A Julia Framework for Graph-Structured Nonlinear Optimization,Industrial & Engineering Chemistry Research

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A Julia Framework for Graph-Structured Nonlinear Optimization
Industrial & Engineering Chemistry Research ( IF 3.8 ) Pub Date : 2022-06-21 , DOI: 10.1021/acs.iecr.2c01253
David L. Cole ₁ , Sungho Shin ₂ , Victor M. Zavala

Affiliation

Graph theory provides a convenient framework for modeling and solving structured optimization problems. Under this framework, the modeler can arrange/assemble the components of an optimization model (variables, constraints, objective functions, and data) within nodes and edges of a graph, and this representation can be used to visualize, manipulate, and solve the problem. In this work, we present a Julia framework for modeling and solving graph-structured nonlinear optimization problems. Our framework integrates the modeling package Plasmo.jl (which facilitates the construction and manipulation of graph models) and the nonlinear optimization solver MadNLP.jl (which provides capabilities for exploiting graph structures to accelerate solution). We illustrate with a simple example how model construction and manipulation can be performed in an intuitive manner using Plasmo.jl and how the model structure can be exploited by MadNLP.jl. We also demonstrate the scalability of the framework by targeting a large-scale, stochastic gas network problem that contains over 1.7 million variables.

中文翻译：

图结构非线性优化的 Julia 框架

图论为建模和解决结构化优化问题提供了一个方便的框架。在这个框架下，建模者可以在图的节点和边内安排/组装优化模型的组件（变量、约束、目标函数和数据），并且这种表示可以用于可视化、操作和解决问题. 在这项工作中，我们提出了一个用于建模和解决图结构非线性优化问题的Julia框架。我们的框架集成了建模包Plasmo.jl（有助于构建和操作图模型）和非线性优化求解器MadNLP.jl（它提供了利用图结构来加速解决方案的能力）。我们通过一个简单的示例说明如何使用Plasmo.jl以直观的方式执行模型构建和操作，以及MadNLP.jl如何利用模型结构。我们还通过针对包含超过 170 万个变量的大规模随机气体网络问题来展示框架的可扩展性。

更新日期：2022-06-21

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