A Julia Framework for Graph-Structured Nonlinear Optimization

TL;DR

This paper introduces a Julia-based framework that models and solves large-scale, graph-structured nonlinear optimization problems by integrating graph modeling and specialized solvers.

Contribution

The framework combines Plasmo.jl for graph modeling and MadNLP.jl for exploiting graph structures, enabling scalable solutions for complex optimization problems.

Findings

Successfully modeled a large-scale gas network with over 1.7 million variables.

Demonstrated the framework's ability to visualize and manipulate structured models.

Showcased improved solution efficiency by exploiting graph structures.

Abstract

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 ${\tt Julia}$ framework for modeling and solving graph-structured nonlinear optimization problems. Our framework integrates the modeling package ${\tt Plasmo.jl}$ (which facilitates the construction and manipulation of graph models) and the nonlinear optimization solver ${\tt MadNLP.jl}$ (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 ${\tt Plasmo.jl}$ and how the model structure can be exploited by ${\tt MadNLP.jl}$. We also demonstrate the scalability of the framework by targeting a large-scale, stochastic gas network problem that contains over 1.7 million variables.