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Representation, Resolution, and Visualization in Multimodal Optimization

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Metaheuristics for Finding Multiple Solutions

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Abstract

This chapter examines the fundamental limits placed on algorithm capabilities due to the internal solution representation used by a search algorithm, and its implications for mode discovery and problem tractability. It presents various approaches to visualizing the problem landscape, based on both exhaustive enumeration and sampling—which may be of use to both practitioners and problem owners. It also provides the first comprehensive examination of the widely used IEEE CEC 2013 benchmark multimodal problems using local optima networks. These visualize the fitness landscape as a directed graph, and convey such information as local optima quality, basin size, and how easy it is to traverse the fitness landscape from one local optimum to another.

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Notes

  1. 1.

    Note that such a visualization is limited to those problems where the optimal quality value is known a priori, and is therefore typically limited to test problems rather than real-world applications. However, it is of course possible to plot the raw quality values achievable as resolution increases.

  2. 2.

    With international workshops running since 2016, see, e.g. http://www.cs.stir.ac.uk/events/gecco-lahs2018/.

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Acknowledgements

This work was financially supported by the Engineering and Physical Sciences Research Council [grant number EP/N017846/1]. The author would like to thank Sébastien Vérel and Gabriela Ochoa for providing inspirational invited talks on LONs at his institution during this grant, and also Ozgur Akman, Khulood Alyahya, and Kevin Doherty.

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Authors and Affiliations

  1. Computer Science, University of Exeter, North Park Road, Exeter, EX4 4QF, UK

    Jonathan E. Fieldsend

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  1. Jonathan E. Fieldsend
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Correspondence to Jonathan E. Fieldsend .

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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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Fieldsend, J.E. (2021). Representation, Resolution, and Visualization in Multimodal Optimization. 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_2

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  • DOI: https://doi.org/10.1007/978-3-030-79553-5_2

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  • Publisher Name: Springer, Cham

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  • Online ISBN: 978-3-030-79553-5

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