The geometric branch-and-bound algorithm

Abstract

The aim of this chapter is the presentation of the fundamental geometric branch-and-bound algorithm including a general convergence theory. To this end, we start with a literature review of these approaches and their applications to facility location problems in Section 2.1. Next, we give some notations and formally define bounding operations in Section 2.2 before the geometric branch-and-bound prototype algorithm is presented and discussed in Section 2.3. The main contribution of the present chapter can be found in Sections 2.4 and 2.5. Therein, we define the rate of convergence and results about the termination of the algorithm are given. Note that parts of these sections have been published in Schöbel and Scholz (2010b).