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Fractal Dimension and Perturbation Strength: A Local Optima Networks View

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Parallel Problem Solving from Nature – PPSN XVII (PPSN 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13398))

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Abstract

We study the effect of varying perturbation strength on the fractal dimensions of Quadratic Assignment Problem (QAP) fitness landscapes induced by iterated local search (ILS). Fitness landscapes are represented as Local Optima Networks (LONs), which are graphs mapping algorithm search connectivity in a landscape. LONs are constructed for QAP instances and fractal dimension measurements taken from the networks. Thereafter, the interplay between perturbation strength, LON fractal dimension, and algorithm difficulty on the underlying combinatorial problems is analysed. The results show that higher-perturbation LONs also have higher fractal dimensions. ILS algorithm performance prediction using fractal dimension features may benefit more from LONs formed using a high perturbation strength; this model configuration enjoyed excellent performance. Around half of variance in Robust Taboo Search performance on the data-set used could be explained with the aid of fractal dimension features.

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Notes

  1. 1.

    http://www.seas.upenn.edu/qaplib/.

  2. 2.

    https://hmakse.ccny.cuny.edu/.

  3. 3.

    https://github.com/sarahlouisethomson/fractal-dimension-perturbation-strength.

  4. 4.

    https://github.com/sarahlouisethomson/compute-fractal-dimension-local-optima-networks.

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Authors and Affiliations

  1. University of Stirling, Stirling, UK

    Sarah L. Thomson & Gabriela Ochoa

  2. Université du Littoral Côte d’Opale (ULCO), Dunkirk, France

    Sébastien Verel

Authors
  1. Sarah L. Thomson
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  2. Gabriela Ochoa
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  3. Sébastien Verel
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Corresponding author

Correspondence to Sarah L. Thomson .

Editor information

Editors and Affiliations

  1. TU Dortmund, Dortmund, Germany

    Günter Rudolph

  2. Leiden University, Leiden, The Netherlands

    Anna V. Kononova

  3. Shinshu University, Nagano, Japan

    Hernán Aguirre

  4. Technische Universität Dresden, Dresden, Germany

    Pascal Kerschke

  5. University of Stirling, Stirling, UK

    Gabriela Ochoa

  6. Jožef Stefan Institute, Ljubljana, Slovenia

    Tea Tušar

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Thomson, S.L., Ochoa, G., Verel, S. (2022). Fractal Dimension and Perturbation Strength: A Local Optima Networks View. In: Rudolph, G., Kononova, A.V., Aguirre, H., Kerschke, P., Ochoa, G., Tušar, T. (eds) Parallel Problem Solving from Nature – PPSN XVII. PPSN 2022. Lecture Notes in Computer Science, vol 13398. Springer, Cham. https://doi.org/10.1007/978-3-031-14714-2_39

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  • DOI: https://doi.org/10.1007/978-3-031-14714-2_39

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