Cutting planes for improved global logic-based outer-approximation for the synthesis of process networks

In this work, we present an improved global logic-based outer approximation method (GLBOA) for the solution of nonconvex generalized disjunctive programs (GDP). The GLBOA allows the solution of nonconvex GDP models, and is particularly useful for optimizing the synthesis of process networks. Two enhancements to the basic GLBOA are presented. The first enhancement seeks to obtain feasible solutions faster by dividing the basic algorithm into two stages. The second enhancement seeks to tighten the lower bound of the algorithm by the use of cutting planes. The proposed method for obtaining cutting planes, the main contribution of this work, is a separation problem based in the convex hull of the feasible region of a subset of the constraints. Results show that the enhancements improve the performance of the algorithm, and that the algorithm is better in finding better feasible solutions than general purpose global solvers in the tested problems.