Cooperative Parallel Decomposition Guided VNS for Solving Weighted CSP

  • Abdelkader Ouali
  • Samir Loudni
  • Lakhdar Loukil
  • Patrice Boizumault
  • Yahia Lebbah
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8457)


Tree decomposition introduced by Robertson and Seymour aims to decompose a problem into clusters constituting an acyclic graph. Recently, Fontaine et al. [8] introduced DGVNS (Decomposition Guided VNS) that uses the graph of clusters provided by a tree decomposition to manage the exploration of large neighborhoods. However, for large scale problems, the performance of DGVNS may decrease significantly due to the large number of clusters to be considered sequentially. To overcome this shortcoming we propose CPDGVNS (Cooperative Parallel DGVNS) in which the clusters are explored in parallel through an asynchronous master-slave architecture. Experiments performed on real life instances show the appropriateness and the efficiency of our approach.


Tree decomposition Weighted CSP Parallelization Meta-heuristics Variable Neighborhood Search (VNS) Master-Slave architecture 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Arnborg, S., Corneil, D.G., Proskurowski, A.: Complexity of finding embeddings in a k-tree. SIAM Journal on Algebraic and Discrete Methods 8, 277–284 (1987)CrossRefzbMATHMathSciNetGoogle Scholar
  2. 2.
    Bensana, E., Lemaître, M., Verfaillie, G.: Earth observation satellite management. Constraints 4(3), 293–299 (1999)CrossRefzbMATHGoogle Scholar
  3. 3.
    Cabon, B., de Givry, S., Lobjois, L., Schiex, T., Warners, J.P.: Radio link frequency assignment. Constraints 4(1), 79–89 (1999)CrossRefzbMATHGoogle Scholar
  4. 4.
    Crainic, T.G., Gendreau, M., Hansen, P., Mladenovic, N.: Cooperative parallel variable neighborhood search for the p-median. Journal of Heuristics 10(3), 293–314 (2004)CrossRefGoogle 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. Artificial Intelligence 38(3), 353–366 (1989)CrossRefzbMATHMathSciNetGoogle Scholar
  7. 7.
    Carlson, C.S., et al.: Selecting a maximally informative set of single-nucleotide polymorphisms for association analyses using linkage disequilibrium. American Journal of Human Genetics 74(1), 106–120 (2004)CrossRefGoogle Scholar
  8. 8.
    Fontaine, M., Loudni, S., Boizumault, P.: Exploiting tree decomposition for guiding neighborhoods exploration for VNS. RAIRO Operations Research 47(2), 91–123 (2013)CrossRefzbMATHMathSciNetGoogle Scholar
  9. 9.
    Gottlob, G., Lee, S.T., Valiant, G.: Size and treewidth bounds for conjunctive queries. In: Paredaens, J., Su, J. (eds.) PODS, pp. 45–54. ACM (2009)Google Scholar
  10. 10.
    Harvey, W.D., Ginsberg, M.L.: Limited discrepancy search. In: IJCAI, pp. 607–615. Morgan Kaufmann (1995)Google Scholar
  11. 11.
    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
  12. 12.
    Loudni, S., Boizumault, P.: Combining VNS with constraint programming for solving anytime optimization problems. European Journal of Operational Research 191, 705–735 (2008)CrossRefzbMATHGoogle Scholar
  13. 13.
    Marinescu, R., Dechter, R.: AND/OR branch-and-bound search for combinatorial optimization in graphical models. Artificial Intelligence 173(16-17), 1457–1491 (2009)CrossRefzbMATHMathSciNetGoogle Scholar
  14. 14.
    Mladenovic, N., Hansen, P.: Variable neighborhood search. Computers and Operations Research 24, 1097–1100 (1997)CrossRefzbMATHMathSciNetGoogle Scholar
  15. 15.
    Pearl, J.: Probabilistic inference in intelligent systems. In: Networks of Plausible Inference. Morgan Kaufmann (1998)Google Scholar
  16. 16.
    Rish, I., Dechter, R.: Resolution versus search: Two strategies for SAT. Journal of Automated Reasoning 24(1/2), 225–275 (2000)CrossRefzbMATHMathSciNetGoogle Scholar
  17. 17.
    Robertson, N., Seymour, P.D.: Graph minors. ii. algorithmic aspects of tree-width. Journal of Algorithms 7(3), 309–322 (1986)CrossRefzbMATHMathSciNetGoogle Scholar
  18. 18.
    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
  19. 19.
    Sánchez, M., de Givry, S., Schiex, T.: Mendelian error detection in complex pedigrees using weighted constraint satisfaction techniques. Constraints 13(1-2), 130–154 (2008)CrossRefzbMATHMathSciNetGoogle Scholar
  20. 20.
    Tarjan, R.E., Yannakakis, M.: Simple linear-time algorithms to test chordality of graphs, test acyclicity of hypergraphs, and selectively reduce acyclic hypergraphs. SIAM Journal on Computing 13(3), 566–579 (1984)CrossRefzbMATHMathSciNetGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Abdelkader Ouali
    • 1
  • Samir Loudni
    • 2
  • Lakhdar Loukil
    • 1
  • Patrice Boizumault
    • 2
  • Yahia Lebbah
    • 1
  1. 1.Laboratoire LITIOUniversité d’OranOranAlgeria
  2. 2.CNRS, UMR 6072 GREYCUniversity of CaenCaenFrance

Personalised recommendations