Abstract
We present a new concept for optimization under uncertainty: recoverable robustness. A solution is recovery robust if it can be recovered by limited means in all likely scenarios. Specializing the general concept to linear programming we can show that recoverable robustness combines the flexibility of stochastic programming with the tractability and performances guarantee of the classical robust approach. We exemplify recoverable robustness in delay resistant, periodic and aperiodic timetabling problems, and train platforming.
This work was partially supported by the Future and Emerging Technologies Unit of EC, under contract no. FP6-021235-2 (FP6 IST/FET Open/Project ARRIVAL).
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References
Special issue on robust optimization. Mathematical Programming A 107(1-2) (2006)
Berger, A., Lorenz, U., Hoffmann, R., Stiller, S.: TOPSU-RDM: A simulation platform for railway delay management. In: Proceedings of SimuTools (2008)
Caprara, A., Galli, L., Stiller, S., Toth, P.: Recoverable-robust platforming by network buffering. Technical Report ARRIVAL-TR-0157, ARRIVAL Project (2008)
Cicerone, S., D’Angelo, G., Di Stefano, G., Frigioni, D., Navarra, A.: On the interaction between robust timetable planning and delay management. Technical Report ARRIVAL-TR-0116, ARRIVAL project (2007); Published at COCOA 2008
Cicerone, S., D’Angelo, G., Di Stefano, G., Frigioni, D., Navarra, A.: Robust algorithms and price of robustness in shunting problems. In: Proceedings of the 7th Workshop on Algorithmic Approaches for Transportation Modeling, Optimization, and Systems, ATOMS (2007)
Cicerone, S., D’Angelo, G., Di Stefano, G., Frigioni, D., Navarra, A.: Recoverable robust timetabling: Complexity results and algorithms. Technical report, ARRIVAL Project (2008)
Cicerone, S., D’Angelo, G., Di Stefano, G., Frigioni, D., Navarra, A., Schachtebeck, M., Schöbel, A.: Recoverable robustness in shunting and timetabling. In: Robust and Online Large-Scale Optimization, pp. 29–61. Springer, Heidelberg (2009)
Cicerone, S., Di Stefano, G., Schachtebeck, M., Schöbel, A.: Dynamic algorithms for recoverable robustness problems. In: Proceedings of the 8th Workshop on Algorithmic Approaches for Transportation Modeling, Optimization, and Systems (ATMOS 2008), Schloss Dagstuhl Seminar Proceedings (2008)
Cicerone, S., Di Stefano, G., Schachtebeck, M., Schöbel, A.: Multi-stage recoverable robustness problems. Technical report, ARRIVAL Project (2009)
Liebchen, C.: Periodic Timetable Optimization in Public Transport. dissertation.de – Verlag im Internet, Berlin (2006)
Liebchen, C., Lübbecke, M., Möhring, R.H., Stiller, S.: Recoverable robustness. Technical Report ARRIVAL-TR-0066, ARRIVAL-Project (2007)
Liebchen, C., Stiller, S.: Delay resistant timetabling. Preprint 024–2006, TU Berlin, Institut für Mathematik (2006)
Tyrrell Rockafellar, R.: Network ows and monotropic optimization. John Wiley & Sons, Inc., Chichester (1984)
Serafini, P., Ukovich, W.: A mathematical model for periodic scheduling problems. SIAM Journal on Discrete Mathematics 2(4), 550–581 (1989)
Soyster, A.L.: Convex programming with set-inclusive constraints and applications to inexact linear programming. Operations Research 21(4), 1154–1157 (1973)
Stiller, S.: Extending Concepts of Reliability. Network Creation Games, Real-time Scheduling, and Robust Optimization. TU Berlin, Dissertation, Berlin (2009)
Vromans, M., Dekker, R., Kroon, L.: Reliability and heterogeneity of railway services. European Journal of Operational Research 172, 647–665 (2006)
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Liebchen, C., Lübbecke, M., Möhring, R., Stiller, S. (2009). The Concept of Recoverable Robustness, Linear Programming Recovery, and Railway Applications. In: Ahuja, R.K., Möhring, R.H., Zaroliagis, C.D. (eds) Robust and Online Large-Scale Optimization. Lecture Notes in Computer Science, vol 5868. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-05465-5_1
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DOI: https://doi.org/10.1007/978-3-642-05465-5_1
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