Parallel branch and cut for capacitated vehicle routing

Parallel Computing

Volumn 29, Issue 5 SPEC., 2003, Pages 607-629

  Ralphs, T K ^a  

^a Lehigh University   (United States)

Author keywords

Branch and cut; Combinatorial optimization; Integer programming; Parallel branch and bound

Indexed keywords

ALGORITHMS; INTEGER PROGRAMMING; INTELLIGENT VEHICLE HIGHWAY SYSTEMS; OPTIMIZATION; PARALLEL PROCESSING SYSTEMS; PROBLEM SOLVING;

VEHICLE ROUTING;

COMBINATORIAL MATHEMATICS;

EID: 0037541117     PISSN: 01678191     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-8191(03)00045-0     Document Type: Article

References (57)

1. Agarwal Y., Mathur K., Salkin H.M. Set partitioning approach to vehicle routing. Networks. 7:1989;731.
2. D. Applegate, R. Bixby, V. Chvátal, W. Cook, On the solution of traveling salesman problems, Documenta Mathematica Journal der Deutschen Mathematiker-Vereinigung, International Congress of Mathematicians (1998) 645.
3. D. Applegate, R. Bixby, V. Chvátal, W. Cook, CONCORDE TSP Solver, Available from www.keck.caam.rice.edu/concorde.html.
4. J.R. Araque, L. Hall, T. Magnanti, Capacitated trees, capacitated routing and associated polyhedra, Discussion Paper 9061, CORE, Louvain La Nueve, 1990.
5. Araque J.R., Kudva G., Morin T.L., Pekny J.F. A branch-and-cut algorithm for vehicle routing problems. Annals of Operations Research. 50:1994;37.
6. Augerat P., Belenguer J.M., Benavent E., Corberán A., Naddef D. Separating capacity constraints in the CVRP using tabu search. European Journal of Operations Research. 106:1998;546.
7. P. Augerat, J.M. Belenguer, E. Benavent, A. Corberán, D. Naddef, G. Rinaldi, Computational results with a branch and cut code for the capacitated vehicle routing problem, Research Report 949-M, Universite Joseph Fourier, Grenoble, France.
8. Balas E., Ceria S., Cornuéjols G. Mixed 0-1 programming by lift-and-project in a branch-and-cut framework. Management Science. 42:1996;9.
9. Barnhart C., Johnson E.L., Nemhauser G.L., Savelsbergh M.W.P., Vance P.H. Branch-and-price: column generation for huge integer programs. Operations Research. 46:1998;316.
10. Benchouche M., Cung V.-D., Dowaji S., Le Cun B., Mautor T., Roucairol C. Building a parallel branch and bound library, in solving combinatorial optimization problems in parallel. Lecture Notes in Computer Science. 1054:1996;221 Springer, Berlin.
11. R. Bixby, W. Cook, A. Cox, E.K. Lee, Parallel mixed integer programming, Rice University Center for Research on Parallel Computation Research Monograph CRPC-TR95554, 1995.
12. U. Blasum, W. Hochstättler, Application of the branch and cut method to the vehicle routing problem, Zentrum für Angewandte Informatik Kol̈n Technical Report zpr2000-386, 2000.
13. A. de Bruin, G.A.P. Kindervater, H.W.J.M. Trienekens, Asynchronous parallel branch and bound and anomalies, Report EUR-CS-95-05, Department of Computer Science, Erasmus University, Rotterdam, 1995.
14. Campos V., Corberán A., Mota E. Polyhedral results for a vehicle routing problem. European Journal of Operations Research. 52:1991;75.
15. Q. Chen, M.C. Ferris, FATCOP: a fault tolerant condor-PVM mixed integer programming solver, University of Wisconsin CS Department Technical Report 99-05, Madison, WI, 1999.
16. Christofides N., Mingozzi A., Toth P. Exact algorithms for solving the vehicle routing problem based on spanning trees and shortest path relaxations. Mathematical Programming. 20:1981;255.
17. Chvátal V. Linear Programming. 1983;W.H. Freeman and Company, New York.
18. Cordier C., Marchand H., Laundy R., Wolsey L.A. bc-opt: A branch-and-cut code for mixed integer programs. Mathematical Programming. 86:1999;335.
19. Cornuéjols G., Harche F. Polyhedral study of the capacitated vehicle routing problem. Mathematical Programming. 60:1993;21.
20. R. Correa, A. Ferreira, Parallel best-first branch and bound in discrete optimization: a framework, Center for Discrete Mathematics and Theoretical Computer Science Technical Report 95-03.
21. Dantzig G.B., Ramser R.H. The truck dispatching problem. Management Science. 6:1959;80.
22. J. Eckstein, C.A. Phillips, W.E. Hart, PICO: an object-oriented framework for parallel branch and bound, RUTCOR Research Report 40-2000, Rutgers University, Piscataway, NJ, 2000.
23. Elf M., Gutwenger C., Jünger M., Rinaldi G. Branch-and-cut algorithms for combinatorial optimization and their implementation in ABACUS. Naddef D., Jünger M. Computational Combinatorial Optimization. 2001;157 Springer, Berlin.
24. Fisher M.L. Optimal solution of vehicle routine problems using minimum k-trees. Operations Research. 42:1988;141.
25. Foster B.A., Ryan D.M. An integer programming approach to the vehicle scheduling problem. Operational Research Quarterly. 27:1976;367.
26. Geist A.et al. PVM: Parallel Virtual Machine, A User's Guide and Tutorial for Networked Parallel Computing. 1994;MIT University Press, Cambridge, MA.
27. Gendron B., Crainic T.G. Parallel branch and bound algorithms: survey and synthesis. Operations Research. 42:1994;1042.
28. Grama A., Kumar V. Parallel search algorithms for discrete optimization problems. ORSA Journal on Computing. 7:1995;365.
29. Grötschel M., Jünger M., Reinelt G. A cutting plane algorithm for the linear ordering problem. Operations Research. 32:1984;1155.
30. Grötschel M., Lovász L., Schrijver A. Geometric Algorithms and Combinatorial Optimization. 1981;Springer-Verlag, Berlin.
31. D. Henrich, Initialization of parallel branch-and-bound algorithms, in: Proceedings of the Second International Workshop on Parallel Processing and Artificial Intelligence, Chamberry, France, 1993.
32. Hoffman K., Padberg M. LP-based combinatorial problem solving. Annals of Operations Research. 4:1985/86;145.
33. Jünger M., Thienel S. The ABACUS system for branch and cut and price algorithms in integer programming and combinatorial optimization. Software Practice and Experience. 30:2000;1325.
34. Jünger M., Thienel S. Introduction to ABACUS - a branch-and-cut system. Operations Research Letters. 22:1998;83.
35. Nemhauser G.L., Savelsbergh M.W.P., Sigismondi G.S. MINTO, a mixed INTeger optimizer. Operations Research Letters. 15:1994;47.
36. Nemhauser G.L., Wolsey L.A. Integer and Combinatorial Optimization. 1988;John Wiley & Sons, New York.
37. Kumar V., Gupta A. Analyzing scalability of parallel algorithms and architectures. Journal of Parallel and Distributed Computing. 22:1994;379.
38. L. Ladányi, T.K. Ralphs, M. Saltzman, Implementing scalable parallel search algorithms for data-intensive applications, in: Proceedings of the International Conference on Computational Science, vol. I, 2002, p. 592.
39. L. Ladányi, T.K. Ralphs, M. Saltzman, A library hierarchy for implementing scalable parallel search algorithms, Lehigh University Industrial and Systems Engineering Technical Report 01T-010, 2001.
40. Ladányi L., Ralphs T.K., Trotter L.E. Branch, cut, and price: sequential and parallel. Naddef D., Jünger M. Computational Combinatorial Optimization. 2001;223 Springer, Berlin.
41. Land A.H., Doig A.G. An automatic method for solving discrete programming problems. Econometrica. 28:1960;497.
42. Laporte G., Nobert Y. Comb inequalities for the vehicle routing problem. Methods of Operations Research. 51:1981;271.
43. Laporte G., Nobert Y., Desrouchers M. Optimal routing with capacity and distance restrictions. Operations Research. 33:1985;1050.
44. A.N. Letchford, R.W. Eglese, J. Lysgaard, Multi-star inequalities for the vehicle routing problem, Technical Report available at http://www.lancs.ac.uk/staff/letchfoa/pubs.htm.
45. J. Linderoth, Topics in parallel integer optimization, Ph.D. Dissertation, School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA, 1998.
46. Mitra G., Hai I., Hajian M.T. A distributed processing algorithm for solving integer programs using a cluster of workstations. Parallel Computing. 23:1997;733.
47. Mitten L.G. Branch-and-bound methods: general formulation and properties. Operations Research. 18:1970;24.
48. Naddef D., Rinaldi G. Branch and cut. Toth P., Vigo D. Vehicle Routing. 2000;SIAM, Philadelphia.
49. Padberg M., Rinaldi G. A branch-and-cut algorithm for the resolution of large-scale traveling salesman problems. SIAM Review. 33:1991;60.
50. T.K. Ralphs, SYMPHONY Version 3.0 User's Guide, Available from www.branchandcut.org/SYMPHONY.
51. T.K. Ralphs, L. Ladányi, COIN/BCP User's Guide, Available from www.coin-or.org.
52. T.K. Ralphs, L. Ladányi, M. Saltzman, Parallel branch, cut, and price for large-scale discrete optimization, to appear in Mathematical Programming, pre-print available from http://www.lehigh.edu/̃tkr2/research/pubs.html.
53. Ralphs T.K., Kopman L., Pulleyblank W.R., Trotter L.E. Jr. On the Capacitated Vehicle Routing Problem. Mathematical Programming Series B. 94:2003;343.
54. Shinano Y., Higaki M., Hirabayashi R. Generalized utility for parallel branch and bound algorithms. Proceedings of the 1995 Seventh Symposium on Parallel and Distributed Processing. 1995;392 IEEE Computer Society Press, Los Alamitos, CA.
55. H.W.J.M. Trienekens, A. de Bruin, Towards a taxonomy of parallel branch and bound algorithms, Report EUR-CS-92-01, Department of Computer Science, Erasmus University Rotterdam, 1992.
56. S. Tschöke, T. Polzer, Portable Parallel Branch and Bound Library User Manual, Library Version 2.0. Department of Computer Science, University of Paderborn.
57. Wright S.J. Solving optimization problems on computational grids. Optima. 65:2001.