Generalized Disjunctive Programming or the Art of Modelling with Binary Variables

Pedro Castro is an Associate Professor at the Department of Chemical Engineering of Instituto Superior Técnico (IST), University of Lisbon (UL). Between 2004 and 2013, he spent a total of 18 months in the Department of Chemical Engineering at Carnegie Mellon University working in collaboration with Dean University Professor of Chemical Engineering, Ignacio Grossmann. His research interests are in Process Systems Engineering (PSE), tackling real-life industrial problems from a variety of sectors. He is known for mixed-integer linear programming (MILP) models and MILP-based algorithms for process scheduling and global optimization of non-convex problems with bilinear terms. These have been based on the Resource-Task Network (RTN), Multiparametric Disaggregation and Generalized Disjunctive Programming. He has coordinated 9 projects worth over k€ 700, authored more than 80 ISI-indexed journal articles, receiving over 3500 citations for an h-index of 33 (Scopus), and has been invited to give over 20 lectures and short courses worldwide. A study by Stanford University listed him in 2022 as One of the World’s top 2% Scientists Ranked 360 (6^th in Portugal) in the subject field of Chemical Engineering. He also appears in the rankings of Research.com as one of the best Engineering and Technology scientists (6916^th  globally and 42^nd in Portugal).  

This short course will focus on the development of computationally efficient mathematical programming models.
We will start by looking into integer programming (IP) models, models with only binary variables. Although this problem class is not relevant per se for chemical engineering, it deserves some attention because important constraints of real-life problems can be formulated using exclusively 0-1 variables. We will explain how to formulate IP constraints from propositional logic, providing a few examples for better understanding. In the second part of the course, the focus will be on mixed-integer linear programming (MILP) problems. Specifically, we will use Generalized Disjunctive Programming (GDP) for deriving MILPs, which relies on disjunctions and logic propositions. Disjunctions are perhaps the easiest way to generate constraints featuring binary and continuous variables since they can systematically be converted to MILP format using big-M and convex hull reformulations. Guidelines will be given on how to choose the most appropriate for a particular problem. The course finishes with a hands-on session, where the students are asked to formulate the constraints to model a piecewise linear function.