Cost-Based Domain Filtering for Stochastic Constraint Programming

  • Roberto Rossi
  • S. Armagan Tarim
  • Brahim Hnich
  • Steven Prestwich
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5202)

Abstract

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 [7]. Stochastic Constraint Programming is a framework for modeling combinatorial optimization problems that involve uncertainty [9]. 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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Apt, K.: Principles of Constraint Programming. Cambridge University Press, Cambridge (2003)Google Scholar
  2. 2.
    Avriel, M., Williams, A.C.: The value of information and stochastic programming. Operations Research 18(5), 947–954 (1970)MATHMathSciNetGoogle Scholar
  3. 3.
    Balafoutis, T., Stergiou, K.: Algorithms for stochastic csps. In: Benhamou, F. (ed.) CP 2006. LNCS, vol. 4204, pp. 44–58. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  4. 4.
    Birge, J.R., Louveaux, F.: Introduction to Stochastic Programming. Springer, New York (1997)MATHGoogle Scholar
  5. 5.
    Boyd, S., Vandenberghe, L.: Convex Optimization. Cambridge University Press, Cambridge (2004)MATHGoogle Scholar
  6. 6.
    Charnes, A., Cooper, W.W.: Deterministic equivalents for optimizing and satisficing under chance constraints. Operations Research 11(1), 18–39 (1963)MATHMathSciNetCrossRefGoogle Scholar
  7. 7.
    Focacci, F., Lodi, A., Milano, M.: Optimization-oriented global constraints. Constraints 7, 351–365 (2002)MATHCrossRefMathSciNetGoogle Scholar
  8. 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. 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
  10. 10.
    Jain, V., Grossmann, I.E.: Algorithms for hybrid milp/cp models for a class of optimization problems. INFORMS Journal on computing 13, 258–276 (2001)CrossRefMathSciNetGoogle Scholar
  11. 11.
    Kall, P., Wallace, S.W.: Stochastic Programming. John Wiley & Sons, Chichester (1994)MATHGoogle Scholar
  12. 12.
    Kleywegt, A.J., Shapiro, A., Homem-De-Mello, T.: The sample average approximation method for stochastic discrete optimization. SIAM Journal of Optimization 12(2), 479–502 (2001)MATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Kuhn, D.: Generalized bounds for convex multistage stochastic programs. Lecture Notes in Economics and Mathematical Systems, vol. 584Google Scholar
  14. 14.
    Laburthe, F.: The OCRE project team. Choco: Implementing a cp kernel. Technical report, Bouygues e-Lab, France (1994)Google Scholar
  15. 15.
    Martello, S., Toth, P.: Knapsack Problems. John Wiley & Sons, NY (1990)MATHGoogle Scholar
  16. 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. 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
  18. 18.
    Tarim, S.A., Manandhar, S., Walsh, T.: Stochastic constraint programming: A scenario-based approach. Constraints 11(1), 53–80 (2006)MATHCrossRefMathSciNetGoogle Scholar
  19. 19.
    Walsh, T.: Stochastic constraint programming. In: Proceedings of the 15th ECAI. European Conference on Artificial Intelligence. IOS Press, Amsterdam (2002)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Roberto Rossi
    • 1
  • S. Armagan Tarim
    • 2
  • Brahim Hnich
    • 3
  • Steven Prestwich
    • 1
  1. 1.Cork Constraint Computation Centre - CTVRUniversity CollegeCorkIreland
  2. 2.Department of ManagementHacettepe UniversityAnkaraTurkey
  3. 3.Faculty of Computer ScienceIzmir University of EconomicsTurkey

Personalised recommendations