Data-Driven Nested Stochastic Robust Optimization: A General Computational Framework and Algorithm for Optimization under Uncertainty in the Big Data Era

A novel data-driven nested stochastic robust optimization (DDNSRO) framework is proposed to systematically and automatically handle labeled multi-class uncertainty data in optimization problems. Uncertainty realizations in large datasets are often collected from various conditions, which are encoded by class labels. A group of Dirichlet process mixture models is employed for uncertainty modeling from the multi-class uncertainty data. The proposed data-driven nonparametric uncertainty model could automatically adjust its complexity based on the data structure and complexity, thus accurately capturing the uncertainty information. A DDNSRO framework is further proposed based on the data-driven uncertainty model through a bi-level optimization structure. The outer optimization problem follows a two-stage stochastic programming approach to optimize the expected objective across different classes of data; robust optimization is nested as the inner problem to ensure the robustness of the solution while maintaining computational tractability. A tailored column-and-constraint generation algorithm is further developed to solve the resulting multi-level optimization problem efficiently. Case studies on strategic planning of process networks are presented to demonstrate the applicability of the proposed framework.