Abstract

Branch-and-cut methods are very successful techniques for solving a wide variety of integer programming problems, and they can provide a guarantee of optimality. We describe how a branch-and-cut method can be tailored to a specific integer programming problem, and how families of general cutting planes can be used to solve a wide variety of problems. Other important aspects of successful implementations are discussed in this chapter. The area of branch-and-cut algorithms is constantly evolving, and it promises to become even more important with the exploitation of faster computers and parallel computing. 1

Citations

1231	Theory of Linear and Integer Programming - Schrijver - 1986
133	A branch-and-cut algorithm for the resolution of large-scale symmetric traveling salesman problems - Padberg, Rinaldi - 1991
125	On the solution of traveling salesman problems - Applegate, Bixby, et al. - 1998
99	Solving large-scale zero-one linear programming problems - Crowder, Johnson, et al. - 1983
58	Mixed 0-1 Programming by Lift-andProject in a Branch-and-Cut Framework, Management Science 42 - Balas, Ceria, et al. - 1996
58	An updated mixed integer programming library: MIPLIB 3.0 - Bixby, Ceria, et al. - 1998
39	Introduction to ABACUS - A BranchAnd-CUt System - Junger, Thienel - 1998
35	a Mixed INTeger Optimizer - MINTO - 1994
29	Wolsey,L.A.: bc-opt: A branch-and-cut code for mixed integer programs - Cordier, Marchand, et al. - 1997
20	Practical problem solving with cutting plane algorithms - Jünger, Reinelt, et al. - 1995
13	Interior point methods for combinatorial optimization - Mitchell, Pardalos, et al. - 1998
2	Branch and cut algorithms - Caprara, Fischetti - 1997
2	A.: ‘Cutting plane algorithms for integer programs with general integer variables’, Mathematical Programming 81 - Ceria, Cordier, et al. - 1998
1	Solution of large-scale travelling salesman problems - Graves, Wolfe, et al. - 1963