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Solving Highly Detailed Gas Transport MINLPs: Block Separability and Penalty Alternating Direction Methods

Author

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  • Björn Geißler

    (Friedrich-Alexander-Universität Erlangen-Nürnberg, Discrete Optimization, 91058 Erlangen, Germany)

  • Antonio Morsi

    (Friedrich-Alexander-Universität Erlangen-Nürnberg, Discrete Optimization, 91058 Erlangen, Germany)

  • Lars Schewe

    (Friedrich-Alexander-Universität Erlangen-Nürnberg, Discrete Optimization, 91058 Erlangen, Germany)

  • Martin Schmidt

    (Friedrich-Alexander-Universität Erlangen-Nürnberg, Discrete Optimization, 91058 Erlangen, Germany; Energie Campus Nürnberg, 90429 Nürnberg, Germany)

Abstract

Detailed modeling of gas transport problems leads to nonlinear and nonconvex mixed-integer optimization or feasibility models (MINLPs) because both the incorporation of discrete controls of the network and accurate physical and technical modeling are required to achieve practical solutions. Hence, ignoring certain parts of the physics model is not valid for practice. In the present contribution we extend an approach based on linear relaxations of the underlying nonlinearities by tailored model reformulation techniques yielding block-separable MINLPs. This combination of techniques allows us to apply a penalty alternating direction method and thus to solve highly detailed MINLPs for large-scale, real-world instances. The practical strength of the proposed method is demonstrated by a computational study in which we apply the method to instances from steady-state gas transport including both pooling effects with respect to the mixing of gases of different composition and a highly detailed compressor station model.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:orijoc:v:30:y:2018:i:2:p:309-323
    DOI: 10.1287/ijoc.2017.0780
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    References listed on IDEAS

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    1. 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.
    2. Jochen Gorski & Frank Pfeuffer & Kathrin Klamroth, 2007. "Biconvex sets and optimization with biconvex functions: a survey and extensions," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 66(3), pages 373-407, December.
    3. Richard E. Wendell & Arthur P. Hurter, 1976. "Minimization of a Non-Separable Objective Function Subject to Disjoint Constraints," Operations Research, INFORMS, vol. 24(4), pages 643-657, August.
    4. Björn Geißler & Oliver Kolb & Jens Lang & Günter Leugering & Alexander Martin & Antonio Morsi, 2011. "Mixed integer linear models for the optimization of dynamical transport networks," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 73(3), pages 339-362, June.
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    Citations

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    Cited by:

    1. Lars Schewe & Martin Schmidt & Johannes Thürauf, 2020. "Computing technical capacities in the European entry-exit gas market is NP-hard," Annals of Operations Research, Springer, vol. 295(1), pages 337-362, December.
    2. Wang, Guotao & Zhao, Wei & Qiu, Rui & Liao, Qi & Lin, Zhenjia & Wang, Chang & Zhang, Haoran, 2023. "Operational optimization of large-scale thermal constrained natural gas pipeline networks: A novel iterative decomposition approach," Energy, Elsevier, vol. 282(C).
    3. 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.
    4. Lars Schewe & Martin Schmidt & Johannes Thürauf, 2020. "Structural properties of feasible bookings in the European entry–exit gas market system," 4OR, Springer, vol. 18(2), pages 197-218, June.
    5. Wen, Kai & Qiao, Dan & Nie, Chaofei & Lu, Yangfan & Wen, Feng & Zhang, Jing & Miao, Qing & Gong, Jing & Li, Cuicui & Hong, Bingyuan, 2023. "Multi-period supply and demand balance of large-scale and complex natural gas pipeline network: Economy and environment," Energy, Elsevier, vol. 264(C).
    6. Mengying Xue & Tianhu Deng & Zuo‐Jun Max Shen, 2019. "Optimizing natural gas pipeline transmission with nonuniform elevation: A new initialization approach," Naval Research Logistics (NRL), John Wiley & Sons, vol. 66(7), pages 547-564, October.
    7. Carina Moreira Costa & Dennis Kreber & Martin Schmidt, 2022. "An Alternating Method for Cardinality-Constrained Optimization: A Computational Study for the Best Subset Selection and Sparse Portfolio Problems," INFORMS Journal on Computing, INFORMS, vol. 34(6), pages 2968-2988, November.
    8. Johannes Thürauf, 2022. "Deciding the feasibility of a booking in the European gas market is coNP-hard," Annals of Operations Research, Springer, vol. 318(1), pages 591-618, November.
    9. Benjamin Hiller & René Saitenmacher & Tom Walther, 2021. "Improved models for operation modes of complex compressor stations," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 94(2), pages 171-195, October.
    10. Falk M. Hante & Martin Schmidt, 2019. "Complementarity-based nonlinear programming techniques for optimal mixing in gas networks," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 7(3), pages 299-323, September.
    11. Thomas Kleinert & Martin Schmidt, 2021. "Computing Feasible Points of Bilevel Problems with a Penalty Alternating Direction Method," INFORMS Journal on Computing, INFORMS, vol. 33(1), pages 198-215, January.

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