Data-driven optimization strategies for interconnected process systems

This thesis explores the application of derivative-free optimization (DFO) and other data-driven approaches to complex, integrated decision-making in enterprise-wide optimization (EWO). Chapter 1 sets the historical backdrop for optimization and Machine Learning (ML) tools in EWO and exposes their limitations through a value chain coordination example under different game-theoretical settings. Chapter 2 reviews dominant mathematical decision-making frameworks for the operation of chemical process systems. Mathematical optimization is introduced, along with various ways it can be enhanced by ML. Chapter 3 presents and assesses different types of DFO solvers on process systems engineering (PSE) applications, setting the scene for subsequent work. A convex quadratic trust-region optimizer CUATRO is introduced, specifically designed to address the limitations of existing DFO solvers in PSE, focusing on safe exploration under noisy evaluations and black-box constraints. Chapter 4 demonstrates how DFO can coordinate complicating variables linking subproblems in EWO, while preserving agent autonomy and privacy. Considered case studies include collaborative model training, facility location, and resource sharing problems. Data-driven coordination outperforms distributed optimization in nonconvex problems with few linking variables. Chapter 5 shifts focus to hierarchical planning-scheduling-control. A data-driven approach is presented that combines DFO with optimality surrogates to enable the solution of previously intractable tri-level formulations. The proposed method balances tractability and accuracy, offering a viable alternative to heuristic sequential approaches. Chapter 6 revisits CUATRO and its application to high-dimensional DFO problems. We learn linear subspaces to optimize over, reducing computational cost in the trust region updates. This approach matches the performance of state-of-the-art model-based solvers in over a hundred dimensions, with significant computational speed-up. This thesis identifies specific scenarios in EWO, where DFO is effectively integrated with mathematical programming, by treating subproblem expressions as black-boxes, and coordinating their optimal outputs with DFO. To conclude, the contributions are discussed alongside promising directions for future research.