Branch-and-Bound Methods

Abstract

These methods are commonly considered as the most efficient tools for solving integer programming problems. In Section 4.1, we describe the idea of the branch-and-bound methods and introduce the basic relations. Any branch-and-bound method, as we mentioned in Section 1.4, consists of two basic procedures: branching or partitioning of the feasible solution set into some number of subsets and bounding or estimating of the optimal value of the objective function on these subsets. In this chapter, we show how linear programming may be used in such an estimation, while the estimations based on Lagrangean relaxations of a given problem are studied in Chapter 7.