## BRANCH-AND-CUT ALGORITHMS FOR INTEGER PROGRAMMING (1998)

Citations: | 6 - 1 self |

### BibTeX

@MISC{Mitchell98branch-and-cutalgorithms,

author = {John E. Mitchell},

title = {BRANCH-AND-CUT ALGORITHMS FOR INTEGER PROGRAMMING},

year = {1998}

}

### OpenURL

### Abstract

Branch-and-cut methods are exact algorithms for integer programming problems. They consist of a combination of a cutting plane method with a branch-and-bound algorithm. These methods work by solving a sequence of linear programming relaxations of the integer programming problem. Cutting plane methods improve the relaxation of the problem to more closely approximate the integer programming problem, and branch-and-bound algorithms proceed by a sophisticated divide and conquer approach to solve problems. The material in this entry builds on the material contained in the entries on cutting plane and branch-and-bound methods. Perhaps the best known branch-and-cut algorithms are those that have been used to solve traveling salesman problems. This approach is able to solve and prove optimality of far larger instances than other methods. Two papers that describe some of this research and also serve as good introductions to the area of branch-andcut algorithms are [21, 32]. A more recent work on the branch-and-cut approach to the traveling salesman problem is [1]. Branch-and-cut methods have also been used to solve other combinatorial optimization problems; recent references