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A Consensus-Based Alternating Direction Method for Mixed-Integer and PDE-Constrained Gas Transport Problems

Author

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  • Richard Krug

    (Department of Data Science, Friedrich-Alexander-Universität Erlangen-Nürnberg, 91058 Erlangen, Germany)

  • Günter Leugering

    (Department of Data Science, Friedrich-Alexander-Universität Erlangen-Nürnberg, 91058 Erlangen, Germany)

  • Alexander Martin

    (Department of Liberal Arts and Sciences, University of Technology Nuremberg, D-90443 Nürnberg, Germany)

  • Martin Schmidt

    (Department of Mathematics, Trier University, 54296 Trier, Germany)

  • Dieter Weninger

    (Department of Data Science, Friedrich-Alexander-Universität Erlangen-Nürnberg, 91058 Erlangen, Germany)

Abstract

We consider dynamic gas transport optimization problems, which lead to large-scale and nonconvex mixed-integer nonlinear optimization problems (MINLPs) on graphs. Usually, the resulting instances are too challenging to be solved by state-of-the-art MINLP solvers. In this paper, we use graph decompositions to obtain multiple optimization problems on smaller blocks, which can be solved in parallel and may result in simpler classes of optimization problems because not every block necessarily contains mixed-integer or nonlinear aspects. For achieving feasibility at the interfaces of the several blocks, we employ a tailored consensus-based penalty alternating direction method. Our numerical results show that such decomposition techniques can outperform the baseline approach of just solving the overall MINLP from scratch. However, a complete answer to the question of how to decompose MINLPs on graphs in dependence of the given model is still an open topic for future research.

Suggested Citation

  • Richard Krug & Günter Leugering & Alexander Martin & Martin Schmidt & Dieter Weninger, 2024. "A Consensus-Based Alternating Direction Method for Mixed-Integer and PDE-Constrained Gas Transport Problems," INFORMS Journal on Computing, INFORMS, vol. 36(2), pages 397-416, March.
    • Handle: RePEc:inm:orijoc:v:36:y:2024:i:2:p:397-416
    DOI: 10.1287/ijoc.2022.0319
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    References listed on IDEAS

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    1. Björn Geißler & Antonio Morsi & Lars Schewe & Martin Schmidt, 2018. "Solving Highly Detailed Gas Transport MINLPs: Block Separability and Penalty Alternating Direction Methods," INFORMS Journal on Computing, INFORMS, vol. 30(2), pages 309-323, May.
    2. Daniel Rose & Martin Schmidt & Marc C. Steinbach & Bernhard M. Willert, 2016. "Computational optimization of gas compressor stations: MINLP models versus continuous reformulations," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 83(3), pages 409-444, June.
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