The Texas A&M Energy Institute will host a special seminar featuring Dr. Pedro Castro, an Associate Professor of chemical engineering at the University of Lisbon, on Thursday, April 18, 2023, from 11:00 a.m. – 12:00 p.m. CDT (UTC -5:00) in the Frederick E. Giesecke Engineering Research Building (GERB) Third Floor Conference Room and on Zoom. The topic will be “Global Optimization of Quadratically Constrained Problems (QCPS) with Mixed-Integer Programming Relaxations.”
Several problems of interest to Process Systems Engineering can be formulated as non-convex quadratically constrained programs (QCPs). These appear in design and operational problems and feature constraints with bilinear terms resulting from the product of two continuous variables, e.g., flows and concentrations. The preferred method used by commercial solvers to solve QCPs to global optimality is through the spatial B&B method with linear programming (LP) relaxations. An alternative is to rely on mixed-integer programming (MIP) relaxations, which make the relaxation harder to solve but that can lead to a search process that is more efficient overall. This is especially true for MIP relaxations using logarithmic partitioning schemes relying on a base-2 numeric representation system. After giving an overview of the key procedures that can be used for global optimization, we propose a new algorithm relying extensively on MIP relaxations, for improving the dual bound and for reducing the variables domain through optimality based bound tightening (OBBT). Using a set of 54 benchmark instances from the literature, we show that the new algorithm significantly outperforms GUROBI and BARON.
Pedro Castro is an Associate Professor at the Department of Chemical Engineering of Instituto Superior Técnico (IST), University of Lisbon (UL). Before, he was a Principal Investigator in the Department of Statistics and Operations Research of the Faculty of Sciences (2014-2022) and an Assistant Researcher at the Portuguese National Laboratory of Energy and Geology (2002-2014). He graduated (1997) in Chemical Engineering from IST, and achieved his PhD (2001) and Habilitation (2020) from the same University. 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, Ignacio Grossmann. A major output was the Cyber-Infrastructure site: www.minlp.org. Pedro Castro has coordinated 9 projects dealing with mathematical programming approaches for optimizing the design and operation of industrial plants. He has authored more than 80 ISI-indexed journal articles, receiving over 3000 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 1% Scientists in Chemical Engineering (Ranked 360).