Associate Professor, Department of Chemical Engineering, Carnegie Mellon University
Robust Optimization with Nonconvex Models: Opportunities and Challenges for Process Systems Engineering
Robust Optimization (RO) has seen tremendous methodological growth over the past few decades, establishing itself as a major paradigm for optimization under uncertainty. Despite these advances, however, the vast majority of works in the area contemplate linear or convex models, which lend themselves to certain solution methodologies and tractability guarantees. In contrast, much less has been achieved in terms of applying RO in the context of more traditional, process design type models that are ubiquitously contemplated by process systems engineers. These models are notorious for the nonconvexities via which both decision variables and parameters participate in their equations, as well as due to the fact that they feature a large fraction of state variables and state equations, which stem from the inclusion of many square sub-models for the simulation of various flowsheet parts.
Whereas solving such models is often challenging even in a deterministic setting, there exists a pressing need to solve them while accounting for the effects parametric uncertainty that they are subject to. Such uncertainty often exists in (a) the physicochemical property models we postulate for the various unit operations, including various parameters associated with equilibria, transfer and kinetics at play, (b) the market conditions we postulate when devising suitable economic objective functions to optimize against, and/or (c) the fact that our processes are affected by variations in the environmental conditions or the performance of various upstream and downstream units, which themselves are not included in our models.
In this talk, we highlight the methodological challenges associated with applying RO principles in the context of nonconvex models, and we present our recent advances in terms of developing a generalized cutting set algorithm to efficiently identify robust process designs under a multitude of uncertainty characterizations, including both continuous and discrete uncertainty sets. Using various forms of decision rules, including nonlinear forms, our algorithm is shown to be able to solve nonconvex RO models in a two-stage setting, supporting also the design-and-operate and/or the design-and-control settings.
Crysanthos Gounaris is Associate Professor in the Department of Chemical Engineering at Carnegie Mellon University. He received a Dipl. in Chemical Engineering (2002) and an M.Sc. in Process Control (2003) from the National Technical University of Athens. He then attended Princeton University, where he earned an M.A. (2005) and a Ph.D. in Chemical Engineering (2008). His doctoral thesis, pursued under the supervision of Chris A. Floudas, is entitled “Advances in Global Optimization and the Rational Design of Shape-Selective Separations” and explores the use of nonlinear modeling and global optimization techniques in the study of porous materials. After graduation, Gounaris joined McKinsey & Co. as an associate, where he provided consultation to petrochemical, pharmaceutical, and consumer packaged-goods companies on a variety of projects of operational and strategic nature (2008-2010). He returned to academia to pursue postdoctoral research at Princeton University (2010-2013), after which he joined the Department of Chemical Engineering at Carnegie Mellon University as an assistant professor (2013-).