(385a) Evolution of Mixed-Integer Programming and Its Applicationss to Process Systems Engineering

In this presentation, which is in honor of Larry Evans for his 80^th birthday, we review the evolution and great progress that has been achieved in mathematical programming, particularly mixed-integer programming, over the last 50 years. We first focus on mixed-integer linear programming (MILP), and its great progress that has been achieved in the development of powerful branch-and-cut methods and its implementation in commercial software. We show the impact that MILP has had in solving large-scale supply chain, process planning and scheduling problems. We then review developments in mixed-integer nonlinear programming (MINLP), where there has been an increased availability of software packages implementing methods ranging from branch and bound to decomposition methods. Furthermore, there has been significant progress in deterministic global optimization algorithms for solving MINLP problems involving nonconvex constraints. We show the impact that MINLP is having in solving increasingly larger and more complex nonlinear planning and scheduling problems, as well as certain classes of process synthesis problems. We next provide next an overview of Generalized Disjunctive Programming (GDP), a logic-based modeling framework which is an alternative to the fully algebraic mixed-integer programming approach. Throughout the presentation we illustrate the application of MILP, MINLP and GDP techniques with a number of examples arising in the synthesis, design and enterprise-wide optimization of process systems. We close by highlighting some of the outstanding challenges in advancing the area of discrete-continuous optimization