Polyhedral results and exact algorithms for the asymmetric travelling salesman problem with replenishment arcs

Discrete Applied Mathematics

Volumn 155, Issue 16, 2007, Pages 2093-2110

  Mak, Vicky ^a   Boland, Natashia ^b  

^a DEAKIN UNIVERSITY   (Australia)

^b UNIVERSITY OF MELBOURNE   (Australia)

Author keywords

Branch and bound method; Combinatorial optimisation; Lagrangean relaxation; Polyhedral analysis; Travelling salesman

Indexed keywords

COMBINATORIAL OPTIMIZATION; LAGRANGE MULTIPLIERS; LINEAR PROGRAMMING; POLYNOMIAL APPROXIMATION; PROBLEM SOLVING;

BRANCH-AND-BOUND METHOD; LAGRANGEAN RELAXATION; POLYHEDRAL ANALYSIS; TRAVELLING SALESMAN;

ALGORITHMS;

EID: 34547807579     PISSN: 0166218X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.dam.2007.05.014     Document Type: Article

References (40)

1. Ascheuer N., Fischetti M., and Grötschel M. A polyhedral study of the asymmetric travelling salesman problem with time windows. Networks 36 (2000) 69-79
2. Ascheuer N., Fischetti M., and Grötschel M. Solving the asymmetric travelling salesman problem with time windows by branch-and-cut. Math. programming 90 (2001) 475-506
3. Balas E., and Christofides N. A restricted Lagrangean approach to the travelling salesman problem. Math. Programming 21 (1981) 19-46
4. Bard J.F., Kontoravdis G., and Gang Yu. A branch-and-cut procedure for the vehicle routing problem with time windows. Transportation Sci. 36 (2002) 250-269
5. Barnhart C., Boland N.L., Clarke L.W., Johnson E.L., Nemhauser G.L., and Shenoi R.G. Flight string models for aircraft fleeting and routing. Transportation Sci. 32 (1998) 208-220
6. Boland N.L., Clarke L.W., and Nemhauser G.L. The asymmetric traveling salesman problem with replenishment arcs. European J. Oper. Res. 123 (2000) 408-427
7. M. Bourgeois, G. Laporte, F. Semet, Heuristics for the black and white travelling salesman problem. Publication CRT-99-33, Centre for Research on Transportation, Montreal, 1999.
8. Butt S.E., and Ryan D.M. An optimal solution procedure for the multiple tour maximum collection problem using column generation. Comput. Oper. Res. 26 (1999) 427-441
9. Carpaneto G., Dell'amico M., and Toth P. Exact solution of large-scale asymmetric travelling salesman problems. ACM Trans. Math. Software 21 4 (1995) 394-409
10. Carpaneto G., and Toth P. Some new branching and bounding criteria for the asymmetric travelling salesman problem. Management Sci. 26 (1980) 736-743
11. Clarke L.W., Johnson E.L., Nemhauser G.L., and Zhu Z. The aircraft rotation problem. Ann. Oper. Res.: Math. Indust. Syst. II 69 (1997) 33-46
12. ILOG S.A. 2004. ILOG CPLEX 9.0.
13. Dantzig G., Fulkerson R., and Johnson S. Solution of a large scale travelling salesman problem. Oper. Res. 2 (1954) 393-410
14. Desrochers M., Desrosiers J., and Solomon M.M. A new optimization algorithm for the vehicle routing problem with time windows. Oper. Res. 40 (1992) 342-354
15. Desrochers M., and Laporte G. Improvements and extensions to the Miller-Tucker-Zemlin subtour elimination constraints. Oper. Res. Lett. 10 (1991) 27-36
16. Desrosiers J., Dumas Y., Solomon M.M., and Soumis F. Time constrained routing and scheduling. In: Ball M.O., Magnanti T.L., Monma C.L., and Nemhauser G.L. (Eds). Handbooks in Operations Research and Management Science: Network Routing vol. 8 (1995), North-Holland, Amsterdam 35-139
17. Escudero L.F., Guignard M., and Malik K. A Lagrangian relax and cut approach for the sequential ordering with precedence constraints. Ann. Oper. Res. 50 (1994) 219-237
18. Fischetti M., and Toth P. An additive bounding procedure for the asymmetric traveling salesman problem. Math. Programming 53 (1992) 173-197
19. Fischetti M., and Toth P. A polyhedral approach to the asymmetric traveling salesman problem. Management Sci. 43 (1992) 1520-1536
20. Fisher M.L. An application oriented guide to Lagrangean relaxation. Interfaces 15 (1985) 10-21
21. Fisher M.L. Optimal solution of vehicle routing problems using minimum k-trees. Oper. Res. 42 4 (1994) 626-642
22. Fukasawa R., Lysgaard J., Poggi de Aragão M., Reis M., Uchoa E., and Werneck R.F. Robust branch-and-cut-and-price for the capacitated vehicle routing problem. In: Bienstock D., and Nemhauser G. (Eds). Integer Programming and Combinatorial Optimization-IPCO 2004, Lecture Notes in Computer Science vol. 3064 (2004), Springer, Berlin, Heidelberg 1-15
23. Garfinkel R.S. On partitioning the feasible set in a branch-and-bound algorithm for the asymmetric travelling salesman problem. Oper. Res. 21 (1973) 340-342
24. G. Ghiani, G. Laporte, F. Semet, The black and white tavelling salesman problem, Publication CRT-99-47, Centre for Research on Transportation, Montreal, 1999.
25. G. Gutin, A. Punnen (Eds.), The Travelling Salesman Problems and its Variations, Kluwer Academic Publishers, Dordrecht, 2002.
26. 〈http://www.iwr.uni-heidelberg.de/iwr/comopt/soft/TSPLIB95/TSPLIB.html〉.
27. Kohl N., Desrosiers J., Madsen O.B.G., Solomon M.M., and Soumis F. 2-path cuts for the vehicle routing problem with time windows. Transportation Sci. 33 (1999) 395-406
28. Kohl N., and Madsen O.B.G. An optimization algorithm for the vehicle routing problem with time windows based on Lagrangean relaxation. Oper. Res. 45 (1997) 101-116
29. Larsson R., Patriksson M., and Stromberg A. Conditional subgradient optimization-theory and applications. European J. Oper. Res. 88 (1996) 382-403
30. V. Mak, On the asymmetric travelling salesman problem with replenishment arcs, Ph.D. Thesis, Department of Math. Statist., University of Melbourne, Australia, 2001.
31. Mak V., and Boland N. Heuristic approaches to asymmetric travelling salesman problem with replenishment arcs. Internat. Trans. Oper. Res. 7 (2000) 431-447
32. Miller C.E., Tucker A.W., and Zemlin R.A. Integer programming formulation of travelling salesman problems. J. Assoc. Comput. Mach. 7 (1960) 326-329
33. Nemhauser G.L., and Wolsey L.A. Integer and Combinatorial Optimization (1988), Wiley, New York
34. Pekny J.F., and Miller D.L. A parallel branch and bound algorithm for solving large asymmetric travelling salesman problems. Math. Programming 55 (1992) 17-33
35. Polyak B.T. Minimization of unsmooth functionals. USSR Comput. Math. Math. Phys. 9 (1969) 14-29
36. Smith T.H.C. A LIFO implicit enumeration algorithm for the asymmetric travelling salesman problem using a one-arborescence relaxation. Math. Programming Stud. 12 (1980) 108-114
37. Smith T.H.C., Srinivasan V., and Thompson G.L. Computational performance of three subtour elimination algorithms for solving asymmetric travelling salesman problems. Ann. Discrete Math. 1 (1977) 495-506
38. Vigo D. A heuristic algorithm for the asymmetric capacitated vehicle routing problem. European J. Oper. Res. 89 (1996) 108-126
39. Wolsey L.A. Integer Programming (1998), Wiley, New York
40. Z. Zhu, The aircraft rotation problem, Ph.D. Thesis, Georgia Institute of Technology, Atlanta, 1994.