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Multimodal Optimization by Evolution Strategies with Repelling Subpopulations

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Metaheuristics for Finding Multiple Solutions

Part of the book series: Natural Computing Series ((NCS))

Abstract

This work presents a niching method based on the concept of repelling subpopulations for multimodal optimization. It utilizes several existing concepts and techniques in order to develop a new multimodal optimization algorithm that does not make any of specific assumptions on the shape, size, and distribution of minima. In the proposed method, several subpopulations explore the search space in parallel. Offspring of weaker subpopulations are forced to maintain a distance from the fitter subpopulations and the previously identified niches. This defines taboo regions to hinder the exploration of the same regions of the search space and previously identified niches. The size of each taboo region is adapted independently so that the method can handle challenges of minima with dissimilar basin sizes and irregular distribution. The local shape of a basin is approximated by the distribution of the subpopulation members converging to that basin. The proposed niching strategy is incorporated into the state-of-the-art evolution strategies, and the resulting method is compared with some of the most successful multimodal optimization methods on composite test problems. A comparison of numerical results demonstrates the superiority of our proposed method.

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Notes

  1. 1.

    Some materials in Sects. 1 and 2 of this work have been excerpted from our previously published paper: "Ali Ahrari, Kalyanmoy Deb, and Mike Preuss, ’Multimodal Optimization by Covariance Matrix Self-Adaptation Evolution Strategy with Repelling Subpopulations’, Evolutionary Computation, 25:3 (Fall, 2017), pp. 439–471. ©2017 by the Massachusetts Institute of Technology, published by the MIT Press". Permission to excerpt the materials from our previous work has been granted by The MIT Press.

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Acknowledgements

Permission to excerpt some parts of this article from the following publication was granted by MIT Press: Ali Ahrari, Kalyanmoy Deb, and Mike Preuss, ‘Multimodal Optimization by Covariance Matrix Self-Adaptation Evolution Strategy with Repelling Subpopulations’, Evolutionary Computation, 25:3 (Fall, 2017), pp. 439–471. ©2017 by the Massachusetts Institute of Technology, published by the MIT Press.

      Computational work in support of this research was performed at Michigan State University’s High-Performance Computing Facility. The source codes for NSDE and LIPS and the tested composite functions were provided by Ponnuthurai N. Suganthan. The source code of PNPCDE was provided by Subhodip Biswas. The source code of NMMSO was provided by Jonathan Fieldsend. The authors would like to thank them for sharing their source codes and providing guidelines to tune the control parameters. The source code of RS-CMSA-ES (in MATLAB) can be found at the COIN lab website: https://coin-lab.org and https://www.researchgate.net/profile/Ali_Ahrari/research.

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Authors and Affiliations

  1. Michigan State University, 48824, East Lansing, MI, USA

    Ali Ahrari & Kalyanmoy Deb

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  1. Ali Ahrari
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Editors and Affiliations

  1. LIACS, Universiteit Leiden, Leiden, The Netherlands

    Mike Preuss

  2. The Signal Group, Athens, Greece

    Michael G. Epitropakis

  3. Computer Science and Software Engineering, RMIT University, Melbourne, VIC, Australia

    Xiaodong Li

  4. Department of Computer Science, University of Exeter, Exeter, UK

    Jonathan E. Fieldsend

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Ahrari, A., Deb, K. (2021). Multimodal Optimization by Evolution Strategies with Repelling Subpopulations. In: Preuss, M., Epitropakis, M.G., Li, X., Fieldsend, J.E. (eds) Metaheuristics for Finding Multiple Solutions. Natural Computing Series. Springer, Cham. https://doi.org/10.1007/978-3-030-79553-5_7

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  • DOI: https://doi.org/10.1007/978-3-030-79553-5_7

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  • Online ISBN: 978-3-030-79553-5

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