Abstract
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.
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
Althoefer, I., Berger, F., Schwarz, S.: Generating True Alternatives with a Penalty Method (2002), http://www.minet.uni-jena.de/MathNet/reports/shadows/02-04report.html
Ben-Tal, A., Nemirovski, A.: Robust Optimization - Methodology and Applications. Mathematical Programming Series B 92, 453–480 (2002)
Birge, J., Louveaux, F.: Introduction to Stochastic Programming. Springer, Heidelberg (1997)
Borodin, A., El-Yaniv, R.: Online Computation and Competitive Analysis. Cambridge University Press, Cambridge (1998)
Chinneck, J.W., Ramadan, K.: Linear programming with interval coefficients. Journal of the Operational Research Society 51(2), 209–220 (2000)
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)
Eppstein, D.: Bibliography on k shortest paths and other ”k best solutions” problems (2001), http://www.ics.uci.edu/~eppstein/-bibs/-kpath.bib
Guestrin, C., Koller, D., Gearhart, C., Kanodia, N.: Generalizing Plans to New Environments in Relational MDPs. In: IJCAI (2003)
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)
Hulgeri, A., Sudarshan, S.: Parametric Query Optimization for Linear and Piecewise Linear Cost Functions. In: VLDB, pp. 167–178 (2002)
Lagoudakis, M., Parr, R.: Least-Squares Policy Iteration. Journal of Machine Learning Research 4, 1107–1149 (2003)
Sameith, I.: On the Generation of Alternative Solutions for Discrete Optimization Problems with Uncertain Data (2004), http://www.minet.uni-jena.de/MathNet/reports/shadows/04-01report.html
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)
Vossen, T., Ball, M., Lotem, A., Nau, D.S.: On the Use of Integer Programming Models in AI Planning. In: IJCAI (1999)
Yorke-Smith, N.: Reliable Constraint Reasoning with Uncertain Data. PhD thesis, IC-Parc, Imperial College London (June 2004)
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)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Kenyon, C., Sellmann, M. (2006). Plan B: Uncertainty/Time Trade-Offs for Linear and Integer Programming. In: Beck, J.C., Smith, B.M. (eds) Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems. CPAIOR 2006. Lecture Notes in Computer Science, vol 3990. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11757375_12
Download citation
DOI: https://doi.org/10.1007/11757375_12
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-34306-6
Online ISBN: 978-3-540-34307-3
eBook Packages: Computer ScienceComputer Science (R0)