Local Optima Networks: A New Model of Combinatorial Fitness Landscapes

  • Gabriela Ochoa
  • Sébastien Verel
  • Fabio Daolio
  • Marco Tomassini

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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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Gabriela Ochoa
    • 1
  • Sébastien Verel
    • 2
  • Fabio Daolio
    • 3
  • Marco Tomassini
    • 3
  1. 1.Department of Computing Science and Mathematics, School of Natural SciencesUniversity of StirlingStirlingScotland, UK
  2. 2.INRIA Lille - Nord Europe and University of Nice Sophia-AntipolisSophia Antipolis CedexFrance
  3. 3.Department of Information SystemsUniversity of LausanneLausanneSwitzerland

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