Large-Scale Dynamic Optimization Under Uncertainty using Parallel Computing

Abstract

This research focuses on the development of a solution strategy for the optimization of large-scale dynamic systems under uncertainty. Uncertainty resides naturally within the external forces posed to the system or from within the system itself. For example, in chemical process systems, external inputs include flow rates, temperatures or compositions; while internal sources include kinetic or mass transport parameters; and empirical parameters used within thermodynamic correlations and expressions. The goal in devising a dynamic optimization approach which explicitly accounts for uncertainty is to do so in a manner which is computationally tractable and is general enough to handle various types and sources of uncertainty. The approach developed in this thesis follows a so-called multiperiod technique whereby the infinite dimensional uncertainty space is discretized at numerous points (known as periods or scenarios) which creates different possible realizations of the uncertain parameters. The resulting optimization formulation encompasses an approximated expected value of a chosen objective functional subject to a dynamic model for all the generated realizations of the uncertain parameters. The dynamic model can be solved, using an appropriate numerical method, in an embedded manner for which the solution is used to construct the optimization formulation constraints; or alternatively the model could be completely discretized over the temporal domain and posed directly as part of the optimization formulation. Our approach in this thesis has mainly focused on the embedded model technique for dynamic optimization which can either follow a single- or multiple-shooting solution method. The first contribution of the thesis investigates a combined multiperiod multiple-shooting dynamic optimization approach for the design of dynamic systems using ordinary differential equation (ODE) or differential-algebraic equation (DAE) process models. A major aspect of this approach is the analysis of the parallel solution of the embedded model within the optimization formulation. As part of this analysis, we further consider the application of the dynamic optimization approach to several design and operation applications. Another vmajor contribution of the thesis is the development of a nonlinear programming (NLP) solver based on an approach that combines sequential quadratic programming (SQP) with an interior-point method (IPM) for the quadratic programming subproblem. A unique aspect of the approach is that the inherent structure (and parallelism) of the multiperiod formulation is exploited at the linear algebra level within the SQP-IPM nonlinear programming algorithm using an explicit Schur-complement decomposition. Our NLP solution approach is further assessed using several static and dynamic optimization benchmark examples.