Cost-based filtering for shorter path constraints

Constraints

Volumn 12, Issue 2, 2007, Pages 207-238

  Sellmann, Meinolf ^a   Gellermann, Thorsten ^b   Wright, Robert ^c  

^a Brown Univerity   (United States)

^b UNIVERSITY OF PADERBORN   (Germany)

^c AIR FORCE RESEARCH LABORATORY   (United States)

Author keywords

Constrained shortest paths; Global constraints; Optimization constraints; Problem reduction; Relaxed consistency

Indexed keywords

COSTS; DATA STRUCTURES; GLOBAL OPTIMIZATION; MATHEMATICAL MODELS; MOTION PLANNING; PROBLEM SOLVING;

CONSTRAINED SHORTEST PATHS; GLOBAL CONSTRAINTS; OPTIMIZATION CONSTRAINTS; PROBLEM REDUCTION; RELAXED CONSISTENCY;

CONSTRAINT THEORY;

EID: 34248572417     PISSN: 13837133     EISSN: 15729354     Source Type: Journal    
DOI: 10.1007/s10601-006-9006-4     Document Type: Article

References (40)

1. Ahuja, R.K., Magnati, T.L., & Orlin, J.B. (1993). Network flows. Prentice-Hall.
2. Aneja, Y., Aggarwal, V., & Nair, K. (1983). Shortest chain subject to side conditions. Netw. 13, 295-302.
3. Apt, K.R. (1999). The rough guide to constraint propagation. In Principles and Practice of Constraint Programming (CP) LNCS1713, pp 1-23. Springer.
4. Barahona, F., & Anbil, R. (2000). The volume algorithm: Producing primal solutions with a subgradient algorithm. Math. Program. 87, 385-399.
5. Beasley, J., & Christofides, N. (1989). An algorithm for the resource constrained shortest path problem. Netw. 19, 379-394.
6. Borndoerfer, R., & Loebel, A. (2001). Scheduling Duties by Adaptive Column Generation. Technical Report, Konrad-Zuse-Zentrum fuer Informationstechink Berlin ZIB-01-02.
7. Cormen, T.H., Leiserson, C.E., & Rivest, R.L. (1993). Introduction to Algorithms. MIT.
8. Crowder, H. (1976). Computational improvements for subgradient optimization. Symp. Math. 19, 357-372.
9. Desrosiers, J., Dumas, Y., Solomon, M., & Soumis, F. (1995). Time constrained routing and scheduling. In Handbook in Operations Research and Management Science 8: Network Routing, 8, 35-139. Amsterdam, The Netherlands: North Holland.
10. Dumitrescu, I., & Boland, N. (2000). The weight-constrained shortest path problem: preprocessing, scaling and dynamic programming algorithms with numerical comparisons. In International Symposium on Mathematical Programming (ISMP). Atlanta, Georgia: Georgia Institute of Technology.
11. Fahle, T., Junker, U., Karisch, S.E., Kohl, N., Sellmann, M., & Vaaben, B. (2002). Constraint programming based column generation for crew assignment. J. Heuristics. 8(1), 59-81.
12. Fahle, T., & Sellmann, M. (2002). Cost-based filtering for the constrained knapsack problem. Ann. Oper. Res. 115, 73-93.
13. Focacci, F., Lodi, A., & Milano, M. (1999). Cost-based domain filtering. In Principles and Practice of Constraint Programming (CP) LNCS 1713, pp 189-203. Springer.
14. Focacci, F., Lodi, A., & Milano, M. (2000). Cutting Planes in Constraint Programming: An Hybrid Approach. Technical Report: tr-001-2000, Paderborn Center for Parallel Computing, University of Paderborn, Germany. (CP-AI-OR'OO, pp 45-51.)
15. Fortune, S., Hopcroft, J., & Wyllie, J. (1980). The directed subgraph homeomorphism problem. Theor. Comp. Sci. 10(2), 111-121.
16. Frangioni, A. (1996). 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)
17. Frangioni, A. (1997). Dual Ascent Methods and Multicommodity Plow Problems. Doctoral Thesis TD-97-05, Dipartimento di Informatica, Universita di Pisa.
18. Fredmann, M.L., & Tarjan, R.E. (1987). Fibonacci heaps and their uses in improved network optimization algorithms. J. ACM34, 596-615.
19. Garey, M.R., & Johnson, D.S. (1979). Computers and Intractability, A Guide to the Theory of NP- Completeness. Freeman.
20. Gellermann, T., Sellmann, M., & Wright, R.W. (2005). Shorter path constraints for the resource constrained shortest path problem. In Second International Conference on the Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems (CP-AI-OR) LNCS3524, pp 201-216. Springer.
21. Handler, G., Zang, I. (1980). A dual algorithm for the restricted shortest path problem. Netw. 10, 293-310.
22. Jahn, O., Moehring, R., & Schulz, A. (1999). Optimal Routing of Traffic Flows with Length Restrictions in Networks with Congestion. Technical Report, TU Berlin, (pp 658-1999)
23. Joksch, H. (1966). The shortest route problem with constraints. J. Math. Anal. Appl. 14, 191-197.
24. Junker, U., Karisch, S.E., Kohl, N., Vaaben, B., Fahle, T., & Sellmann, M. (1999). A framework for constraint programming based column generation. In Principles and Practice of Constraint Programming (CP), LNCS1713, pp 261-274. Springer.
25. Kelley, J.E. (1960). The cutting plane method for solving convex programs. J. SIAM. 8, 703-712.
26. Kumar, V. (1992). Algorithms for constraints satisfaction problems: a survey. AI Mag. 13, 32-44.(AAAI)
27. Luebbecke, M., & Zimmermann, U. (2000). Computer aided scheduling of switching engines. CASPT. Springer.
28. Mehlhorn, K., & Ziegelmann, M. (2000). Resource constrained shortest paths. In Proc. 8th European Symposium on Algorithms (ESA) LNCS 1879, pp 326-337. Springer.
29. Orda, A. (1998). Routing with end to end QoS guarantees in broadband networks. In Conference on Computer Communications (Infocom), pp 27-34. IEEE.
30. Ottosson, G., & Thorsteinsson, E.S. (2000). Linear Relaxation and Reduced-cost Based Propagation of Continuous Variable Subscripts. Technical Report, Paderborn Center for Parallel Computing. (tr-001-2000, CP-AI-OR'00, pp 129-138)
31. Pettie, S., & Ramachandran, V. (2002). Computing undirected shortest paths using comparisons and additions. In ACM-SIAM Symposium on Discrete Algorithms, pp 267-276. Society for Industrial and Applied Mathematics. (January).
32. Régin, J.C. (1999). Arc consistency for global cardinality constraints with costs. In Principles and Practice of Constraint Programming (CP) LNCS 1.713, pp 390-404. Springer.
33. Sellmann, M. (2002a). An arc-consistency algorithm for the weighted all different constraint. In Principles and Practice of Constraint Programming (CP) LNCS 2470, pp 744-749. Springer.
34. Sellmann, M. (2003). Cost-based filtering for shorter path constraints. In Principles and Practice of Constraint Programming (CP) LNCS, 2833, pp 679-693. Springer.
35. Sellmann, M. (2004). Theoretical foundations of CP-based Lagrangian relaxation. In Principles and Practice of Constraint Programming (CP) LNCS 3258, pp 634-647. Springer.
36. Sellmann, M., & Fahle, T. (2001). Coupling variable fixing algorithms for the automatic recording problem. In Annual European Symposium on Algorithms (ESA) LNCS 2161, pp 134-145. Springer.
37. Sellmann, M., & Fahle, T. (2003). Constraint programming based lagrangian relaxation for the automatic recording problem. Ann. Oper. Res. 118, 17-33.
38. Thorup, M. (1997). Undirected single source shortest paths in linear time. In Annual Symposium on Foundations of Computer Science (FOCS), pp 12-21. IEEE Computer Society.
39. Xue, G. (2000). Primal-dual algorithms for computing weight-constrained shortest paths and weight-constrained minimum spanning trees. In International Performance, Computing, and Communications Conference (IPCCC), pp 271-277. IEEE.
40. Yunes, T.H., Moura, A.V., & Souza, C.C. (2000). A hybrid approach for solving large crew scheduling problems. In International Workshop on Practical Aspects of Declarative Languages (PADL) LNCS 1753, pp 293-307. Springer.