Novel Decomposition Techniques Enabling Scalable Computational Frameworks for Large-Scale Nonlinear Optimization Problems

新颖的分解技术为大规模非线性优化问题提供可扩展的计算框架

• 批准号: 2012410
• 负责人: Andreas Waechter
• 金额: $ 18万
• 依托单位: Northwestern University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2020
• 资助国家: 美国
• 起止时间: 2020-09-01 至 2023-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2012410&HistoricalAwards=false
• 关键词: Novel; Decomposition; Techniques; Enabling; Scalable

This research project aims to develop improved numerical optimization algorithms. The research considers situations in which decisions must be made in the absence of perfect information, either due to the lack of reliable data or due to unforeseen events. Most state-of-the-art methods tackle optimization in this setting by considering many potential scenarios, which can result in formulations that are too large to be solved directly. The methodology in this project is fundamentally different and aims to create new decomposition frameworks for large-scale nonlinear continuous optimization. The algorithms under development will be tested on realistic questions in electrical power systems. For example, the decomposition algorithm will be able to break down the optimization of a large-scale power grid into computations for the high-voltage transmission grid and computations related to the many distribution networks that are attached to the transmission grid. This project provides research training opportunities for a graduate student.The project aims to create novel decomposition frameworks that lead to new practical numerical algorithms able to tackle significantly larger instances of certain structured problems in nonlinear nonconvex optimization than currently possible. This will result in computational tools for the solution of stochastic optimization problems when sample average approximation gives rise to very large deterministic instances and will significantly expand the array of tractable stochastic two-stage and bi-level optimization problems. The key innovation is a smoothing technique that overcomes the predicament that optimal subsystem solutions need not be differentiable functions of the overarching system variables. In all aspects of the research, theory will be developed that characterizes the properties of problem reformulations and the convergence guarantees for new algorithms. One expected outcome of this project is high-quality open-source software for public use, capable of exploiting parallel computing resources.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.

该研究项目旨在开发改进的数值优化算法。该研究考虑了由于缺乏可靠数据或由于不可预见的事件而必须在缺乏完美信息的情况下做出决策的情况。大多数最先进的方法通过考虑许多潜在场景来解决这种情况下的优化问题，这可能会导致公式太大而无法直接求解。该项目的方法根本不同，旨在为大规模非线性连续优化创建新的分解框架。正在开发的算法将在电力系统的实际问题上进行测试。例如，分解算法将能够将大规模电网的优化分解为高压输电网的计算和与输电网相连的许多配电网相关的计算。该项目为研究生提供研究培训机会。该项目旨在创建新颖的分解框架，从而产生新的实用数值算法，能够解决非线性非凸优化中某些结构化问题的比目前更大的实例。当样本平均近似产生非常大的确定性实例时，这将产生用于解决随机优化问题的计算工具，并将显着扩展可处理的随机两阶段和双层优化问题的范围。关键的创新是平滑技术，它克服了最优子系统解决方案不必是总体系统变量的可微函数的困境。在研究的各个方面，将发展表征问题重构的特性和新算法的收敛保证的理论。该项目的预期成果之一是供公众使用的高质量开源软件，能够利用并行计算资源。该奖项反映了 NSF 的法定使命，并通过使用基金会的智力优点和更广泛的影响审查标准进行评估，被认为值得支持。