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A graph-based modeling abstraction for optimization: concepts and implementation in Plasmo.jl

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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 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.

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Data Availability Statement

The most recent code and data required to run the case studies is available at https://github.com/plasmo-dev/PlasmoExamples. The original data used for this manuscript is at https://1194doi.org/10.5281/zenodo.6626409.

Code Availability

The full code is open source and is publicly available. Additional packages used in this manuscript are either open source or available for academic use. Specific references are included in this published article.

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Acknowledgements

The authors acknowledge Yankai Cao from the University of British Columbia for his work developing the original PIPS-NLP interface for Plasmo.jl. The authors also acknowledge Michel Schanen from Argonne National Laboratory for his assistance using and debugging PIPS-NLP as well as Kibaek Kim from Argonne National Laboratory for his help in the conceptualization of Plasmo.jl. The authors also wish to thank the associate editor and the three anonymous reviewers, whose insightful comments helped to improve the manuscript.

Funding

This material is based on work supported by the U.S. Department of Energy (DOE), Office of Science, under Contract No. DE-AC02-06CH11357 as well as the DOE Office of Electricity Delivery and Energy Reliability’s Advanced Grid Research and Development program (AGR &D). This work was also partially supported by the U.S. Department of Energy Grant DE-SC0014114. We also acknowledge partial support from the National Science Foundation under award NSF-EECS-1609183.

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  1. Department of Chemical and Biological Engineering, University of Wisconsin-Madison, 1415 Engineering Dr, Madison, WI, 53706, USA

    Jordan Jalving, Sungho Shin & Victor M. Zavala

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  1. Jordan Jalving
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Jalving, J., Shin, S. & Zavala, V.M. A graph-based modeling abstraction for optimization: concepts and implementation in Plasmo.jl. Math. Prog. Comp. 14, 699–747 (2022). https://doi.org/10.1007/s12532-022-00223-3

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