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Communities of Local Optima as Funnels in Fitness Landscapes

Author

Listed:
  • Sebastian Herrmann

    (Johannes Gutenberg University Mainz)

  • Gabriela Ochoa

    (University of Stirling)

  • Franz Rothlauf

    (Johannes Gutenberg University Mainz)

Abstract

We conduct an analysis of local optima networks extracted from ?tness landscapes of the Kauffman NK model under iterated local search. Applying the Markov Cluster Algorithm for community detection to the local optima networks, we ?nd that the landscapes consist of multiple clusters. This result complements recent ?ndings in the literature that landscapes often decompose into multiple funnels, which increases their difficulty for iterated local search. Our results suggest that the number of clusters as well as the size of the cluster in which the global optimum is located are correlated to the search difficulty of landscapes. We conclude that clusters found by community detection in local optima networks offer a new way to characterize the multi-funnel structure of ?tness landscapes.

Suggested Citation

  • Sebastian Herrmann & Gabriela Ochoa & Franz Rothlauf, 2016. "Communities of Local Optima as Funnels in Fitness Landscapes," Working Papers 1609, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz.
    • Handle: RePEc:jgu:wpaper:1609
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    1. David Applegate & William Cook & André Rohe, 2003. "Chained Lin-Kernighan for Large Traveling Salesman Problems," INFORMS Journal on Computing, INFORMS, vol. 15(1), pages 82-92, February.
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    Cited by:

    1. Gabriela Ochoa & Nadarajen Veerapen, 2018. "Mapping the global structure of TSP fitness landscapes," Journal of Heuristics, Springer, vol. 24(3), pages 265-294, June.

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    Keywords

    Fitness landscape analysis; search difficulty; local optima networks; NK-landscapes.;
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