Abstract
This paper proposes to use local search inside filtering algorithms of combinatorial structures for which achieving a desired level of consistency is too computationally expensive. Local search quickly provides supports for many variable-value pairs, thus reducing the effort required to check and potentially filter the rest of them. The idea is demonstrated on the SomeDifferent constraint, a graph coloring substructure. An experimental evaluation confirms its significant computational gain in many cases.
Access this article
Rent this article via DeepDyve
Similar content being viewed by others
References
Biro, M., Hujter, M., & Zsolt, T. (1992). Precoloring extension 1. Interval graphs. Discrete Mathematics, 100, 267–279.
Galinier, P., Hertz, A., Paroz, S., & Pesant, G. (2008). Using local search to speed up filtering algorithms for some NP-hard constraints. In L. Perron & M. A. Trick (Eds.), Lecture notes in computer science : Vol. 5015. CPAIOR (pp. 298–302). Berlin: Springer.
Gendreau, M., Hertz, A., & Laporte, G. (1994). A tabu search heuristic for the vehicle routing problem. Management Science, 40, 1276–1290.
Glover, F., & Laguna, M. (1997). Tabu search. Boston: Kluwer Academic.
Hertz, A., & de Werra, D. (1987). Using tabu search for graph coloring. Computing, 39, 345–351.
Jansen, K., & Scheffler, P. (1997). Generalized coloring for tree-like graphs. Discrete Applied Mathematics, 75, 135–155.
Katriel, I. (2006). Expected-case analysis for delayed filtering. In Lecture notes in computer science : Vol. 3990. Proceedings of the third international conference on integration of AI and OR techniques in constraint programming for combinatorial optimisation problems (CP-AI-OR’06) (pp. 119–125). Berlin: Springer.
Mahdian, M., & Mahmoodian, E. S. (1999). A characterization of uniquely 2-list colorable graphs. Ars Combinatoria, 51, 295–305.
Peemoeller, J. (1983). A correction to Brélaz’s modification of Brown’s coloring algorithm. Communications of the ACM, 26(8), 593–597.
Richter, Y., Freund, A., & Naveh, Y. (2006). Generalizing alldifferent: the somedifferent constraint. In Lecture notes in computer science : Vol. 4204. Proc. 12th international conference on principles and practice of constraint programming (CP06) (pp. 468–483). Berlin: Springer.
Sellmann, M. (2003). Approximated consistency for knapsack constraints. In Lecture notes in computer science : Vol. 2833. Proceedings of the ninth international conference on the principles and practice of constraint programming (CP’03) (pp. 679–693). Berlin: Springer.
Sellmann, M., & Harvey, W. (2002). Heuristic constraint propagation. In Proceedings of the fourth international workshop on integration of AI and OR techniques in constraint programming for combinatorial optimisation problems (CP-AI-OR’02) 2002 (pp. 191–204).
Trick, M. (1994). http://mat.gsia.cmu.edu/COLOR/solvers/trick.c.
Author information
Authors and Affiliations
Corresponding author
Additional information
An earlier version of this paper appeared as Galinier et al. (Lecture notes in computer science, Vol. 5015, pp. 298–302, 2008).
Rights and permissions
About this article
Cite this article
Galinier, P., Hertz, A., Paroz, S. et al. Using local search to speed up filtering algorithms for some NP-hard constraints. Ann Oper Res 184, 121–135 (2011). https://doi.org/10.1007/s10479-010-0715-0
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10479-010-0715-0