Computational Experience with Applications of Bilinear Cutting Planes

Abstract

This work analyzes the effectiveness of cutting planes applied during the global optimization of nonconvex nonlinear and mixed-integer nonlinear programming problems arising from process synthesis and process operations. In a previous publication, we introduced algorithms for bilinear substructure detection, cutting plane identification, cut filtering, and cut selection. Our implementation embeds reformulation–linearization, lift-and-project, and advanced convex envelope construction techniques that exploit underlying bilinear substructures and tighten factorable programming reformulations at every node in the branch-and-bound tree. In this work, we utilize industrial examples to demonstrate a variety of relaxation tightening strategies afforded by these bilinear cutting plane algorithms. A detailed description and associated computational experience are presented for applied cutting planes.