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Feature-Based Benchmarking of Distance-Based Multi/Many-objective Optimisation Problems: A Machine Learning Perspective

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Evolutionary Multi-Criterion Optimization (EMO 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13970))

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Abstract

We consider the application of machine learning techniques to gain insights into the effect of problem features on algorithm performance, and to automate the task of algorithm selection for distance-based multi- and many-objective optimisation problems. This is the most extensive benchmark study of such problems to date. The problem features can be set directly by the problem generator, and include e.g. the number of variables, objectives, local fronts, and disconnected Pareto sets. Using 945 problem configurations (leading to \(28\,350\) instances) of varying complexity, we find that the problem features and the available optimisation budget (i) affect the considered algorithms (NSGA-II, IBEA, MOEA/D, and random search) in different ways and that (ii) it is possible to recommend a relevant algorithm based on problem features.

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Notes

  1. 1.

    Available in Matlab (https://github.com/fieldsend/DBMOPP_generator), and in Python (https://github.com/industrial-optimization-group/desdeo-problem/tree/master/desdeo_problem/testproblems/DBMOPP).

  2. 2.

    \(1\,000\) members drawn from the Pareto front plus all non-dominated points found by the union of the algorithms’ approximation sets for each instance. The reference point for hypervolume was \(1.1 \times \text {maximum of objective values on the Pareto front}\) and estimated via Monte Carlo [7] with \(50\,000\) samples for \(4+\) objectives.

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Acknowledgements

This research is part of the thematic research area DEMO, Decision Analytics utilising Causal Models and Multiobjective Optimisation, jyu.fi/demo, at the University of Jyvaskyla.

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Authors and Affiliations

  1. Univ. Lille, CNRS, Inria, Centrale Lille, UMR 9189 CRIStAL, 59000, Lille, France

    Arnaud Liefooghe

  2. Univ. Littoral Côte d’Opale, LISIC, 62100, Calais, France

    Sébastien Verel

  3. University of Exeter, Exeter, EX4 4QD, UK

    Tinkle Chugh & Jonathan Fieldsend

  4. The University of Manchester, Manchester, M15 6PB, UK

    Richard Allmendinger

  5. University of Jyvaskyla, Faculty of Information Technology, FI-40014, University of Jyvaskyla, Finland

    Kaisa Miettinen

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  1. Arnaud Liefooghe
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  2. Sébastien Verel
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  3. Tinkle Chugh
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  4. Jonathan Fieldsend
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  5. Richard Allmendinger
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  6. Kaisa Miettinen
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Corresponding author

Correspondence to Arnaud Liefooghe .

Editor information

Editors and Affiliations

  1. Leiden University, Leiden, The Netherlands

    Michael Emmerich

  2. Leiden University, Leiden, The Netherlands

    André Deutz

  3. Leiden University, Leiden, The Netherlands

    Hao Wang

  4. Leiden University, Leiden, The Netherlands

    Anna V. Kononova

  5. TH Köln, Gummersbach, Germany

    Boris Naujoks

  6. University of Exeter, Exeter, UK

    Ke Li

  7. University of Jyvaskyla, Jyvaskyla, Finland

    Kaisa Miettinen

  8. De Montfort University, Leicester, UK

    Iryna Yevseyeva

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Liefooghe, A., Verel, S., Chugh, T., Fieldsend, J., Allmendinger, R., Miettinen, K. (2023). Feature-Based Benchmarking of Distance-Based Multi/Many-objective Optimisation Problems: A Machine Learning Perspective. In: Emmerich, M., et al. Evolutionary Multi-Criterion Optimization. EMO 2023. Lecture Notes in Computer Science, vol 13970. Springer, Cham. https://doi.org/10.1007/978-3-031-27250-9_19

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