The SMIN-αBB Approach : Theory and Computations

Abstract

This chapter presents the Special structure Mixed Integer Nonlinear αBB global optimization approach, denoted as SMIN-αBB, for nonconvex MINLP problems. Section 21.1 describes the classes of mathematical problems to which the SMIN-αBB is applicable. Section 21.2 focuses on the generation of valid lower bounds. Section 21.3 discusses the generation of upper bounds. Section 21.4 presents the strategies for the selection of the branching variables. Section 21.5 discusses the updates of the variable bounds via an optimization-based and an interval analysis based approach. Section 21.6 outlines the algorithmic steps of the SMIN-αBB approach and provides an illustration. Finally, in section 21.7 computational studies are presented on (i) small literature problems, and (ii) heat exchanger network synthesis problems. The material in this chapter is based on the work of Adjiman et al. (1997c), (1998d).