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Intensification/Diversification in Decomposition Guided VNS

  • Samir Loudni
  • Mathieu Fontaine
  • Patrice Boizumault
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7919)

Abstract

Tree decomposition introduced by Robertson and Seymour aims to decompose a problem into clusters constituting an acyclic graph. In a previous paper, we have introduced DGVNS (Decomposition Guided VNS) which uses the graph of clusters to manage the exploration of large neighborhoods. In this paper, we go one step further by proposing three new strategies that exploit the graph of clusters enabling a better intensification and diversification in DGVNS. Experiments performed on random instances (GRAPH) and real life instances (RLFAP, SPOT5 and tagSNP) show the appropriateness and the efficiency of our proposals.

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References

  1. 1.
  2. 2.
    Arnborg, S., Corneil, D.G., Proskurowski, A.: Complexity of finding embeddings in a k-tree. SIAM. J. on Algebraic and Discrete Methods 8, 277–284 (1987)MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Bensana, E., Lemaître, M., Verfaillie, G.: Earth observation satellite management. Constraints 4(3), 293–299 (1999)zbMATHCrossRefGoogle Scholar
  4. 4.
    Cabon, B., de Givry, S., Lobjois, L., Schiex, T., Warners, J.P.: Radio link frequency assignment. Constraints 4(1), 79–89 (1999)zbMATHCrossRefGoogle Scholar
  5. 5.
    de Givry, S., Schiex, T., Verfaillie, G.: Exploiting tree decomposition and soft local consistency in weighted CSP. In: AAAI, pp. 22–27. AAAI Press (2006)Google Scholar
  6. 6.
    Dechter, R., Pearl, J.: Tree clustering for constraint networks. Artif. Intell. 38(3), 353–366 (1989)MathSciNetzbMATHCrossRefGoogle Scholar
  7. 7.
    Carlson, C.S., et al.: Selecting a maximally informative set of single-nucleotide polymorphisms for association analyses using linkage disequilibrium. Am. J. of Hum. Genetics 74(1), 106–120 (2004)CrossRefGoogle Scholar
  8. 8.
    Fontaine, M., Loudni, S., Boizumault, P.: Guiding VNS with tree decomposition. In: ICTAI, pp. 505–512. IEEE (2011)Google Scholar
  9. 9.
    Gottlob, G., Lee, S.T., Valiant, G.: Size and treewidth bounds for conjunctive queries. In: PODS, pp. 45–54 (2009)Google Scholar
  10. 10.
    Gottlob, G., Miklós, Z., Schwentick, T.: Generalized hypertree decompositions: Np-hardness and tractable variants. J. ACM 56(6) (2009)Google Scholar
  11. 11.
    Hansen, P., Mladenovic, N., Perez-Brito, D.: Variable neighborhood decomposition search. Journal of Heuristics 7(4), 335–350 (2001)zbMATHCrossRefGoogle Scholar
  12. 12.
    Harvey, W.D., Ginsberg, M.L.: Limited discrepancy search. In: IJCAI (1), pp. 607–615. Morgan Kaufmann (1995)Google Scholar
  13. 13.
    Koster, A.M.C.A., Bodlaender, H.L., van Hoesel, S.P.M.: Treewidth: Computational experiments. ENDM 8, 54–57 (2001)Google Scholar
  14. 14.
    Larrosa, J., Schiex, T.: In the quest of the best form of local consistency for Weighted CSP. In: IJCAI, pp. 239–244 (2003)Google Scholar
  15. 15.
    Linhares, A., Yanasse, H.H.: Search intensity versus search diversity: a false trade off? Appl. Intell. 32(3), 279–291 (2010)CrossRefGoogle Scholar
  16. 16.
    Loudni, S., Boizumault, P.: Combining VNS with constraint programming for solving anytime optimization problems. EJOR 191, 705–735 (2008)zbMATHCrossRefGoogle Scholar
  17. 17.
    Marinescu, R., Dechter, R.: AND/OR branch-and-bound search for combinatorial optimization in graphical models. Artif. Intell. 173(16-17), 1457–1491 (2009)MathSciNetzbMATHCrossRefGoogle Scholar
  18. 18.
    Mladenovic, N., Hansen, P.: Variable neighborhood search. Computers and Operations Research 24, 1097–1100 (1997)MathSciNetzbMATHCrossRefGoogle Scholar
  19. 19.
    Neveu, B., Trombettoni, G., Glover, F.: ID Walk: A candidate list strategy with a simple diversification device. In: Wallace, M. (ed.) CP 2004. LNCS, vol. 3258, pp. 423–437. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  20. 20.
    Rish, I., Dechter, R.: Resolution versus search: Two strategies for SAT. J. Autom. Reasoning 24(1/2), 225–275 (2000)MathSciNetzbMATHCrossRefGoogle Scholar
  21. 21.
    Robertson, N., Seymour, P.D.: Graph minors. ii. Algorithmic aspects of tree-width. J. Algorithms 7(3), 309–322 (1986)MathSciNetzbMATHCrossRefGoogle Scholar
  22. 22.
    Sánchez, M., Allouche, D., de Givry, S., Schiex, T.: Russian doll search with tree decomposition. In: Boutilier, C. (ed.) IJCAI, pp. 603–608 (2009)Google Scholar
  23. 23.
    Shaw, P.: Using constraint programming and local search methods to solve vehicle routing problems. In: Maher, M.J., Puget, J.-F. (eds.) CP 1998. LNCS, vol. 1520, pp. 417–431. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  24. 24.
    Tarjan, R.E., Yannakakis, M.: Simple linear-time algorithms to test chordality of graphs, test acyclicity of hypergraphs, and selectively reduce acyclic hypergraphs. SIAM J. Comput. 13(3), 566–579 (1984)MathSciNetzbMATHCrossRefGoogle Scholar
  25. 25.
    Terrioux, C., Jégou, P.: Hybrid backtracking bounded by tree-decomposition of constraint networks. Artificial Intelligence 146(1), 43–75 (2003)MathSciNetzbMATHCrossRefGoogle Scholar
  26. 26.
    van Benthem, H.: GRAPH: Generating radiolink frequency assignment problems heuristically (1995)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Samir Loudni
    • 1
    • 2
  • Mathieu Fontaine
    • 1
    • 2
  • Patrice Boizumault
    • 1
    • 2
  1. 1.UMR 6072 GREYCUniversité de Caen Basse-NormandieCaenFrance
  2. 2.UMR 6072 GREYCCNRSCaenFrance

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