Comparison of MINLP formulations for global superstructure optimization

Abstract Superstructure optimization is a powerful but computationally demanding task that can be used to select the optimal structure among many alternatives within single optimization. In chemical engineering, such problems naturally arise in process design, where different need considered simultaneously minimize specific objective function (e.g., production costs or global warming impact). Conventionally, superstructure are either formulated with Big-M Convex Hull reformulation approach. However, for containing nonconvex functions, it not clear whether these yield most efficient formulations. We therefore compare conventional problem formulations less common ones (using equilibrium constraints, step multiplications of binary and continuous variables model disjunctions) using three case studies. First, minimalist derive conjectures about their computational performance. These then further investigated by two more complex literature benchmarks. Our analysis shows approaches tend result smaller size, while keeping relaxations comparably tight—despite introduction additional nonconvexities. For studies, we demonstrate all benefit from eliminating reduced-space formulation. encourage also consider introduce nonconvexities reduce number variables.