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Local Optima Networks: A New Model of Combinatorial Fitness Landscapes

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Recent Advances in the Theory and Application of Fitness Landscapes

Part of the book series: Emergence, Complexity and Computation ((ECC,volume 6))

Abstract

This chapter overviews a recently introduced network-based model of combinatorial landscapes: Local Optima Networks (LON). The model compresses the information given by the whole search space into a smaller mathematical object that is a graph having as vertices the local optima and as edges the possible weighted transitions between them. Two definitions of edges have been proposed: basin-transition and escape-edges, which capture relevant topological features of the underlying search spaces. This network model brings a new set of metrics to characterize the structure of combinatorial landscapes, those associated with the science of complex networks. These metrics are described, and results are presented of local optima network extraction and analysis for two selected combinatorial landscapes: NK landscapes and the quadratic assignment problem. Network features are found to correlate with and even predict the performance of heuristic search algorithms operating on these problems.

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Author information

Authors and Affiliations

  1. Department of Computing Science and Mathematics, School of Natural Sciences, University of Stirling, Stirling, FK9 4LA, Scotland, UK

    Gabriela Ochoa

  2. INRIA Lille - Nord Europe and University of Nice Sophia-Antipolis, 06903, Sophia Antipolis Cedex, France

    Sébastien Verel

  3. Department of Information Systems, University of Lausanne, 1015, Lausanne, Switzerland

    Fabio Daolio & Marco Tomassini

Authors
  1. Gabriela Ochoa
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  2. Sébastien Verel
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  3. Fabio Daolio
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  4. Marco Tomassini
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Corresponding author

Correspondence to Gabriela Ochoa .

Editor information

Editors and Affiliations

  1. Faculty of Electrical Engineering & Information Technology, HTWK Leipzig University of Applied Sciences, Leipzig, Germany

    Hendrik Richter

  2. Department of Computer Science, University of Pretoria, Pretoria, South Africa

    Andries Engelbrecht

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Ochoa, G., Verel, S., Daolio, F., Tomassini, M. (2014). Local Optima Networks: A New Model of Combinatorial Fitness Landscapes. In: Richter, H., Engelbrecht, A. (eds) Recent Advances in the Theory and Application of Fitness Landscapes. Emergence, Complexity and Computation, vol 6. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-41888-4_9

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  • DOI: https://doi.org/10.1007/978-3-642-41888-4_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-41887-7

  • Online ISBN: 978-3-642-41888-4

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