Abstract
This paper presents a CSPs filtering method combining arc-consistency and dual Lagrangean relaxation techniques. First, we model the constraint satisfaction problem as a 0/1 linear integer program (IP); then, the consistency of a value is defined as an optimization problem on which a dual Lagrangean relaxation is defined. While solving the dual Lagrangean relaxation, values inconsistencies may be detected (dual Lagrangean inconsistent values); the constraint propagation of this inconsistency can be performed by arc-consistency. After having made the CSP arc-consistent, the process iteratively selects values of variables which may be dual Lagrangean inconsistent. Computational experiments performed over randomly generated problems show the advantages of the hybrid filtering technique combining arc-consistency and dual Lagrangean relaxation.
This work is supported in part by the French Electricity Board (EDF).
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Affane, M.S., Bennaceur, H.: A Weighted Arc Consistency Technique for MAX-CSP. In: ECAI, pp. 209–213 (1998)
Benoist, T., Gaudin, E., Rottembourg, B.: Constraint Programming Contribution to Benders Decomposition: A Case Study. In: Van Hentenryck, P. (ed.) CP 2002. LNCS, vol. 2470, pp. 603–617. Springer, Heidelberg (2002)
Bessière, C., Cordier, M.: Arc-consistency and Arc-consistency Again. Artificial Intelligence 65(1), 179–190 (1994)
Camerini, P.M., Fratta, L., Maffioli, F.: On improving relaxation methods by modified gradient techniques. Mathematical programming Study 3, 26–34 (1975)
Darby-Dowman, K., Little, J.: Properties of some combinatorial optimization problems and their effect on the performance of integer programming and constraint logic programming. INFORMS Journal on Computing 10(3), 276–286 (1998)
Darby-Dowman, K., Little, J., Mitra, G., Zaffalon, M.: Constraint Logic Programming and Integer Programming Approaches and their Collaboration in Solving an Assignment Scheduling Problem. Constraints, An International Journal 1(3), 245–264 (1997)
Dechter, R., Meiri, I.: Experimental evaluation of preprocessing algorithms for constraint satisfaction problems. Artificial Intelligence 68, 211–241 (1994)
Focacci, F., Lodi, A., Milano, M.: Cost-Based Domain Filtering. In: Jaffar, J. (ed.) CP 1999. LNCS, vol. 1713, pp. 189–203. Springer, Heidelberg (1999)
Focacci, F., Lodi, A., Milano, M.: Optimization-Oriented Global Constraints. Constraints 7(3-4), 351–365 (2002)
Frost, D., Dechter, R.: In search of the best constraint satisfaction search. In: Proceedings AAAI 1994, Seatlle WA, pp. 301–306 (1994)
Geoffrion, A.M.: The Lagrangean Relaxation for Integer Programming. Mathematical Programming 2, 82–114 (1974)
Hooker, J.N., Osorio, M.A.: Mixed Logical/Linear Programming. Discrete Applied Mathematics 96-97(1-3), 395–442 (1999)
Hooker, J.N., Ottosson, G., Thornsteinsson, E.S., Kim, H.-J.: A scheme for unifying optimization and constraint satisfaction methods. Knowledge Engineering Review 15, 11–30 (2000)
Koster, A.M.C.: Frequency Assignment Problem, Models and Algorithms. Proefschrift Universiteit Maastricht. (1999)
Mackworth, A.: Consistency in networks of relations. Artificial Intelligence 8, 99–118 (1977)
Maculan, N., Passini, M.M., Brito, J.A.M., Loiseau, I.: Column-Generation in Integer Linear Programming. RAIRO - Operations Research 37, 67–83 (2003)
Milano, M., Ottosson, G., Refalo, P., Erlendur, S.: The Benefits of Global Constraints for the Integration of Constraint Programming and Integer Programming. In: Thorsteinsson, E.S. (ed.) Proceedings of the Seventeenth National Conference on Artificial Intelligence. AAAI, Menlo Park (2000)
Mohr, R., Henderson, T.: Arc and Path consistency revisited. Artificial Intelligence 28, 225–233 (1986)
Sellmann, M.: Theoretical Foundations of CP-based Lagrangian Relaxation. In: Wallace, M. (ed.) CP 2004. LNCS, vol. 3258, pp. 634–647. Springer, Heidelberg (2004)
Zhao, X., Luh, P.B.: New bundle methods for solving Lagrangian relaxation dual problems. Journal of Optimization Theory and Applications 113(2), 373–397 (2002)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Khemmoudj, M.O.I., Bennaceur, H., Nagih, A. (2005). Combining Arc-Consistency and Dual Lagrangean Relaxation for Filtering CSPs. In: Barták, R., Milano, M. (eds) Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems. CPAIOR 2005. Lecture Notes in Computer Science, vol 3524. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11493853_20
Download citation
DOI: https://doi.org/10.1007/11493853_20
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-26152-0
Online ISBN: 978-3-540-32264-1
eBook Packages: Computer ScienceComputer Science (R0)