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Funnels in Multi-objective Fitness Landscapes

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Parallel Problem Solving from Nature – PPSN XVIII (PPSN 2024)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 15148))

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Abstract

Funnels are related to the big-valley hypothesis in combinatorial fitness landscapes. It suggests that local optima are not randomly distributed but are instead clustered around the global optimum, forming a coarse-grained global structure. Multi-funnel structures emerge when more than one cluster of local optima is present, some surrounding sub-optimal solutions. These multi-funnel landscapes can be challenging to search, as the optimisation process may get trapped in a sub-optimal funnel. We propose a characterisation of funnels in multi-objective combinatorial landscapes based on the solution ranks using non-dominated sorting, and a variation of the recent graph model of multi-objective landscapes: the compressed Pareto local optimal solution network (C-PLOS-net). Using a set of \(\rho \)mnk-landscapes, we construct and visualise monotonic C-PLOS-nets, and introduce a set of metrics to characterise the landscapes’ funnel structure. The proposed metrics are found to capture the landscape global structure, to correlate with benchmark parameters, and to explain the performance of well-established multi-objective local search and evolutionary algorithms.

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Authors and Affiliations

  1. University of Stirling, Scotland, UK

    Gabriela Ochoa

  2. LISIC, Université du Littoral Côte d’Opale, Calais, France

    Arnaud Liefooghe & Sébastien Verel

Authors
  1. Gabriela Ochoa
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  2. Arnaud Liefooghe
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  3. Sébastien Verel
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Corresponding author

Correspondence to Gabriela Ochoa .

Editor information

Editors and Affiliations

  1. University of Applied Sciences Upper Austria, Wels, Austria

    Michael Affenzeller

  2. University of Applied Sciences Upper Austria, Hagenberg, Austria

    Stephan M. Winkler

  3. Leiden University, Leiden, The Netherlands

    Anna V. Kononova

  4. University of Paderborn, Paderborn, Germany

    Heike Trautmann

  5. Jožef Stefan Institute, Ljubljana, Slovenia

    Tea Tušar

  6. University of Coimbra, Coimbra, Portugal

    Penousal Machado

  7. Leiden University, LEIDEN, The Netherlands

    Thomas Bäck

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Ochoa, G., Liefooghe, A., Verel, S. (2024). Funnels in Multi-objective Fitness Landscapes. In: Affenzeller, M., et al. Parallel Problem Solving from Nature – PPSN XVIII. PPSN 2024. Lecture Notes in Computer Science, vol 15148. Springer, Cham. https://doi.org/10.1007/978-3-031-70055-2_21

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  • DOI: https://doi.org/10.1007/978-3-031-70055-2_21

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