CAREER: End-to-end Constrained Optimization Learning

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This award is funded in whole or in part under the American Rescue Plan Act of 2021 (Public Law 117-2).Constrained optimization is used daily in our society with applications ranging from supply chains and logistics to electricity grids, organ exchanges, marketing campaigns, and manufacturing. Although these problems are often computationally challenging even for medium-sized instances, they constitute fundamental building blocks for the optimization of many industrial processes with profound effects on our society and economy. Yet the complexity of many constrained optimization problems often prevents them from being effectively adopted in contexts where many instances must be solved over a long-term horizon or when solutions must be produced under stringent time constraints. This project proposes a new paradigm that tightly integrates fundamental optimization techniques with machine learning algorithms to solve constraint optimization problems in real-time. This research holds the promise to create a new and transformative generation of optimization tools that solve hard constraint optimization problems under stringent time constraints leading to significant economic and societal benefits. From a scientific standpoint, this project will develop a new integration of optimization and machine learning tools that deliver high-quality solutions to large-scale hard constraint optimization problems at unprecedented computational speeds. The proposed end-to-end Constraint Optimization Learning (e2e-COL) contributes to new scientific knowledge along three main directions: (1) It accommodates the presence of domain knowledge or complex problem constraints by combining fundamental methodologies from optimization into the training cycle of deep neural networks. (2) It addresses the need of generating large datasets to train high-quality models by devising efficient data generation procedures, linking methodologies from optimization with the model learning ability, and developing semi-supervised models requiring small amounts of labeled data. (3) Finally, to scale to large problem instances, this proposal enables e2e-COL to learn decompositions and approximations of the problem structure.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.