Abstract
Within the context of solving Mixed-Integer Linear Programs by a Branch-and-Cut algorithm, we propose a new strategy for branching. Computational experiments show that, on the majority of our test instances, this approach enumerates fewer nodes than traditional branching. On average, on instances that contain both integer and continuous variables the number of nodes in the enumeration tree is reduced by more than a factor of two, and computing time is comparable. On a few instances, the improvements are of several orders of magnitude in both number of nodes and computing time.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Aardal, K., Bixby, R.E., Hurkens, C.A.J., Lenstra, A.K., Smeltink, J.W.: Market split and basis reduction: towards a solution of the Cornuéjols-Dawande instances. Inf. J. Comput. 12(3), 192–202 (2000). doi:10.1287/ijoc.12.3.192.12635
Ajtai, M.: The shortest vector problem in l 2 is NP-hard for randomized reductions. In: Proceedings of the 30th annual ACM symposium on theory of computing. Dallas, TX (1998)
Andersen K., Cornuéjols G., Li Y.: Reduce-and-split cuts: improving the performance of mixed integer Gomory cuts. Manag. Sci. 51(11), 1720–1732 (2005)
Balas E.: Intersection cuts—a new type of cutting planes for integer programming. Oper. Res. 19(1), 19–39 (1971)
Balas E.: Disjunctive programming. Ann. Discret. Math. 5, 3–51 (1979)
Balas E., Ceria S., Cornuéjols G.: Mixed 0–1 programming by lift-and-project in a branch-and-cut framework. Manag. Sci. 42(9), 1229–1246 (1996)
Balas, E. , Saxena, A.: Optimizing over the split closure. Math. Program. 113(2), 219–240 (2008)
Gomory, R.E. : An algorithm for integer solutions to linear programs. In: Wolfe, P. (ed.) Recent Advances in Mathematical Programming, pp. 269–302. McGraw-Hill, New York (1963)
ILOG: ILOG CPLEX 11.0 User’s Manual. ILOG S.A., Gentilly, France (2007)
Karamanov, M., Cornuéjols, G.: Branching on general disjunctions. Math. Program. A. doi:10.1007/s10107-009-0332-3
Owen, J., Mehrotra, S.: Experimental results on using general disjunctions in branch-and-bound for general-integer linear program. Comput. Optim. Appl. 20, 159--170 (2001)
Author information
Authors and Affiliations
Corresponding author
Additional information
G. Cornuéjols was supported by NSF grant CMMI0653419, ONR grant N00014-03-1-0188 and ANR grant BLAN06-1-138894.
L. Liberti and G. Nannicini was supported by ANR grant 07-JCJC-0151.
Rights and permissions
About this article
Cite this article
Cornuéjols, G., Liberti, L. & Nannicini, G. Improved strategies for branching on general disjunctions. Math. Program. 130, 225–247 (2011). https://doi.org/10.1007/s10107-009-0333-2
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10107-009-0333-2