Global optimization of nonlinear generalized disjunctive programming with bilinear equality constraints: applications to process networks

A global optimization method is proposed for the solution of nonconvex generalized disjunctive programming problems that have bilinear equality constraints in terms of flows, compositions and split fractions. Tight convex under/over estimators are introduced for the relaxation of nonconvex constraints to construct the lower bound problem. Discrete choices for process networks are expressed as disjunctions, which are relaxed by a convex hull formulation. The relaxed convex NLP problem is solved with a two-level branch and bound algorithm proposed by Lee and Grossmann (Comput. Chem. Eng. 25 (2001) 1675), which branches on the discrete variables at the first level and the continuous variables on the second level. This global optimization algorithm is guaranteed to find an F-optimal solution in a finite number of steps. Applications are presented in pooling problems, wastewater network problems, and water usage network problems. (C) 2003 Elsevier Science Ltd. All rights reserved.