CAREER: Machine Learning Based 4D Decomposition and Distributed Optimization

分布式优化在包括电力系统在内的工程系统中有着广泛的应用。虽然文献中已经提出了分布式算法，但对于空间和时间等多维基础上的优化问题的分解，综合框架是不完整的。此外，由于分解、协调和建模步骤方面的不足和挑战，现有的大多数算法缺乏可扩展性，当应用于大型现实世界问题时，计算代价很高。该方案的重点是可伸缩分布式优化的基础研究。提出了几种机器学习与数学模型和方法相结合的方法，以创建用于电力系统运行和规划的高度可扩展、快速和高效的四维分布式优化算法。该项目将涉及不同的学生，特别是代表不足的少数民族，并显著改善工程教育、STEM课程、劳动力培训和K12学生参与工程教育的情况。这项研究将建立机器学习和基于数学的分解和分布式算法，不仅改革电力系统运行和规划，而且开辟新的研究途径，解决分布式优化的计算缺陷。通过这个项目，将开发一个时间分解，然后将创建一个全面的四维分解。将开发基于机器学习的策略来最优地分解优化问题。此外，还将设计学习和数学方法来创建高效和可扩展的异步分布式算法。为了进一步降低计算成本，提出了利用分类和回归技术来缩小优化问题的可行空间的迭代方法。此外，项目组将开发方法，使分布式算法对优化变量和目标函数的初始值的选择具有健壮性，并将设计创新的信息共享方法，以降低计算复杂性并提高所提出的算法在集成到电力系统运行和规划中时的准确性。项目团队将在各种综合测试系统和数据集以及现实世界的实际电网上实施开发的模型和算法。该项目由ECCS部门/EPCN计划和既定的激励竞争研究计划(EPSCoR)联合资助。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

Distributed optimization arises in a broad range of applications in engineering systems, including electric power systems. While distributed algorithms have been proposed in the literature, comprehensive frameworks are incomplete for decomposing optimization problems on a multi-dimensional basis, such as space and time. In addition, because of deficiencies and challenges in decomposition, coordination, and modeling steps, the majority of existing algorithms suffer from lack of scalability and become computationally expensive when applied to large real-world problems. This proposal focuses on fundamental research on scalable distributed optimization. Several combined machine learning and mathematical models and methods are proposed to create highly scalable, fast, and efficient four-dimensional distributed optimization algorithms for power systems operation and planning. The project will involve diverse students, particularly underrepresented minorities, and significantly improve engineering education, STEM curriculum, workforce training, and K12 students involvement in engineering education.This research will establish machine learning and mathematical-based decomposition and distributed algorithms, which not only reform power system operation and planning but also open new avenues of research to solve computational deficiencies of distributed optimization. Through this project, a temporal decomposition will be developed, and then a comprehensive four-dimensional decomposition will be created. Machine learning-based strategies will be developed to optimally decompose optimization problems. In addition, learning and mathematical approaches will be devised to create highly efficient and scalable asynchronous distributed algorithms. To further reduce computational costs, iterative methods are proposed to reduce the feasible space of optimization problems taking advantage of classification and regression techniques. Furthermore, the project team will develop methods to make distributed algorithms robust against the choice of initial values of optimization variables and objective functions and will devise innovative information-sharing approaches to reduce the computational complexity and enhance the accuracy of the proposed algorithms when integrated into power system operation and planning. The project team will implement the developed models and algorithms on various synthetic test systems and data sets, as well as real-world practical power grids.This project is jointly funded by the ECCS division / EPCN program and the Established Program to Stimulate Competitive Research (EPSCOR).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.