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

TL;DR

This paper introduces a comprehensive data-driven stochastic robust optimization framework that integrates machine learning for uncertainty modeling and a bi-level optimization approach to handle large, multi-class uncertainty data in the big data era.

Contribution

It develops a novel DDSRO framework combining machine learning, bi-level optimization, and decomposition algorithms for robust decision-making under uncertainty.

Findings

Effective in process network design and planning

Handles large multi-class uncertainty data efficiently

Maintains computational tractability in complex problems

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.