The Concept of Recoverable Robustness, Linear Programming Recovery, and Railway Applications

  • Christian Liebchen
  • Marco Lübbecke
  • Rolf Möhring
  • Sebastian Stiller
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5868)

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.

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References

  1. 1.
    Special issue on robust optimization. Mathematical Programming A 107(1-2) (2006)Google Scholar
  2. 2.
    Berger, A., Lorenz, U., Hoffmann, R., Stiller, S.: TOPSU-RDM: A simulation platform for railway delay management. In: Proceedings of SimuTools (2008)Google Scholar
  3. 3.
    Caprara, A., Galli, L., Stiller, S., Toth, P.: Recoverable-robust platforming by network buffering. Technical Report ARRIVAL-TR-0157, ARRIVAL Project (2008)Google Scholar
  4. 4.
    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 2008Google Scholar
  5. 5.
    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)Google Scholar
  6. 6.
    Cicerone, S., D’Angelo, G., Di Stefano, G., Frigioni, D., Navarra, A.: Recoverable robust timetabling: Complexity results and algorithms. Technical report, ARRIVAL Project (2008)Google Scholar
  7. 7.
    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)Google Scholar
  8. 8.
    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)Google Scholar
  9. 9.
    Cicerone, S., Di Stefano, G., Schachtebeck, M., Schöbel, A.: Multi-stage recoverable robustness problems. Technical report, ARRIVAL Project (2009)Google Scholar
  10. 10.
    Liebchen, C.: Periodic Timetable Optimization in Public Transport. dissertation.de – Verlag im Internet, Berlin (2006)Google Scholar
  11. 11.
    Liebchen, C., Lübbecke, M., Möhring, R.H., Stiller, S.: Recoverable robustness. Technical Report ARRIVAL-TR-0066, ARRIVAL-Project (2007)Google Scholar
  12. 12.
    Liebchen, C., Stiller, S.: Delay resistant timetabling. Preprint 024–2006, TU Berlin, Institut für Mathematik (2006)Google Scholar
  13. 13.
    Tyrrell Rockafellar, R.: Network ows and monotropic optimization. John Wiley & Sons, Inc., Chichester (1984)Google Scholar
  14. 14.
    Serafini, P., Ukovich, W.: A mathematical model for periodic scheduling problems. SIAM Journal on Discrete Mathematics 2(4), 550–581 (1989)MATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Soyster, A.L.: Convex programming with set-inclusive constraints and applications to inexact linear programming. Operations Research 21(4), 1154–1157 (1973)MATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    Stiller, S.: Extending Concepts of Reliability. Network Creation Games, Real-time Scheduling, and Robust Optimization. TU Berlin, Dissertation, Berlin (2009)Google Scholar
  17. 17.
    Vromans, M., Dekker, R., Kroon, L.: Reliability and heterogeneity of railway services. European Journal of Operational Research 172, 647–665 (2006)MATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Christian Liebchen
    • 1
  • Marco Lübbecke
    • 1
  • Rolf Möhring
    • 1
  • Sebastian Stiller
    • 1
  1. 1.Technische Universität BerlinBerlinGermany

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