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Multimodal Optimization: Formulation, Heuristics, and a Decade of Advances

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Metaheuristics for Finding Multiple Solutions

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Abstract

Multimodal optimization is a relatively young term for the aim of finding several solutions of a complex objective function simultaneously. This has been attempted under the denomination ‘niching’ since the 1970s, transferring ideas from biological evolution in a very loose fashion. In this chapter we more formally define it, and then highlight its most important perspectives: how do we measure what is good? On what problems do we measure it? Which type of algorithms may be effectively employed for multimodal optimization? How do they relate to each other? Competitions at two major evolutionary computation conferences have driven algorithm development in recent years. We therefore report, in a concise fashion, what we have learned from competition results and give an outlook on interesting future developments.

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Notes

  1. 1.

    http://www.epitropakis.co.uk/ieee-mmo/.

  2. 2.

    Note that, due to space limitation on graphs, the SSGA-DMRTS-DDC and SSGA-DMRTS-DDC-F entries are denoted as SSGA-D and SSGA-DF accordingly.

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Author information

Authors and Affiliations

  1. Universiteit Leiden, Leiden, Netherlands

    Mike Preuss

  2. The Signal Group, Athens, Greece

    Michael Epitropakis

  3. RMIT University, Melbourne, VIC, Australia

    Xiaodong Li

  4. University of Exeter, Exeter, UK

    Jonathan E. Fieldsend

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  1. Mike Preuss
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  2. Michael Epitropakis
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  3. Xiaodong Li
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  4. Jonathan E. Fieldsend
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Correspondence to Mike Preuss .

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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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Preuss, M., Epitropakis, M., Li, X., Fieldsend, J.E. (2021). Multimodal Optimization: Formulation, Heuristics, and a Decade of Advances. 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_1

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  • DOI: https://doi.org/10.1007/978-3-030-79553-5_1

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