We address the following dilemma: When making decisions in real life, we often face the problem that, while we have time to contemplate about a problem, we are not entirely sure what the exact parameters of our problem will be. And, on the other hand, as soon as the real world is revealed to us, we need to act quickly and have no more time to rethink our actions extensively.

We suggest an approach that allows to trade uncertainty for time and marginal quality loss and discuss its applicability to combinatorial optimization problems that can be formulated as linear and integer linear programs. The core idea consists in solving a polynomial number of problems in the extensive time period before the day of operation, so that, as soon as complete information is available, a feasible near-optimal solution to the problem can be found in sublinear time.


Feasible Solution Integer Program Integer Linear Program Robust Optimization Constraint Satisfaction Problem 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Althoefer, I., Berger, F., Schwarz, S.: Generating True Alternatives with a Penalty Method (2002),
  2. 2.
    Ben-Tal, A., Nemirovski, A.: Robust Optimization - Methodology and Applications. Mathematical Programming Series B 92, 453–480 (2002)MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Birge, J., Louveaux, F.: Introduction to Stochastic Programming. Springer, Heidelberg (1997)MATHGoogle Scholar
  4. 4.
    Borodin, A., El-Yaniv, R.: Online Computation and Competitive Analysis. Cambridge University Press, Cambridge (1998)MATHGoogle Scholar
  5. 5.
    Chinneck, J.W., Ramadan, K.: Linear programming with interval coefficients. Journal of the Operational Research Society 51(2), 209–220 (2000)CrossRefMATHGoogle Scholar
  6. 6.
    Elbassioni, K., Katriel, I.: Multiconsistency and Robustness with Global Constraints. In: Barták, R., Milano, M. (eds.) CPAIOR 2005. LNCS, vol. 3524, pp. 168–182. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  7. 7.
    Eppstein, D.: Bibliography on k shortest paths and other ”k best solutions” problems (2001),
  8. 8.
    Guestrin, C., Koller, D., Gearhart, C., Kanodia, N.: Generalizing Plans to New Environments in Relational MDPs. In: IJCAI (2003)Google Scholar
  9. 9.
    Hebrard, E., Hnich, B., Walsh, T.: Super Solutions in Constraint Programming. In: Régin, J.-C., Rueher, M. (eds.) CPAIOR 2004. LNCS, vol. 3011, pp. 157–172. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  10. 10.
    Hulgeri, A., Sudarshan, S.: Parametric Query Optimization for Linear and Piecewise Linear Cost Functions. In: VLDB, pp. 167–178 (2002)Google Scholar
  11. 11.
    Lagoudakis, M., Parr, R.: Least-Squares Policy Iteration. Journal of Machine Learning Research 4, 1107–1149 (2003)MathSciNetMATHGoogle Scholar
  12. 12.
    Sameith, I.: On the Generation of Alternative Solutions for Discrete Optimization Problems with Uncertain Data (2004),
  13. 13.
    Verweij, B., Ahmed, S., Kleywegt, A., Nemhauser, G., Shapiro, A.: The Sample Average Approximation Method Applied to Stochastic Routing Problems: A Computational Study. Computational Optimization and Applications 24(2-3), 289–333 (2003)MathSciNetCrossRefMATHGoogle Scholar
  14. 14.
    Vossen, T., Ball, M., Lotem, A., Nau, D.S.: On the Use of Integer Programming Models in AI Planning. In: IJCAI (1999)Google Scholar
  15. 15.
    Yorke-Smith, N.: Reliable Constraint Reasoning with Uncertain Data. PhD thesis, IC-Parc, Imperial College London (June 2004)Google Scholar
  16. 16.
    Yorke-Smith, N., Gervet, C.: Tight and Tractable Reformulations for Uncertain CSPs. In: Proceedings of CP 2004 Workshop on Modelling and Reformulating Constraint Satisfaction Problems, Toronto, Canada (September 2004)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Claire Kenyon
    • 1
  • Meinolf Sellmann
    • 1
  1. 1.Department of Computer ScienceBrown UniversityProvidenceU.S.A.

Personalised recommendations