Title: Data-Driven Stochastic Robust Optimization: A General Computational Framework and Algorithm for Optimization under Uncertainty in the Big Data Era,
Abstract: A novel data-driven stochastic robust optimization (DDSRO) framework is
proposed for optimization under uncertainty leveraging labeled multi-class
uncertainty data. Uncertainty data in large datasets are often collected from
various conditions, which are encoded by class labels. Machine learning methods
including Dirichlet process mixture model and maximum likelihood estimation are
employed for uncertainty modeling. A DDSRO 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 data classes;
adaptive robust optimization is nested as the inner problem to ensure the
robustness of the solution while maintaining computational tractability. A
decomposition-based algorithm is further developed to solve the resulting
multi-level optimization problem efficiently. Case studies on process network
design and planning are presented to demonstrate the applicability of the
proposed framework and algorithm.