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Mixed integer linear models for the optimization of dynamical transport networks

Author

Listed:
  • Björn Geißler
  • Oliver Kolb
  • Jens Lang
  • Günter Leugering
  • Alexander Martin
  • Antonio Morsi

Abstract

We introduce a mixed integer linear modeling approach for the optimization of dynamic transport networks based on the piecewise linearization of nonlinear constraints and we show how to apply this method by two examples, transient gas and water supply network optimization. We state the mixed integer linear programs for both cases and provide numerical evidence for their suitability. Copyright Springer-Verlag 2011

Suggested Citation

  • 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.
    • Handle: RePEc:spr:mathme:v:73:y:2011:i:3:p:339-362
    DOI: 10.1007/s00186-011-0354-5
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    Citations

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    Cited by:

    1. Martin Gugat & Günter Leugering & Alexander Martin & Martin Schmidt & Mathias Sirvent & David Wintergerst, 2018. "MIP-based instantaneous control of mixed-integer PDE-constrained gas transport problems," Computational Optimization and Applications, Springer, vol. 70(1), pages 267-294, May.
    2. D’Ambrosio, Claudia & Lodi, Andrea & Wiese, Sven & Bragalli, Cristiana, 2015. "Mathematical programming techniques in water network optimization," European Journal of Operational Research, Elsevier, vol. 243(3), pages 774-788.
    3. Kazda, Kody & Li, Xiang, 2024. "A linear programming approach to difference-of-convex piecewise linear approximation," European Journal of Operational Research, Elsevier, vol. 312(2), pages 493-511.
    4. 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.
    5. Christoph Buchheim & Renke Kuhlmann & Christian Meyer, 2018. "Combinatorial optimal control of semilinear elliptic PDEs," Computational Optimization and Applications, Springer, vol. 70(3), pages 641-675, July.
    6. 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.
    7. Bonvin, Gratien & Demassey, Sophie & Le Pape, Claude & Maïzi, Nadia & Mazauric, Vincent & Samperio, Alfredo, 2017. "A convex mathematical program for pump scheduling in a class of branched water networks," Applied Energy, Elsevier, vol. 185(P2), pages 1702-1711.
    8. Steffen Rebennack, 2016. "Computing tight bounds via piecewise linear functions through the example of circle cutting problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 84(1), pages 3-57, August.
    9. Er-Rahmadi, Btissam & Ma, Tiejun, 2022. "Data-driven mixed-Integer linear programming-based optimisation for efficient failure detection in large-scale distributed systems," European Journal of Operational Research, Elsevier, vol. 303(1), pages 337-353.

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