Data-Driven Optimization under Uncertainty in the Era of Big Data and Deep Learning: General Frameworks, Algorithms, and Applications - Ning, Chao (ProQuest Dissertations & Theses, 2020)
This dissertation deals with the development of fundamental data-driven optimization under uncertainty, including its modeling frameworks, solution algorithms, and a wide variety of applications. Specifically, three research aims are proposed, including data-driven distributionally robust optimization for hedging against distributional uncertainties in energy systems, online learning based receding-horizon optimization that accommodates real-time uncertainty data, and an efficient solution algorithm for solving large-scale data-driven multistage robust optimization problems.There are two distinct research projects under the first research aim. In the first related project, we propose a novel data-driven Wasserstein distributionally robust mixed-integer nonlinear programming model for the optimal biomass with agricultural waste-to-energy network design under uncertainty. A data-driven uncertainty set of feedstock price distributions is devised using the Wasserstein metric. To address computational challenges, we propose a reformulation-based branch-and-refine algorithm. In the second related project, we develop a novel deep learning based distributionally robust joint chance constrained economic dispatch optimization framework for a high penetration of renewable energy. By leveraging a deep generative adversarial network (GAN), an f-divergence-based ambiguity set of wind power distributions is constructed as a ball in the probability space centered at the distribution induced by a generator neural network. To facilitate its solution process, the resulting distributionally robust chance constraints are equivalently reformulated as ambiguity-free chance constraints, which are further tackled using a scenario approach. Additionally, we derive a priori bound on the required number of synthetic wind power data generated by f-GAN to guarantee a predefined risk level. To facilitate large-scale applications, we further develop a prescreening technique to increase computational and memory efficiencies by exploiting problem structure.The second research aim addresses the online learning of real-time uncertainty data for receding-horizon optimization-based control. In the related project, data-driven stochastic model predictive control is proposed for linear time-invariant systems under additive stochastic disturbance, whose probability distribution is unknown but can be partially inferred from real-time disturbance data. The conditional value-at-risk constraints on system states are required to hold for an ambiguity set of disturbance distributions. By leveraging a Dirichlet process mixture model, the first and second-order moment information of each mixture component is incorporated into the ambiguity set. As more data are gathered during the runtime of controller, the ambiguity set is updated based on real-time data. We then develop a novel constraint tightening strategy based on an equivalent reformulation of distributionally robust constraints over the proposed ambiguity set. Additionally, we establish theoretical guarantees on recursive feasibility and closed-loop stability of the proposed model predictive control.The third research aim focuses on algorithm development for data-driven multistage adaptive robust mixed-integer linear programs. In the related project, we propose a multi-to-two transformation theory and develop a novel transformation-proximal bundle algorithm. By partitioning recourse decisions into state and control decisions, affine decision rules are applied exclusively on the state decisions. In this way, the original multistage robust optimization problem is shown to be transformed into an equivalent two-stage robust optimization problem, which is further addressed using a proximal bundle method. The finite convergence of the proposed solution algorithm is guaranteed for the multistage robust optimization problem with a generic uncertainty set. To quantitatively assess solution quality, we further develop a scenario-tree-based lower bounding technique. The effectiveness and advantages of the proposed algorithm are fully demonstrated in inventory control and process network planning.