Tailored formulations to accelerate deterministic global optimisation of mixed-integer nonlinear programs

Mixed-Integer Nonlinear Programs (MINLPs) are ubiquitous in Chemical Engineering and are challenging to solve to global optimality. One such class of problems in chemical engineering is Computer-aided mixture/blend design (CAMbD). Two approaches are used in this thesis to accelerate global optimisation of MINLPs, particularly CAMbD problems: (1) Classifier-based surrogate (CBS) formulations, and (2) Exact reformulations. Part one outlines the CBS formulation for checking phase stability. In CAMbD problems, ensuring phase stability of the candidate design mixture is crucial for the efficient design of chemical processes. Rigorously checking for phase stability directly in the CAMbD framework entails solving a bi-level optimisation problem, which in most cases is intractable, as opposed to a single-level MINLP if a rigorous check is omitted. The CBS formulation is developed to approximate the phase boundaries of a family of mixtures under consideration for design. Using two solvent mixture design case studies, it is demonstrated that solving CBS-embedded CAMbD problems can generate physically realisable solvent mixture candidates and improve their tractability. Part two investigates two exact reformulation approaches: quadratic reformulation and factorable reduced-space formulations. Quadratic reformulations involve recognising polynomial and rational expressions in the model and reformulating them to the equivalent quadratic expressions. Factorable reduced-space formulations involve selectively eliminating variables from the problem formulation via equality constraints in the optimisation model. Numerical experiments were conducted on an extensive collection of MINLPs and the CAMbD problem to establish the effectiveness of the reformulation approaches. The results from the numerical experiments support the integration of investigated reformulation strategies into state-of-the-art global MINLP solvers such as BARON and SCIP as pre-processing steps to improve their effectiveness.