A Graph-Based Modeling Abstraction for Optimization: Concepts and Implementation in Plasmo.jl

Abstract

We present a general graph-based modeling abstraction for optimization that we call an OptiGraph. Under this abstraction, any optimization problem is treated as a hierarchical hypergraph in which nodes represent optimization subproblems and edges represent connectivity between such subproblems. The abstraction enables the modular construction of highly complex models in an intuitive manner, facilitates the use of graph analysis tools (to perform partitioning, aggregation, and visualization tasks), and facilitates communication of structures to decomposition algorithms. We provide an open-source implementation of the abstraction in the Julia-based package Plasmo.jl. We provide tutorial examples and large application case studies to illustrate the capabilities.

A Julia Framework for Graph-Structured Nonlinear Optimization

“…The complexity of such problems continuously pushes the boundary of existing computational tools and limits application scope. To overcome these challenges, it is necessary to develop tools that can facilitate the detection, manipulation, and exploitation of problem structure [6,10,11,12,16,35,38,39].…”

“…Recently, it has been proposed to represent optimization problem structures in the form of graphs [1,3,7,15,16,22,23,24,33]. Under a graph representation, the components of an optimization problem (variables, constraints, and objectives) are assigned to nodes and edges [16,31].…”

“…Recently, it has been proposed to represent optimization problem structures in the form of graphs [1,3,7,15,16,22,23,24,33]. Under a graph representation, the components of an optimization problem (variables, constraints, and objectives) are assigned to nodes and edges [16,31]. Representing the problem structure as a graph has several benefits; specifically, the graph structure can be used to visualize and manipulate the model (e.g., graph partitioning) using powerful tools such as Metis [19] or KaHyPar [28].…”

“…There are currently a few software frameworks that enable the construction and solution of structured optimization problems: Pyomo (available in Python) [13,14], the Graph-Based Optimization Modeling Language, GBOML [3,4], and Plasmo.jl (available in Julia) [16]. Pyomo uses a modeling extension called a "network" to model structured optimization problems; this approach creates ports (collections of variables) with arcs placed to link objects on separate ports.…”

Graph-Based Modeling and Decomposition of Energy Infrastructures

“…Large-scale NLPs arising in infrastructures have the key characteristic that they exhibit structures in the form of sparsely connected graphs; we refer to such problems as graph-structured optimization problems (Jalving et al, 2019;Shin et al, 2020b;Jalving et al, 2020). Graphstructured problems can be conveniently modeled by using specialized modeling platforms such as Plasmo.jl (Jalving et al, 2019(Jalving et al, , 2020 and solved by using structure-exploiting optimization solvers such as PIPS-NLP (Chiang et al, 2014)). Plasmo.jl is a graph-based modeling platform that enables the modular construction and analysis of highly complex models; this platform also leverages the We acknowledge support from the Grainger Wisconsin Distinguished Graduate Fellowship.…”