A branch and cut approach to the cardinality constrained circuit problem

Mathematical Programming, Series B

Volumn 91, Issue 2, 2002, Pages 307-348

  Bauer, P ^a   Linderoth, J T ^b   Savelsbergh, M W P ^c  

^a SIEMENS AG   (Germany)

^b Axioma Inc   (United States)

^c Georgia Institute of Technology   (United States)

Author keywords

Branch and cut; Cardinality constrained circuit problem; Circuit polytope

Indexed keywords

COMPUTATIONAL COMPLEXITY; CONSTRAINT THEORY; GRAPH THEORY; NUMERICAL METHODS;

BRANCH AND CUT; CARDINALITY CONSTRAINED CIRCUIT PROBLEM; CIRCUIT POLYTOPE;

PROBLEM SOLVING;

EID: 29044436230     PISSN: 00255610     EISSN: None     Source Type: Journal    
DOI: 10.1007/s101070100209     Document Type: Article

References (39)

1. Applegate, D., Bixby, R., Cook, W., Chvátal, V. (1996): Personal communication
2. Augerat, Ph. (1995): Polyhedral study of the capacitated vehicle routing. PhD thesis, Universite Joseph Fourrier, Grenoble
3. Balas, E. (1989): The prize collecting traveling salesman problem. Networks 19, 621-636
4. Balas, E., Ceria, S., Cornuejols, G. (1996): Mixed 0-1 programming by lift-and-project in a branch-and-cut framework. Management Science 42, 1229-1246
5. Bauer, P. (1994): A Polyhedral Approach to the Weighted Girth Problem. PhD thesis, Universität zu Köln
6. Bauer, P. (1997): The circuit polytope: facets. Mathematics of Operations Research 22, 110-145
7. Bauer, P., Linderoth, J.T., Savelsbcrgh, M.W.P. (1998): A branch and cut approach to the cardinality constrained circuit problem. Technical Report TLI-98-04, The Logistics Institute, Georgia Institute of Technology, 1998. Available from http://tli.isye.gatech.edu/research/papers/files/TLI9804.pdf
8. Bienstock, D., Goemans, M., Simchi-Levi, D., Williamson, D. (1993): A note on the prize collecting traveling salesman problem. Mathematical Programming 59, 413-120
9. Bixby, A., Coullard, C., Simchi-Levi, D. (1996): The capacitated prize-collecting traveling salesman problem. Technical Report TR 96-10, Northwestern University
10. Carr, R. (1997): Separating clique trees and bipartition inequalities having a fixed number of handles and teeth in polynomial time. Mathematics of Operations Research 22, 257-265
11. CPLEX Optimization, Inc. Using the CPLEX Callable Library, 1995
12. Desrosiers, J., Soumis, F., Desrochers, M. (1984): Routing with time windows by column generation. Networks 14, 545-565
13. Edmonds, J., Karp, R.M. (1972): Theoretical improvements in algorithmic efficiency of network flow problems. Journal of ACM 19, 248-264
14. Fischetti, M., Gonzalez, J.J.S., Toth, P. (1998): Solving the orienteering problem through branch-and-cut. INFORMS Journal on Computing 10, 133-148
15. Fleischer, L., Tardos, É. (1999): Separating maximally violated combs in planar graphs. Mathematics of Operations Research 24, 130-148
16. Garey, M.R., Johnson, D.S. (1979): Computers and intractability: a guide to the theory of NP-completeness. W.H. Freeman and Company, New York
17. Golden, B.L., Wang, Q., Liu, L. (1988): A multifacted heuristic for the orienteering problem. Naval Research Logistics 35, 359-366
18. Goldschmidt, O., Hochbaum, D. (1994): A polynomial algorithm for the k-cut problem for fixed k. Mathematics of Operations Research 19, 24-37
19. Grötschel, M., Pulleyblank, W.R. (1986): Clique tree inequalities and the symmetric travelling salesman problem. Mathematics of Operations Research 11, 537-569
20. Gusfield, D. (1990): Very simple methods for all pairs network flow analysis. SIAM Journal of Computing 19, 143-155
21. Hartmann, M., Ozluk, O. (1998): Facets of the p-cycle polytope. Technical Report UNC/OR TR98-1, Department of Operations Research, University of North Carolina
22. Hu, T.C. (1974): Optimum communication spanning trees. SIAM Journal on Computing 3, 188-195
23. Hyafil, L., Rivest, R.L. (1973): Graph partitioning and constructing optimal decision trees and polynomial complete problems. Technical Report 33, IRIA-Laboria, Rocquencourt, France
24. Johnson, D.S., Lenstra, J.K., Rinnooy Kan, A.H.G. (1978): The complexity of the network design problem. Networks 8, 279-285
25. Jünger, M., Reinelt, G., Thienel, S. (1994): Provably good solutions for the traveling salesman problem. Zeitschrift für Operations Research 40, 183-217
26. Leifer, A.C., Rosenwein, M.B. (1994): Strong linear programming relaxations for the orienteering problem. European Journal of Operational Research 73, 517-523
27. Nemhauser, G.L., Savelsbergh, M.W.P., Sigismondi, G.C. (1994): MINTO, a Mixed INTeger Optimizer. Operations Research Letters 15, 47-58
28. Nguyen, V.-H., Maurras, J.-F. (2000): The k-cycle polytope: I. Lifting theorems and lifting algorithms. Technical report 358, Laboratoire d'Informatique de Marseille, Marseille, France
29. Nguyen, V.-H., Maurras, J.-F. (2000): The k-cycle polytope: II. Facets. Technical report 359, Laboratoire d'Informatique de Marseille, Marseille, France
30. Padberg, M.W., Rao, M.R. (1982): Odd minimum cut sets and b-matchings. Mathematics of Operations Research 7, 67-80
31. Padberg, M.W., Rinaldi, G. (1990): Facet identification for the symmetric traveling salesman problem. Mathematical Programming 47, 219-257
32. Pillai, R. (1992): The Traveling Salesman Subset-Tour Problem with one Additional Constraint (TSSP+1). PhD thesis. University of Tennessee, Knoxville
33. Prim, R.C. (1957): Shortest connection networks and some generalizations. Bell System Technological Journal 36, 1389-1401
34. Ramesh, R., Yoon, Y.S., Karwan, M.H. (1992): An optimal algorithm for the orienteering tour problem. ORSA Journal on Computing 4, 155-165
35. Reinelt, G. (1991): TSPLIB - a traveling salesman problem library. ORSA Journal on Computing 3, 376-384
36. Saran, H., Vazirani, V.V. (1995): Finding k cuts within twice the optimal. SIAM Journal of Computing 24, 101-108
37. Savelsbergh, M.W.P., Uma, R.N., Wein, J. (1998): An experimental study of LP-based approximation algorithms for scheduling problems. In: Proceedings of the 9th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 453-461
38. Seymour, P.D. (1979): Sums of circuits. In: Bondy, Murty, eds., Graph Theory and Related Topics, pp. 341-355, Academic Press, New York
39. Wang, Y. (1995): Fleet assignment, Eulerian subtours and extended Steiner trees. PhD thesis, Georgia Institute of Technology