(Platform for Scalable Modeling and Optimization)

Plasmo.jl is a graph-based algebraic modeling framework for building, managing, and solving optimization problems that utilizes graph-theoretic concepts and modular data structures. The package extends JuMP.jl to offer concise syntax, interfaces with MathOptInterface.jl to access standard optimization solvers, and utilizes Graphs.jl to provide graph analysis and processing methods. Plasmo.jl facilitates developing optimization models for networked systems such as supply chains, power systems, industrial processes, or any coupled system that involves multiple components and connections. The package also acts as a high-level platform to develop customized optimization-based decomposition techniques and meta-algorithms to optimize problems over large systems.

The core object in Plasmo.jl is the OptiGraph, a graph data structure that represents optimization problems as a set of optinodes and optiedges. Optinodes encapsulate variables, expressions, and constraints (and objective functions) as modular models and edges encapsulate linking constraints that couple variables across optinodes. Optigraphs can be embedded within other optigraphs to induce nested hierarchical structures, or they can be partitioned using different graph projections and partitioning algorithms to create new decomposition structures.

The core data structure in Plasmo.jl is the OptiGraph. The optigraph contains a set of optinodes which represent self-contained optimization problems and optiedges that represent coupling between optinodes (which produces an underlying hypergraph structure of optinodes and optiedges). Optigraphs can further be embedded within other optigraphs to create nested hierarchical graph structures. The graph structures obtained using Plasmo.jl can be used for simple model and data management, but they can also be used to perform graph partitioning or develop interfaces to structured optimization solvers.

Plasmo.jl is licensed under the MPL 2.0 license.

Install Plasmo using Pkg.add:

import Pkg
Pkg.add("Plasmo")

The current documentation is available through GitHub Pages. Additional examples can be found in the examples folder.

using Plasmo
using Ipopt

#create an optigraph
graph = OptiGraph()

#add nodes to an optigraph
@optinode(graph, n1)
@optinode(graph, n2)

#add variables and constraints to nodes
@variable(n1, 0 <= x <= 2)
@variable(n1, 0 <= y <= 3)
@constraint(n1, x+y <= 4)

@variable(n2,x)
@constraint(n2, exp(x) >= 2)

#add linking constraints that couple nodes
@linkconstraint(graph, n1[:x] == n2[:x])

# set an optigraph objective
@objective(graph, Min, n1[:x] + n2[:x])

#optimize with Ipopt
set_optimizer(graph, Ipopt.Optimizer)
optimize!(graph)

#Print solution values
println("n1[:x] = ", value(n1[:x]))
println("n2[:x] = ", value(n2[:x]))

This code is based on work supported by the following funding agencies:

• U.S. Department of Energy (DOE), Office of Science, under Contract No. DE-AC02-06CH11357
• DOE Office of Electricity Delivery and Energy Reliability’s Advanced Grid Research and Development program at Argonne National Laboratory
• National Science Foundation under award NSF-EECS-1609183 and under award CBET-1748516

The primary developer is Jordan Jalving (@jalving) with support from the following contributors.

• Victor Zavala (University of Wisconsin-Madison)
• Yankai Cao (University of British Columbia)
• Kibaek Kim (Argonne National Laboratory)
• Sungho Shin (University of Wisconsin-Madison)

If you find Plasmo.jl useful for your work, you may cite the manuscript as:

@article{Jalving2022,
  title={A Graph-Based Modeling Abstraction for Optimization: Concepts and Implementation in Plasmo.jl},
  author={Jordan Jalving and Sungho Shin and Victor M. Zavala},
  journal={Mathematical Programming Computation},
  year={2022},
  volume={14},
  pages={699 - 747},
  doi={10.1007/s12532-022-00223-3}
}

You can also access a freely available pre-print.

There is also an earlier manuscript where we presented the initial ideas behind Plasmo.jl which you can find here:

@article{JalvingCaoZavala2019,
author = {Jalving, Jordan and Cao, Yankai and Zavala, Victor M},
journal = {Computers {\&} Chemical Engineering},
pages = {134--154},
title = {Graph-based modeling and simulation of complex systems},
volume = {125},
year = {2019},
doi = {10.1016/j.compchemeng.2019.03.009}
}

A pre-print of this paper can be found here