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Value Interchangeability in Scenario Generation

  • Steven D. Prestwich
  • Marco Laumanns
  • Ban Kawas
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8124)

Abstract

Several types of symmetry have been identified and exploited in Constraint Programming, leading to large reductions in search time. We present a novel application of one such form of symmetry: detecting dynamic value interchangeability in the random variables of a 2-stage stochastic problem. We use a real-world problem from the literature: finding an optimal investment plan to strengthen a transportation network, given that a future earthquake probabilistically destroys links in the network. Detecting interchangeabilities enables us to bundle together many equivalent scenarios, drastically reducing the size of the problem and allowing the exact solution of cases previously considered intractable and solved only approximately.

Keywords

Mixed Integer Programming Stochastic Program Constraint Programming Constraint Satisfaction Problem Stochastic Dominance 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Apt, K.R., Wallace, M.: Constraint Logic Programming using Eclipse. Cambridge University Press (2007)Google Scholar
  2. 2.
    Beckwith, A.M., Choueiry, B.Y.: On the Dynamic Detection of Interchangeability in Finite Constraint Satisfaction Problems. In: Walsh, T. (ed.) CP 2001. LNCS, vol. 2239, p. 760. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  3. 3.
    Bianchi, L., Dorigo, M., Gambardella, L.M., Gutjahr, W.J.: A Survey on Metaheuristics for Stochastic Combinatorial Optimization. Natural Computing 8(2), 239–287 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Birge, J., Louveaux, F.: Introduction to Stochastic Programming. Springer Series in Operations Research (1997)Google Scholar
  5. 5.
    Choueiry, B.Y., Davis, A.M.: Dynamic Bundling: Less Effort for More Solutions. In: Koenig, S., Holte, R. (eds.) SARA 2002. LNCS (LNAI), vol. 2371, pp. 64–82. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  6. 6.
    Choueiry, B.Y., Noubir, G.: On the Computation of Local Interchangeability in Discrete Constraint Satisfaction Problems. In: 15th National Conference on Artificial Intelligence and 10th Innovative Applications of Artificial Intelligence Conference, pp. 326–333 (1998)Google Scholar
  7. 7.
    Colbourn, C.J.: Concepts of Network Reliability. Wiley Encyclopedia of Operations Research and Management Science. John Wiley & Sons, Inc. (2010)Google Scholar
  8. 8.
    Dupǎcová, J., Gröwe-Kuska, N., Römisch, W.: Scenario Reduction in Stochastic Programming: an Approach Using Probability Metrics. Mathematical Programming Series A 95, 493–511 (2003)CrossRefGoogle Scholar
  9. 9.
    Freuder, E.C.: Eliminating Interchangeable Values in Constraint Satisfaction Problems. In: National Conference on Artificial Intelligence, pp. 227–233 (1991)Google Scholar
  10. 10.
    Gent, I.P., Kelsey, T., Linton, S.A., Pearson, J., Roney-Dougal, C.M.: Groupoids and Conditional Symmetry. In: Bessière, C. (ed.) CP 2007. LNCS, vol. 4741, pp. 823–830. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  11. 11.
    Haselböck, A.: Exploiting Interchangeabilities in Constraint Satisfaction Problems. In: 13th International Joint Conference on Artificial Intelligence, pp. 282–287 (1993)Google Scholar
  12. 12.
    Hnich, B., Rossi, R., Tarim, S.A., Prestwich, S.: A Survey on CP-AI-OR Hybrids for Decision Making under Uncertainty. In: Milano, M., Van Hentenryck, P. (eds.) Hybrid Optimization: the 10 Years of CP-AI-OR. Springer Optimization and its Applications 45, 227–270 (2011)Google Scholar
  13. 13.
    Hubbe, P.D., Freuder, E.C.: An Efficient Cross Product Representation of the Constraint Satisfaction Problem Search Space. In: 10th National Conference on Artificial Intelligence, San Jose, California, USA, pp. 421–427 (1992)Google Scholar
  14. 14.
    Karakashian, S., Woodward, R., Choueiry, B.Y., Prestwich, S.D., Freuder, E.C.: A Partial Taxonomy of Substitutability and Interchangeability. In: 10th International Workshop on Symmetry in Constraint Satisfaction Problems (2010) (Journal paper in preparation) Google Scholar
  15. 15.
    Lal, A., Choueiry, B.Y., Freuder, E.C.: Neighborhood Interchangeability and Dynamic Bundling for Non-Binary Finite CSPs. In: 10th National Conference on Artificial Intelligence and 17th Innovative Applications of Artificial Intelligence Conference, pp. 397–404 (2005)Google Scholar
  16. 16.
    Lesaint, D.: Maximal Sets of Solutions for Constraint Satisfaction Problems. In: 11th European Conference on Artificial Intelligence, pp. 110–114 (1994)Google Scholar
  17. 17.
    Levy, H.: Stochastic Dominance and Expected Utility: Survey and Analysis. Management Science 38, 555–593 (1992)CrossRefzbMATHGoogle Scholar
  18. 18.
    Margot, F.: Symmetry in Integer Linear Programming. 50 Years of Integer Programming 1958–2008, pp. 647–686 (2010)Google Scholar
  19. 19.
    Neagu, N.: Studying Interchangeability in Constraint Satisfaction Problems. In: Van Hentenryck, P. (ed.) CP 2002. LNCS, vol. 2470, pp. 787–788. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  20. 20.
    Parkes, A.J.: Exploiting Solution Clusters for Coarse-Grained Distributed Search. In: IJCAI Workshop on Distributed Constraint Reasoning (2001)Google Scholar
  21. 21.
    Peeta, S., Salman, F.S., Gunnec, D., Viswanath, K.: Pre-Disaster Investment Decisions for Strengthening a Highway Network. Computers & Operations Research 37, 1708–1719 (2010)CrossRefzbMATHGoogle Scholar
  22. 22.
    Prestwich, S.D.: Full Dynamic Interchangeability with Forward Checking and Arc Consistency. In: ECAI Workshop on Modeling and Solving Problems With Constraints (2004)Google Scholar
  23. 23.
    Prestwich, S.D.: Full Dynamic Substitutability by SAT Encoding. In: Wallace, M. (ed.) CP 2004. LNCS, vol. 3258, pp. 512–526. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  24. 24.
    Ruszczyński, A.: Decomposition Methods in Stochastic Programming. Mathematical Programming 79, 333–353 (1997)MathSciNetzbMATHGoogle Scholar
  25. 25.
    Salman, S.: Personal communicationGoogle Scholar
  26. 26.
    Walsh, T.: Stochastic Constraint Programming. In: 15th European Conference on Artificial Intelligence, pp. 111–115 (2002)Google Scholar
  27. 27.
    Weigel, R., Faltings, B.V., Choueiry, B.Y.: Context in Discrete Constraint Satisfaction Problems. In: 12th European Conference on Artificial Intelligence, pp. 205–209 (1996)Google Scholar
  28. 28.
    Zantema, H., Bodlaender, H.L.: Sizes of Ordered Decision Trees. International Journal of Foundations of Computer Science 13(3), 445–458 (2002)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Steven D. Prestwich
    • 1
  • Marco Laumanns
    • 2
  • Ban Kawas
    • 3
  1. 1.Cork Constraint Computation Centre, Department of Computer ScienceUniversity College CorkIreland
  2. 2.IBM Research – ZurichRueschlikonSwitzerland
  3. 3.IBM Thomas J. Watson Research CenterUSA

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