
| Library of Congress Subject Headings (LCSH): | Nonconvex programming, Mathematical optimization, Stochastic processes, Biomathematics | ||||||||||||
| Journal or Publication Title: | Mathematical Biosciences and Engineering | ||||||||||||
| Publisher: | American Institute of Mathematical Sciences (A I M S Press) | ||||||||||||
| ISSN: | 1547-1063 | ||||||||||||
| Official Date: | 11 September 2020 | ||||||||||||
| Dates: |
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| Volume: | 17 | ||||||||||||
| Number: | 5 | ||||||||||||
| Page Range: | pp. 6026-6044 | ||||||||||||
| DOI: | 10.3934/mbe.2020320 | ||||||||||||
| Status: | Peer Reviewed | ||||||||||||
| Publication Status: | Published | ||||||||||||
| Access rights to Published version: | Open Access (Creative Commons) | ||||||||||||
| Date of first compliant deposit: | 9 September 2020 | ||||||||||||
| Date of first compliant Open Access: | 24 November 2020 | ||||||||||||
| RIOXX Funder/Project Grant: |
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