CRII: CIF: A Machine Learning-based Computational Framework for Large-Scale Stochastic Programming

不确定性下的优化问题的建模被称为随机规划（SP）。它有各种重要的应用，包括灾害管理，供应链设计，医疗保健和收获计划。大多数现实世界中的问题都非常复杂，足以生成一个非常大规模的SP模型，这是很难解决的。快速找到这些模型的最优解对于面对不确定性时的决策至关重要。现有的优化算法对大规模SP问题的求解能力有限。在没有明确编程的情况下，机器学习可以让计算机通过使用统计技术来“学习”数据。该项目的目标是创建一个基于机器学习的计算框架，通过将机器学习技术集成到优化算法中，有效地解决大规模随机规划问题。该项目将扩大机器学习在运筹学中的范围和适用性。此外，该研究将支持工程和计算机科学研究生和本科生的跨学科培训，以及机器学习和优化算法接口的新课程开发。该项目将是将机器学习应用于随机规划的开创性研究，而现有的工作通常集中在使用随机规划来提高机器学习算法的效率。针对当前优化算法的局限性和实践中的挑战，以样本平均逼近和L形算法为例，提出了两个研究目标：有效的样本生成和加速收敛。第一个研究目标是设计一个基于解信息的半监督学习算法，以有效地生成样本平均逼近的样本。第二个研究目标是开发一个监督学习算法来估计一个紧的上界，以加快收敛的L形方法。这两个研究目标将通过五个任务来实现：（1）基于半监督学习的场景分组;（2）基于监督学习的代表性场景选择;（3）样本生成的性能分析;（4）基于监督学习的上限预测;（5）基于机器学习的L形方法的性能分析。该项目的成功将产生一种新的理论优化方法，促进灾害管理、供应链设计、医疗保健和收获规划等领域的各种实际应用。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

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.