CAREER: Foundations of Machine Learning-Enhanced Branch-and-Bound Algorithms for Scalable Global Optimization

Virginia Polytechnic Institute And State University, Blacksburg VA

Investigators

Abstract

This Faculty Early Career Development Program (CAREER) grant will advance national energy security and economic welfare by developing improved tools for optimizing complex energy and industrial systems. Critical infrastructures, such as electric power grids and chemical refineries, depend on solving large optimization problems to determine safe and efficient operating conditions. Current optimization tools are inadequate for large-scale planning and operational needs, limiting the ability to operate these energy systems efficiently, modernize them, and maintain resilient operations. This project will create a new generation of optimization algorithms that use machine learning to leverage shared structure in real-world applications, significantly accelerating solution times while preserving mathematical guarantees. It will develop new machine learning techniques to guide key algorithmic decisions in optimization algorithms while ensuring scalability, generalizability, and data efficiency. These advances have the potential to transform how energy systems are designed and operated, enabling more efficient operations, improved reliability, and lower operational costs and environmental impact. The educational plan will introduce optimization and machine learning concepts into high-school classrooms through an interactive web-based tool, teacher workshops, and partnerships with regional schools. Undergraduate research, new graduate modules, and interdisciplinary workshops will prepare the next-generation workforce at the interface of artificial intelligence, optimization, and engineering. This research will build a unified, theory-driven framework that leverages machine learning to enhance branch-and-bound algorithms for the guaranteed global optimization of mixed-integer nonlinear programs. It will (1) formulate new expert branching policies and develop supervised graph-based machine learning methods to imitate them; (2) create semi-supervised learning methods to generate high-quality feasible solutions and warm-starts; (3) use machine learning to accelerate decomposition algorithms; and (4) design generative machine learning models that construct realistic and varied families of mixed-integer nonlinear programs. These contributions will advance the understanding of effective branching strategies, reduce reliance on expensive labeled data, enable generalization to large-scale problems, and aid in benchmarking and sustained innovation. The project will produce open-source algorithms and benchmark libraries for power systems and refinery optimization, enabling rigorous evaluation of machine learning-guided global optimization methods. These contributions will significantly improve the efficiency, robustness, and scalability of global solvers, advancing the scientific foundations of global optimization and supporting high-impact applications across energy and large-scale industrial systems. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.