Modeling optimization problems under uncertainty is known as stochastic programming (SP). It has a variety of important applications, including disaster management, supply chain design, health care, and harvest planning. Most real-world problems are complicated enough to generate a very large-size SP model, which is difficult to solve. Quickly finding the optimal solutions of these models is critical for decision-making when facing uncertainties. Existing optimization algorithms have a limited capability of solving large-scale SP problems. Without being explicitly programmed, machine learning can give computers the ability to "learn" with data by using statistical techniques. The goal of this project is to create a machine learning-based computational framework to solve large-scale stochastic programming problems effectively and efficiently by integrating machine learning techniques into optimization algorithms. The project will broaden the scope and applicability of machine learning in operations research. Furthermore, this research will support the cross-disciplinary training of graduate and undergraduate students in engineering and computer sciences, as well as the development of new curricula in the interface of machine learning and optimization algorithms.
The project will be the pioneering study of applying machine learning into stochastic programming, while existing works usually focus on using stochastic programming to improve the efficiency of machine learning algorithms. Motivated by the challenges from practices and limitations of current optimization algorithms, two research objectives are proposed: efficient sample generation and convergence acceleration, by taking sample average approximation and L-shaped algorithm as examples. The first research objective is to design a semi-supervised learning algorithm based on solution information to efficiently generate samples for sample average approximation. The second research objective is to develop a supervised learning algorithm to estimate a tight upper bound for expediting convergence of L-shaped method. The two research objectives will be achieved through five tasks: (1) semi-supervised learning-based scenario grouping; (2) supervised learning based representative scenario selection; (3) performance analysis for sample generation; (4) supervised learning based upper bound prediction; and (5) performance analysis for the machine learning-based L-shaped method. The successes of this project will generate a new class of theoretical optimization methods that facilitate various real-world applications in disaster management, supply chain design, health care and harvest planning.
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.