A branch-and-cut algorithm for the undirected selective traveling salesman problem

Networks

Volumn 32, Issue 4, 1998, Pages 263-273

  Gendreau, Michel ^a   Laporte, Gilbert ^a   Semet, Frédéric ^a  

^a UNIVERSITÉ DE MONTRÉAL   (Canada)

Author keywords

Branch and cut algorithm; Orienteering; Selective traveling salesman problem

Indexed keywords

EID: 0039392730     PISSN: 00283045     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1097-0037(199812)32:4<263::AID-NET3>3.0.CO;2-Q     Document Type: Article

References (23)

1. E. Balas, The prize collecting traveling salesman problem. Networks 19 (1989) 621-636.
2. I-M. Chao, Algorithms and solutions to multi-level vehicle routing problems. Ph.D. Dissertation, University of Maryland, College Park, MD (1993).
3. I-M. Chao, B. L. Golden, and E. A. Wasil, A fast and effective heuristic for the orienteering problem. Eur. J. Oper. Res. 88 (1996) 475-489.
4. CPLEX Optimization Inc., using the CPLEX Callable Library and CPLEX Mixed Integer Library (1993).
5. H. Crowder, E. L. Johnson, and M. W. Padberg, Solving large-scale zero-one linear programming problems. Oper. Res. 31 (1983) 803-834.
6. M. Fischetti, J. J. Salazar, and P. Toth, A branch-and-cut algorithm for the symmetric generalized traveling salesman problem. Oper. Res. 45 (1997) 378-394.
7. M. Fischetti and P. Toth, An additive approach for the optimal solution of the prize-collecting traveling salesman problem. Vehicle Routing: Methods and Studies (B. L. Golden and A. A. Assad, Eds.). North-Holland, Amsterdam (1988) 319-343.
8. M. Gendreau, A. Hertz, and G. Laporte, New insertion and postoptimization procedures for the traveling salesman problem. Oper. Res. 40 (1992) 1086-1094.
9. M. Gendreau, G. Laporte, and F. Semet, The covering tour problem. Oper. Res. 45 (1997) 568-576.
10. B. L. Golden, L. Levy, and R. Vohra, The orienteering problem. Naval Res. Log. 34 (1987) 307-318.
11. B. L. Golden, Q. Wang, and L. Liu, A multi-faceted heuristic for the orienteering problem. Naval. Res. Log. 35 (1988) 359-366.
12. M. Göthe-Lundgren, K. Jörnsten, and P. Värbrand, On the nucleolus of the basic vehicle routing game. Research report LiTH-MAT-R-1992-26, Linköping University, Sweden (1992).
13. M. Göthe-Lundgren, F. Maffioli, and P. Värbrand, A Lagrangean decomposition approach for a prize collecting traveling salesman type problem. Research report LiTH-MAT-R-1995-10, Linköping University, Sweden (1994).
14. M. Hayes and J. M. Norman, Dynamic programming in orienteering: Route choice and siting of controls. J. Oper. Res. Soc. 35 (1984) 791-796.
15. C. P. Keller, Algorithms to solve the orienteering problem: A comparison. Eur. J. Oper. Res. 41 (1989) 224-231.
16. G. Laporte, Generalized subtour elimination constraints and connectivity constraints. J. Oper. Res. Soc. 37 (1986) 509-514.
17. G. Laporte and S. Martello, The selective traveling salesman problem. Discr. Appl. Math. 26 (1990) 193-207.
18. G. Laporte and F. Semet, An optimality cut for mixed integer linear programs. Working paper CRT-97-31, Centre for Research on Transportation, Montreal (1997).
19. A. C. Leifer and M. B. Rosenwein, Strong linear programming relaxations for the orienteering problem. Eur. J. Oper. Res. 73 (1994) 517-523.
20. M. W. Padberg and G. Rinaldi, Facet identification for the symmetric traveling salesman problem. Math. Program. 47 (1990) 219-257.
21. P. Ramesh and K. M. Brown, An efficient four-phase heuristic for the generalized orienteering problem. Comput. Oper. Res. 18 (1991) 151-165.
22. R. Ramesh, Y. Yong-Seok, and M. H. Karwan, An optimal algorithm for the orienteering tour problem. ORSA J. Comput. 4 (1992) 155-165.
23. T. Tsiligirides, Heuristic methods applied to orienteering. J. Oper. Res. Soc. 35 (1984) 797-809.