Cost-Based Domain Filtering for Stochastic Constraint Programming
Cost-based filtering is a novel approach that combines techniques from Operations Research and Constraint Programming to filter from decision variable domains values that do not lead to better solutions . Stochastic Constraint Programming is a framework for modeling combinatorial optimization problems that involve uncertainty . In this work, we show how to perform cost-based filtering for certain classes of stochastic constraint programs. Our approach is based on a set of known inequalities borrowed from Stochastic Programming — a branch of OR concerned with modeling and solving problems involving uncertainty. We discuss bound generation and cost-based domain filtering procedures for a well-known problem in the Stochastic Programming literature, the static stochastic knapsack problem. We also apply our technique to a stochastic sequencing problem. Our results clearly show the value of the proposed approach over a pure scenario-based Stochastic Constraint Programming formulation both in terms of explored nodes and run times.
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- 1.Apt, K.: Principles of Constraint Programming. Cambridge University Press, Cambridge (2003)Google Scholar
- 8.Garey, M.R., Johnson, D.S.: Computer and Intractability. A guide to the theory of NP-Completeness. Bell Laboratories, Murray Hill, New Jersey (1979)Google Scholar
- 9.Hooker, J.N., Ottosson, G., Thorsteinsson, E.S., Kim, H.J.: On integrating constraint propagation and linear programming for combinatorial optimization. In: Proceedings of the Sixteenth National Conference on Artificial Intelligence (AAAI 1999), pp. 136–141. The AAAI Press/MIT Press, Cambridge (1999)Google Scholar
- 13.Kuhn, D.: Generalized bounds for convex multistage stochastic programs. Lecture Notes in Economics and Mathematical Systems, vol. 584Google Scholar
- 14.Laburthe, F.: The OCRE project team. Choco: Implementing a cp kernel. Technical report, Bouygues e-Lab, France (1994)Google Scholar
- 16.Rossi, R., Tarim, S.A., Hnich, B., Prestwich, S.: A global chance-constraint for stochastic inventory systems under service level constraints. Constraints 13(4) (2008)Google Scholar
- 17.Tarim, S.A., Hnich, B., Rossi, R., Prestwich, S.: Cost-based filtering techniques for stochastic inventory control under service level constraints. Constraints (forthcoming) (2008)Google Scholar
- 19.Walsh, T.: Stochastic constraint programming. In: Proceedings of the 15th ECAI. European Conference on Artificial Intelligence. IOS Press, Amsterdam (2002)Google Scholar