Global optimization algorithm for nonlinear generalized disjunctive programming and applications to process systems engineering

In this thesis, the modeling and solution algorithms for nonlinear discrete/continuous optimization problems are presented with Generalized Disjunctive Programming (GDP). The advantage of the GDP model is that it includes algebraic constraints, disjunctions and logic propositions.; A relaxation of the GDP model is derived that is based in considering the convex hull relaxation of each disjunction, which is assumed to involve nonlinear convex inequalities. This convex relaxation problem yields a tighter relaxation of disjunctions when compared to the big-M MINLP problem. A special purpose branch and bound algorithm is presented that makes use of the proposed relaxation of the GDP problem. A reformulation of the GDP model as an MINLP problem is also given, and numerical comparisons are reported. A number of different types of disjunctions are also discussed and the characterization of these disjunctions and their relaxations are discussed with examples.; A global optimization algorithm for the GDP model, which has structured nonconvex functions, is proposed. By using convex underestimators, a two-level branch and bound method is proposed that branches first on the discrete variables and then performs a spatial search in the continuous variables. The application of the proposed algorithm has shown that the global optimum can be found with reasonable computational expense for a number of nonconvex GDP problems. The special case of process networks with bilinear constraints is also considered for which a tight relaxation is derived.; Industrial applications of the GDP model and its optimization are presented with an industrial monomer process where the superstructure of the process is modeled as a GDP problem. An MILP solution algorithm for finding all the alternate optima of an LP system is proposed and used for an E. coli glucose network.