| Systems engineering combines optimization with process planning and decision-making. Typically, mathematical optimization models in process systems engineering are formulated using a set of algebraic equations yielding a set of feasible combinations of continuous conditions and discrete decisions. Solutions to the set of algebraic constraints are compared by evaluating their effect on a modeled outcome or objective. In the most general case, the resulting combination of constraints and objectives is a mixed-integer nonlinear program (MINLP).;In order to assure that a proposed solution to this general class of problems is the best available, a deterministic global optimization method is required. Certification of a globally optimal solution, however, is a computationally expensive process. In general, this class of problems is known to be NP-hard, with solution times that scale exponentially with problem size. Consequently, clever and efficient algorithmic advances are necessary to prevent increasingly complex problem formulations from becoming intractable.;In this thesis, we address opportunities for algorithmic improvement in a standard branch-and-bound global optimization framework. Theoretical knowledge for accelerating the solution of specific classes of problems, including reformulation-linearization techniques [89] and lift-and-project [6], has been available for more than twenty years. In fact, the mathematical foundations behind the rigorous convexification used in the global optimization of general nonconvex problems date back more than forty years [77]. Yet, no previous theoretical or implemented work successfully combines and generalizes these concepts in a way that is applicable to the general class of MINLPs.;We design and introduce algorithms incorporating simultaneous convexification techniques to exploit nonconvex substructures in general mathematical programs. We implement the proposed algorithms in a general purpose branch-and-bound global optimization framework. This effort is the first generalized implementation combining reformulation-linearization, lift-and-project, and advanced convex envelope construction in a way that is applicable to the most general MINLP problem formulations. Performance of the proposed implementations is assessed by extensive computational studies, including random problems; process synthesis and process operations applications; and standard literature test libraries. Results show that an overall reduction of required branch-and-bound iterations, maximum required storage size, and total computational effort is achieved by our implementations. |
