Optimization under Uncertainty in the Era of Big Data and Deep Learning: When Machine Learning Meets Mathematical Programming

TL;DR

This paper reviews recent advances in data-driven optimization under uncertainty, emphasizing the integration of machine learning and mathematical programming for improved decision-making in complex systems.

Contribution

It provides a comprehensive classification of recent research, highlights key challenges, and proposes future directions for integrating deep learning with optimization under uncertainty.

Findings

Classification of data-driven optimization methods

Identification of research challenges and opportunities

Proposals for integrating deep learning with optimization

Abstract

This paper reviews recent advances in the field of optimization under uncertainty via a modern data lens, highlights key research challenges and promise of data-driven optimization that organically integrates machine learning and mathematical programming for decision-making under uncertainty, and identifies potential research opportunities. A brief review of classical mathematical programming techniques for hedging against uncertainty is first presented, along with their wide spectrum of applications in Process Systems Engineering. A comprehensive review and classification of the relevant publications on data-driven distributionally robust optimization, data-driven chance constrained program, data-driven robust optimization, and data-driven scenario-based optimization is then presented. This paper also identifies fertile avenues for future research that focuses on a closed-loop data-driven optimization framework, which allows the feedback from mathematical programming to machine learning, as well as scenario-based optimization leveraging the power of deep learning techniques. Perspectives on online learning-based data-driven multistage optimization with a learning-while-optimizing scheme is presented.