Operating system

Algorithm

Online machine learning

Machine learning

Data mining

Mathematical optimization

Engineering

Stochastic programming

Optimization problem

Lens (geology)

Artificial intelligence

Robust optimization

Pure mathematics

Data-driven

Mathematics

Computer science

Through-the-lens metering

Big data

Active learning (machine learning)

Petroleum engineering

Field (mathematics)

Process (computing)

Computers & Chemical Engineering

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.

Optimization under uncertainty in the era of big data and deep learning: When machine learning meets mathematical programming