The GMIN-αBB Approach : Theory and Computations

Abstract

This chapter presents the General structure Mixed Integer Nonlinear αBB global optimization approach, GMIN-αBB, for general nonconvex MINLP problems. Section 22.1 describes the mathematical models that the GMIN-αBB can address. Section 22.2 focuses on the generation of valid lower bounds. Section 22.3 discusses the generation of upper bounds. Section 22.4 outlines the strategies for the selection of the branching variables. Section 22.5 describes the updates of the variable bounds through an optimization-based approach and an interval analysis based approach. Section 22.6 presents the algorithmic steps of the GMIN-αBB approach and a small illustrative example. Finally, in section 22.7 computational studies are reported on (i) small literature problems, (ii) pump configuration problems, and (iii) trim loss optimization problems. The material of this chapter is based on the work of Adjiman et al. (1997c), (1998d).