Global and Robust Optimization of Process Models with Embedded Simulations

Simulations arising from first-principles models or data-driven approaches find ubiquitous applications across technical fields. In the chemical industry, simulations are used to control unit operations, establish safe/efficient process configurations for producing a wide variety of products, and design key experiments. In a broader context, simulations often help to define value propositions for numerous products. Furthermore, robust optimization approaches, which rigorously account for uncertainty, are desirable when the consequences of decisions are extremely high. However, deterministic optimization (and, in turn, robust optimization) of general nonlinear forms remains a significant challenge due to the inherent computational complexity. This thesis addresses two key problems in nonconvex and robust optimization.
The focus of the first section is on advancing general methods for reduced-space deterministic global and robust optimization. The use of these methods for nonlinear models remains limited by high computational costs and strict structural requirements. The former problem may be mitigated by using fast and accurate relaxation methods. I present the development of two such methods. The first focuses on a specialized relaxation approach for emergent artificial neural networks, and the second advances reduced-space relaxation methods for intermediate composite bilinear terms. The development of the global optimizer EAGO, in which each of these methods is implemented, is described. The composite relaxation approach used in EAGO allows for deterministic global and robust optimization of highly complex model formulations surmounting strict structural requirements.
The second portion of this thesis concerns the global solution of optimization problems with embedded systems of parametric ordinary differential equations. These extremely difficult problems are of interest in the verification of recurrent neural networks, optimal control of batch processes, as well as in methods for the detection and isolation of faults. The handful of existing algorithms which address these problems are subject to significant limitations. Prior work has focused on explicit discrete-time methods and continuous-time relaxation approaches, in contrast to this thesis which describes previously unexplored implicit relaxation approaches. These methods are typically more accurate than explicit approaches, less expansive, and are well-suited to challenging problems which embed stiff dynamical systems.