论文标题
基于图的建模和能源基础设施的分解
Graph-Based Modeling and Decomposition of Energy Infrastructures
论文作者
论文摘要
非线性优化问题是关键基础设施的实时操作的核心。这些问题在计算上具有挑战性，因为它们嵌入了表现出时空动力学的复杂物理模型。我们建议将这些问题建模为图形结构化优化问题，并说明如何在建模级别（用于并行化函数/导数计算）和求解器级别（用于并行化线性代数操作）上利用它们的结构。具体而言，我们提出了一个受限制的加性Schwarz方案，该方案能够在内点算法中灵活地分解复杂的图形结构。所提出的方法是作为通用的非线性编程求解器实施的，我们称为madnlp.jl；该基于朱莉娅的求解器与基于图的建模软件包Plasmo.jl连接。通过在瞬态气体网络优化和多周期AC最佳功率流中引起的问题来证明该框架的效率。我们表明，我们的框架可以加速解决方案（与现成工具相比）超过300％；具体而言，解决气体问题的溶液时间从72.36秒减少到23.84秒，从515.81秒降低到功率流问题的149.45秒。
Nonlinear optimization problems are found at the heart of real-time operations of critical infrastructures. These problems are computationally challenging because they embed complex physical models that exhibit space-time dynamics. We propose modeling these problems as graph-structured optimization problems, and illustrate how their structure can be exploited at the modeling level (for parallelizing function/derivative computations) and at the solver level (for parallelizing linear algebra operations). Specifically, we present a restricted additive Schwarz scheme that enables flexible decomposition of complex graph structures within an interior-point algorithm. The proposed approach is implemented as a general-purpose nonlinear programming solver that we call MadNLP.jl; this Julia-based solver is interfaced to the graph-based modeling package Plasmo.jl. The efficiency of this framework is demonstrated via problems arising in transient gas network optimization and multi-period AC optimal power flow. We show that our framework accelerates the solution (compared to off-the-shelf tools) by over 300%; specifically, solution times are reduced from 72.36 sec to 23.84 sec for the gas problem and from 515.81 sec to 149.45 sec for the power flow problem.
