Recoverable Robustness by Column Generation
Real-life planning problems are often complicated by the occurrence of disturbances, which imply that the original plan cannot be followed anymore and some recovery action must be taken to cope with the disturbance. In such a situation it is worthwhile to arm yourself against common disturbances. Well-known approaches to create plans that take possible, common disturbances into account are robust optimization and stochastic programming. Recently, a new approach has been developed that combines the best of these two: recoverable robustness. In this paper, we apply the technique of column generation to find solutions to recoverable robustness problems. We consider two types of solution approaches: separate recovery and combined recovery. We show our approach on two example problems: the size robust knapsack problem, in which the knapsack size may get reduced, and the demand robust shortest path problem, in which the sink is uncertain and the cost of edges may increase.
KeywordsKnapsack Problem Column Generation Robust Optimization Master Problem Short Path Problem
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- 5.Büsing, C., Koster, A.M.C.A., Kutschka, M.: Recoverable Robust Knapsacks: the Discrete Scenario Case (2010), ftp://ftp.math.tu-berlin.de/pub/Preprints/combi/Report-018-2010.pdf
- 6.Cacchiani, V., Caprara, A., Galli, L., Kroon, L., Maroti, G., Toth, P.: Recoverable Robustness for Railway Rolling Stock Planning. In: 8th Workshop on Algorithmic Approaches for Transportation Modeling, Optimization, and Systems, ATMOS 2008 (2008), http://drops.dagstuhl.de/opus/volltexte/2008/1590/
- 7.Caprara, A., Galli, L., Kroon, L.G., Maróti, G., Toth, P.: Robust Train Routing and Online Re-scheduling. In: ATMOS (2010), http://drops.dagstuhl.de/opus/volltexte/2010/2747/
- 8.Cicerone, S., D’angelo, G., Di Stefano, G., Frigioni, D., Navarra, A., Schachtebeck, M., Schöbel, A.: Recoverable Robustness in Shunting and Timetabling. In: Ahuja, R.K., Möhring, R.H., Zaroliagis, C.D. (eds.) Robust and Online Large-Scale Optimization. LNCS, vol. 5868, pp. 28–60. Springer, Heidelberg (2009)CrossRefGoogle Scholar
- 9.Dhamdhere, K., Goyal, V., Ravi, R., Singh, M.: How to pay, come what may: Approximation algorithms for demand-robust covering problems. In: Proceedings of the Annual IEEE Symposium on Foundations of Computer Science (FOCS 2005), pp. 367–378. IEEE Computer Society, Los Alamitos (2005)CrossRefGoogle Scholar
- 12.Puhl, C.: Recoverable robust shortest path problems. Report 034-2008. Mathematics. Technical University, Berlin (2008)Google Scholar