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Fitness Landscape Analysis and Metaheuristics Efficiency

  • Marie-Éléonore MarmionEmail author
  • Laetitia Jourdan
  • Clarisse Dhaenens
Article
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Abstract

Landscape analysis has been identified as a promising way to develop efficient optimization methods. Nevertheless, the links between properties of the landscape and efficiency of methods is not easy to understand. In this article, we propose to give a contribution in this field using a vehicle routing problem as an illustration. Metaheuristics use a neighborhood operator that connects solutions of the search space. Thus, this operator acts on the dynamics of the search and impacts metaheuristics efficiency. Therefore, we characterize two landscapes differenciated by their neighborhood function and then, we analyze the performance of classical metaheuristics using one or the other neighborhood operator. Finally, a discussion provides insights on the relations between results of the landscape analysis and results of methods performance.

Keywords

Landscape analysis Operator efficiency Routing problems 

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References

  1. 1.
    Bachelet, V., Preux, P., Talbi, E.G.: The landscape of the quadratic assignment problem and local search methods. In: Tenth meeting of the European Chapter on Combinatorial Optimization (1997)Google Scholar
  2. 2.
    Beasley, J.: Route-first cluster-second methods for vehicle routing. Omega 11, 403–408 (1983)CrossRefGoogle Scholar
  3. 3.
    Cahon, S., Melab, N., Talbi, E.G.: Paradiseo: a framework for the reusable design of parallel and distributed metaheuristics. Journal of Heuristics 10(3), 357–380 (2004)CrossRefGoogle Scholar
  4. 4.
    Collard, P., Verel, S., Clergue, M.: How to use the scuba diving metaphor to solve problem with neutrality? In: de Mantaras, R.L., Saitta, L. (eds.) ECAI’2004 ECAI’2004, pp. 166–170. IOS Press, Valencia Espagne. http://hal.archives-ouvertes.fr/hal-00160051/en/ (2004)
  5. 5.
    Fischetti, M., Toth, P., Vigo, D.: A branch and bound algorithm for the capacitated vehicle routing problem on directed graphs. Oper. Res. 42, 846–859 (1994)MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    Glover, F., Laguna, M.: Tabu Search. Kluwer Academic Publishers (1998)Google Scholar
  7. 7.
    Grefenstette, J.J.: Incorporating problem specific knowledge into genetic algorithms. Genetic Algorithms and Simulated Annealing. Morgan Kaufmann Publishers Inc. (1987)Google Scholar
  8. 8.
    Kubiak, M.: Distance measures and fitness-distance analysis for the capacitated vehicle routing problem. In: Operations Research/Computer Science Interfaces Series, vol. 39, chap. 18, pp. 345–364. Springer US (2007)Google Scholar
  9. 9.
    Laporte, G., Mercure, H., Nobert, Y.: An exact algorithm for the asymmetrical capacitated vehicle routing problem. Networks 16, 33–46 (1986)MathSciNetzbMATHCrossRefGoogle Scholar
  10. 10.
    Levenshtein, V.: Binary codes capable of correcting deletions, insertions and reversals. Sov. Phys. Dokl. 10, 707–710 (1966)MathSciNetGoogle Scholar
  11. 11.
    Marmion, M.E., Dhaenens, C., Jourdan, L.: A new distance measure based on the exchange operator for the HFF-AVRP. Interne RR-7263, INRIA. http://hal.inria.fr/inria-00475710/en/ (2010)
  12. 12.
    Marmion, M.E., Dhaenens, C., Jourdan, L., Liefooghe, A., Verel, S.: On the neutrality of flowshop scheduling fitness landscapes. In: Learning and Intelligent Optimization (LION 5), LNCS. Springer (2011)Google Scholar
  13. 13.
    Marmion, M.E., Dhaenens, C., Jourdan, L., Liefooghe, A., Verel, S.: NILS: a neutrality-based iterated local search and its application to flowshop scheduling. In: Proceedings of the 12th European Conference of Evolutionary Computation in Combinatorial Optimization, EvoCOP 2011, pp. 191– 202. LNCS, Springer (2011)Google Scholar
  14. 14.
    Merz, P.: Memetic algorithms for combinatorial optimization problems: fitness landscapes and effective search strategies. Ph.D. thesis, Department of Electrical Engineering and Computer Science, University of Siegen, Germany (2000)Google Scholar
  15. 15.
    Michalewicz, Z., Fogel, D.B.: How to Solve it: Modern Heuristics. Springer (2000)Google Scholar
  16. 16.
    Mitchell, M., Forrest, S., Holland, J.H.: The royal road for genetic algorithms: fitness landscapes and ga performance. In: Proceedings of the First European Conference on Artificial Life, pp. 245–254. MIT Press (1991)Google Scholar
  17. 17.
    Schiavinotto, T., Stützle, T.: A review of metrics on permutations for search landscape analysis. Comput. Oper. Res. 34, 3143–3153 (2007)zbMATHCrossRefGoogle Scholar
  18. 18.
    Stadler, P.F.: Towards a Theory of Landscapes, vol. 461, pp. 78–163. Springer Berlin/Heidelberg (1995)Google Scholar
  19. 19.
    Toth, P., Vigo, D.: An Overview of Vehicle Routing Problems, pp. 1–26. Society for Industrial and Applied Mathematics, Philadelphia, PA, USA (2001)Google Scholar
  20. 20.
    Verel, S., Ochoa, G., Tomassini, M.: Local optima networks of nk landscapes with neutrality. Evol. Comput. PP(99), 1 (2011). doi: 10.1109/TEVC.2010.2046175 Google Scholar
  21. 21.
    Weinberger, E.: Correlated and uncorrelated fitness landscapes and how to tell the difference. Biol. Cybern. 63, 325–336 (1990)zbMATHCrossRefGoogle Scholar
  22. 22.
    Wright, S.: The roles of mutation, inbreeding, crossbreeding and selection in evolution. In: Jones, D. (ed.) Proceedings of the Sixth International Congress on Genetics, vol. 1 (1932)Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  • Marie-Éléonore Marmion
    • 1
    Email author
  • Laetitia Jourdan
    • 1
  • Clarisse Dhaenens
    • 1
  1. 1.LIFL, Université Lille 1, Inria Lille-Nord EuropeVilleneuve d’AscqFrance

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