Incorporating facet-inducing inequalities into graphical-construct-based Lagrangian relaxation methodologies

Operations Research Letters

Volumn 18, Issue 4, 1996, Pages 177-184

  Ali, Agha Iqbal ^a   Shmerling, Shirley ^a  

^a UNIVERSITY OF MASSACHUSETTS   (United States)

Author keywords

Facet inducing inequalities; Hamiltonian paths; Integer programming; Lagrangian relaxation; Routing problems; Spanning trees; Travelling salesman problem

Indexed keywords

EID: 0042625999     PISSN: 01676377     EISSN: None     Source Type: Journal    
DOI: 10.1016/0167-6377(95)00038-0     Document Type: Article

References (32)

1. A.I. Ali and C.H. Huang, "Graphical-structure-based models for routing problems", Internat. J. Systems Sci. 19, 1667-1686 (1988).
2. A.I. Ali and J.L. Kennington, "The asymmetric m-travelling salesmen problem: a duality based branch-and-bound algorithm", Discrete Appl. Math. 13, 259-276 (1986).
3. A.I. Ali and S. Shmerling, "A graphical-construct-based algorithm for optimal solutions to a Lagrangian dual of the Hamiltonian path problem", Working paper, SOM, University of Massachusetts at Amtierst, Amherst, MA, 1993.
4. E. Balas and P. Toth, "Branch and bound methods", in: Lawler et al. (eds.), The Travelling Salesman Problem, pp. 371-378.
5. S.C. Boyd and W.R. Pulleyblank, "Optimizing over the subtour polytope of the travelling salesman problem", Math. Programming 49, 163-187 (1991).
6. H. Crowder and M.W. Padberg, "Solving large-scale travelling salesman problem to optimality", Manage. Sci 26, 495-509 (1980).
7. G.B. Dantzig, D.R. Fulkerson and S.M. Johnson, "Solutions of a large-scale travelling salesman problem", Oper. Res. 2, 393-410 (1954).
8. G.B. Dantzig, D.R. Fulkerson and S.M. Johnson, On a linear-programming, combinatorial approach to the travelling salesman problem", Oper. Res. 7, 58-66 (1959).
9. B. Fleischmann, "A new class of cutting planes for the symmetric travelling salesman problem", Math. Programming 40, 225-246 (1988).
10. B. Gavish and K. Srikanth, "An optimal solution method for large-scale multiple travelling salesmen problems", Oper. Res. 34, 698-717 (1986).
11. M. Grötschel, "On the symmetric travelling salesman problem: solution of a 120-city problem", Math. Programming Study 12, 61-77 (1980).
12. M. Grötschel and O. Holland, "A cutting plane algorithm for minimum perfect 2-matchings", Computing 39, 327-344 (1987).
13. M. Grötschel and O. Holland, "Solutions of large-scale travelling salesman problems", Math. Programming 51, 141-202 (1991).
14. M. Grötschel and M.W. Padberg, "On the symmetric travelling salesman problem I: inequalities", Math. Programming 16, 265-280 (1979).
15. M. Grötschel and M.W. Padberg, "Polyhedral theory, in: Lawler et al. (eds.), The Travelling Salesman Problem, pp. 251-302 (1985).
16. M. Grötschel and W.R. Pulleyblank, "Clique tree inequalities and the symmetric travelling salesman problem", Math. Oper. Res. 11, 537-569 (1986).
17. K. Helbig Hansen and J. Krarup, "Improvements of the Held-Karp algorithm for the symmetric travelling salesman problem", Math. Programming 7, 87-96 (1974).
18. M. Held and R.M. Karp, "The travelling salesman problem and minimum spanning trees", Oper. Res. 18, 1138-1162 (1970).
19. M. Held and R.M. Karp, "The travelling salesman problem and minimum spanning trees: part II", Math. Programming 1, 6-25 (1971).
20. R.L. Karg and G.L. Thompson, "A heuristic approach to solving travelling salesman problems", Manage. Sci. 10, 225-247 (1964).
21. K. Malik and M.L. Fisher, "A dual Ascent algorithm for the 1-tree relaxation of the symmetric travelling salesman problem", Oper. Res. Lett. 9, 1-7 (1990).
22. D. Nadef and G. Rinaldi, "The symmetric travelling salesman polytope and its graphical relaxation: composition of valid inequalities", Math. Programming 51, 359-400 (1991).
23. G.L. Nemhauser and L.A. Wolsey, Integer and Combinatorial Optimization, Wiley, Chichester, UK, 1988.
24. M.W. Padberg and M. Grötschel, "Polyhedral computations", in: Lawler et al. (eds.), The Travelling Salesman Problem, pp. 307-360 (1995).
25. M.W. Padberg and S. Hong, "On the symmetric travelling salesman problem: a computational study", Math. Programming Study 12, 78-107 (1980).
26. M.W. Padberg and M.R. Rao, "Odd minimum cut-sets and b-matchings", Math. Oper. Res. 7, 67-80 (1982).
27. M.W. Padberg and G. Rinaldi, "Optimization of a 532-city travelling salesman problem by branch and cut", Oper. Res. Lett. 6, 1-8 (1987).
28. M.W. Padberg and G. Rinaldi, "Facet identification for the travelling salesman polytope", Math. Programming 47, 219-257 (1990).
29. M.W. Padberg and G. Rinaldi, "A branch-and-cut algorithm for the resolution of large-scale travelling salesman problems", SIAM Rev. 33, 60-100 (1991).
30. G. Reinelt, "TSPLIB - a travelling salesman problem library", ORSA J. Comput. 3, 376-384 (1991).
31. T.H.C. Smith, T.W.S. Meyer and G.L. Thompson, "Lower bounds for the STSP for Lagrangian relaxation", Discrete Appl. Math. 26, 209-217 (1990).
32. T. Volgenant and R. Jonker, "A branch and bound algorithm for the symmetric travelling salesman problem based on the 1-tree relaxation", European J. Oper. Res. 9, 83-89 (1982).