Advertisement

Abstract

Recently, new cost-based filtering algorithms for shorter-path constraints have been developed. However, so far only the theoretical properties of shorter-path constraint filtering have been studied. We provide the first extensive experimental evaluation of the new algorithms in the context of the resource constrained shortest path problem. We show how reasoning about path-substructures in combination with CP-based Lagrangian relaxation can help to improve significantly over previously developed problem-tailored filtering algorithms and investigate the impact of required-edge detection, undirected versus directed filtering, and the choice of the algorithm optimizing the Lagrangian dual.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Aneja, Y., Aggarwal, V., Nair, K.: Shortest chain subject to side conditions. Networks 13, 295–302 (1983)CrossRefMathSciNetGoogle Scholar
  2. 2.
    Applegate, D., Bixby, R., Chvátal, V., Cook, W.: On the solution of Traveling Salesman Problems. Doc. Math. J. DMV, Extra Volume ICM III, 645–656 (1998)Google Scholar
  3. 3.
    Barahona, F., Anbil, R.: The Volume Algorithm: producing primal solutions with a subgradient algorithm. Mathematical Programming 87, 385–399 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Beasley, J., Christofides, N.: An Algorithm for the Resource Constrained Shortest Path Problem. Networks 19, 379–394 (1989)zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Crowder, H.: Computational improvements for subgradient optimization. Symposia Mathematica XIX, 357–372 (1976)Google Scholar
  6. 6.
    Desrosiers, J., Dumas, Y., Solomon, M., Soumis, F.: Time Constrained Routing and Scheduling. In: Handbook in Operations Research and Management Science 8: Network Routing, vol. 8, pp. 35–139. North-Holland, Amsterdam (1995)Google Scholar
  7. 7.
    Dumitrescu, I., Boland, N.: The weight-constrained shortest path problem: preprocessing, scaling and dynamic programming algorithms with numerical comparisons. In: International Symposium on Mathematical Programming, ISMP (2000)Google Scholar
  8. 8.
    Fahle, T., Junker, U., Karisch, S.E., Kohl, N., Sellmann, M., Vaaben, B.: Constraint programming based column generation for crew assignment. Journal of Heuristics 8(1), 59–81 (2002)zbMATHCrossRefGoogle Scholar
  9. 9.
    Focacci, F., Lodi, A., Milano, M.: Cost-Based Domain Filtering. In: Jaffar, J. (ed.) CP 1999. LNCS, vol. 1713, pp. 189–203. Springer, Heidelberg (1999)Google Scholar
  10. 10.
    Frangioni, A.: A Bundle type Dual-ascent Approach to Linear Multi-Commodity Min Cost Flow Problems. Technical Report, Dipartimento di Informatica, Universita di Pisa, TR-96-01 (1996)Google Scholar
  11. 11.
    Frangioni, A.: Dual Ascent Methods and Multicommodity Flow Problems. Doctoral Thesis, Dipartimento di Informatica, Universita di Pisa, TD-97-05 (1997)Google Scholar
  12. 12.
    Handler, G., Zang, I.: A Dual Algorithm for the Restricted Shortest Path Problem. Networks 10, 293–310 (1980)CrossRefMathSciNetGoogle Scholar
  13. 13.
    Kelley, J.E.: The Cutting Plane Method for Solving Convex Programs. Journal of the SIAM 8, 703–712 (1960)MathSciNetGoogle Scholar
  14. 14.
    Makri, A., Klabjan, D.: A New Pricing Scheme for Airline Crew Scheduling. INFORMS Journal on Computing 16, 56–67 (2004)CrossRefGoogle Scholar
  15. 15.
    Mehlhorn, K., Ziegelmann, M.: Resource Constrained Shortest Paths. In: Paterson, M. (ed.) ESA 2000. LNCS, vol. 1879, pp. 326–337. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  16. 16.
    Sellmann, M.: Theoretical Foundations of CP-Based Lagrangian Relaxation. In: Wallace, M. (ed.) CP 2004. LNCS, vol. 3258, pp. 634–647. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  17. 17.
    Sellmann, M.: Cost-Based Filtering for Shorter Path Constraints. In: Rossi, F. (ed.) CP 2003. LNCS, vol. 2833, pp. 679–693. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  18. 18.
    Sellmann, M., Fahle, T.: Coupling Variable Fixing Algorithms for the Automatic Recording Problem. In: Meyer auf der Heide, F. (ed.) ESA 2001. LNCS, vol. 2161, pp. 134–145. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  19. 19.
    Sellmann, M., Fahle, T.: Constraint Programming Based Lagrangian Relaxation for the Automatic Recording Problem. Annals of Operations Research 118, 17–33 (2003)zbMATHCrossRefMathSciNetGoogle Scholar
  20. 20.
    Toth, P., Vigo, D.: The Vehicle Routing Problem. In: Monographs on Discrete Mathematics and Applications. SIAM, Philadelphia (2001)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Thorsten Gellermann
    • 1
  • Meinolf Sellmann
    • 2
  • Robert Wright
    • 3
  1. 1.Computer ScienceUniversity of PaderbornPaderborn
  2. 2.Computer ScienceBrown UniversityProvidenceUSA
  3. 3.Air Force Research Lab, Inform. DirectorateRomeUSA

Personalised recommendations