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Local Optima Networks with Escape Edges

  • Sébastien Vérel
  • Fabio Daolio
  • Gabriela Ochoa
  • Marco Tomassini
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7401)

Abstract

This paper proposes an alternative definition of edges (escape edges) for the 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 the graph having as vertices the local optima and as edges the possible weighted transitions between them. The original definition of edges accounted for the notion of transitions between the basins of attraction of local optima. This definition, although informative, produced densely connected networks and required the exhaustive sampling of the basins of attraction. The alternative escape edges proposed here do not require a full computation of the basins. Instead, they account for the chances of escaping a local optima after a controlled mutation (e.g. 1 or 2 bit-flips) followed by hill-climbing. A statistical analysis comparing the two LON models for a set of NK landscapes, is presented and discussed. Moreover, a preliminary study is presented, which aims at validating the LON models as a tool for analyzing the dynamics of stochastic local search in combinatorial optimization.

Keywords

Search Space Local Search Local Optimum Iterate Local Search Local Search Heuristic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Barthélemy, M., Barrat, A., Pastor-Satorras, R., Vespignani, A.: Characterization and modeling of weighted networks. Physica A 346, 34–43 (2005)CrossRefGoogle Scholar
  2. 2.
    Cahon, S., Melab, N., Talbi, E.G.: Paradiseo: A framework for the reusable design of parallel and distributed metaheuristics. Journal of Heuristics 10, 357–380 (2004)CrossRefGoogle Scholar
  3. 3.
    Csardi, G., Nepusz, T.: The igraph software package for complex network research. InterJournal Complex Systems, 1695 (2006)Google Scholar
  4. 4.
    Glover, F., Laguna, M.: Tabu Search. Kluwer Academic Publishers, Norwell (1997)zbMATHCrossRefGoogle Scholar
  5. 5.
    Kauffman, S.A.: The Origins of Order. Oxford University Press, New York (1993)Google Scholar
  6. 6.
    Lourenço, H.R., Martin, O., Stützle, T.: Iterated local search. In: Handbook of Metaheuristics. International Series in Operations Research & Management Science, vol. 57, pp. 321–353. Kluwer Academic Publishers (2002)Google Scholar
  7. 7.
    Newman, M.E.J.: The structure and function of complex networks. SIAM Review 45, 167–256 (2003)MathSciNetzbMATHCrossRefGoogle Scholar
  8. 8.
    Ochoa, G., Verel, S., Tomassini, M.: First-Improvement vs. Best-Improvement Local Optima Networks of NK Landscapes. In: Schaefer, R., Cotta, C., Kołodziej, J., Rudolph, G. (eds.) PPSN XI. LNCS, vol. 6238, pp. 104–113. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  9. 9.
    Reidys, C., Stadler, P.: Combinatorial landscapes. SIAM Review 44(1), 3–54 (2002)MathSciNetzbMATHCrossRefGoogle Scholar
  10. 10.
    Tomassini, M., Verel, S., Ochoa, G.: Complex-network analysis of combinatorial spaces: The NK landscape case. Phys. Rev. E 78(6), 066114 (2008)CrossRefGoogle Scholar
  11. 11.
    Verel, S., Ochoa, G., Tomassini, M.: Local optima networks of NK landscapes with neutrality. IEEE Transactions on Evolutionary Computation 15(6), 783–797 (2011)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Sébastien Vérel
    • 2
  • Fabio Daolio
    • 3
  • Gabriela Ochoa
    • 1
  • Marco Tomassini
    • 3
  1. 1.Department of Computing Science and MathematicsUniversity of StirlingStirlingScotland
  2. 2.INRIA LilleNord Europe and University of Nice Sophia-AntipolisFrance
  3. 3.Faculty of Business and EconomicsUniversity of LausanneLausanneSwitzerland

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