A global optimization algorithm for nonconvex generalized disjunctive programming and applications to process systems

Sang-Bum Lee

doi:10.1016/S0098-1354(01)00732-3

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A global optimization algorithm for nonconvex generalized disjunctive programming and applications to process systems

2001-11-01

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Sang-Bum Lee

Ignacio E. Grossmann

DOI：10.1016/S0098-1354(01)00732-3

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Abstract

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A global optimization algorithm for nonconvex Generalized Disjunctive Programming (GDP) problems is proposed in this paper. By making use of convex underestimating functions for bilinear, linear fractional and concave separable functions in the continuous variables, the convex hull of each nonlinear disjunction is constructed. The relaxed convex GDP problem is then solved in the first level of a two-level branch and bound algorithm, in which a discrete branch and bound search is performed on the disjunctions to predict lower bounds. In the second level, a spatial branch and bound method is used to solve nonconvex NLP problems for updating the upper bound. The proposed algorithm exploits the convex hull relaxation for the discrete search, and the fact that the spatial branch and bound is restricted to fixed discrete variables in order to predict tight lower bounds. Application of the proposed algorithm to several example problems is shown, as well as a comparison with other algorithms. (C) 2001 Elsevier Science Ltd. All rights reserved.

Keywords:

nonconvex GDP

nonconvex MINLP

convex hull relaxation

branch and bound

global optimization

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