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, which yields MINLP models that can be highly nonconvex. However, in many cases the NLP that results from fixing the discrete decisions is much simpler to solve than the original problem. The proposed method exploits this property. 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 first stage seeks to find feasible solutions faster by restricting the solution time of the problems and diversifying the search. The second stage guarantees the convergence by solving the original algorithm. 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 on the convex hull of the feasible region of a subset of the constraints. Results and comparison with other global solvers show that the enhancements improve the performance of the algorithm, and that it is more effective in the tested problems at finding near optimal solutions compared to general-purpose global solvers.