IDEAS home Printed from https://ideas.repec.org/a/spr/coopap/v62y2015i3p717-759.html
   My bibliography  Save this article

Convex reformulations for solving a nonlinear network design problem

Author

Abstract

We consider a nonlinear nonconvex network design problem that arises, for example, in natural gas or water transmission networks. Given is such a network with active and passive components, that is, valves, compressors, control valves (active) and pipelines (passive), and a desired amount of flow at certain specified entry and exit nodes in the network. The active elements are associated with costs when used. Besides flow conservation constraints in the nodes, the flow must fulfill nonlinear nonconvex pressure loss constraints on the arcs subject to potential values (i.e., pressure levels) in both end nodes of each arc. The problem is to compute a cost minimal setting of the active components and numerical values for the flow and node potentials. We examine different (convex) relaxations for a subproblem of the design problem and benefit from them within a branch-and-bound approach. We compare different approaches based on nonlinear optimization numerically on a set of test instances. Copyright Springer Science+Business Media New York 2015

Suggested Citation

  • Jesco Humpola & Armin Fügenschuh, 2015. "Convex reformulations for solving a nonlinear network design problem," Computational Optimization and Applications, Springer, vol. 62(3), pages 717-759, December.
    • Handle: RePEc:spr:coopap:v:62:y:2015:i:3:p:717-759
    DOI: 10.1007/s10589-015-9756-2
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10589-015-9756-2
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10589-015-9756-2?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. De Wolf, D. & Smeers, Y., 1996. "Optimal dimensioning of pipe networks with application to gas transmission networks," LIDAM Reprints CORE 1249, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Frédéric Babonneau & Yurii Nesterov & Jean-Philippe Vial, 2012. "Design and Operations of Gas Transmission Networks," Operations Research, INFORMS, vol. 60(1), pages 34-47, February.
    3. DE WOLF, Daniel & SMEERS, Yves, 2000. "The gas transmission problem solved by an extension of the simplex algorithm," LIDAM Reprints CORE 1489, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. Daniel de Wolf & Yves Smeers, 1996. "Optimal Dimensioning of Pipe Networks with Application to Gas Transmission Networks," Operations Research, INFORMS, vol. 44(4), pages 596-608, August.
    5. M. Collins & L. Cooper & R. Helgason & J. Kennington & L. LeBlanc, 1978. "Solving the Pipe Network Analysis Problem Using Optimization Techniques," Management Science, INFORMS, vol. 24(7), pages 747-760, March.
    6. Daniel De Wolf & Yves Smeers, 2000. "The Gas Transmission Problem Solved by an Extension of the Simplex Algorithm," Management Science, INFORMS, vol. 46(11), pages 1454-1465, November.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Filippo Pecci & Edo Abraham & Ivan Stoianov, 2017. "Penalty and relaxation methods for the optimal placement and operation of control valves in water supply networks," Computational Optimization and Applications, Springer, vol. 67(1), pages 201-223, May.
    2. Jesco Humpola & Felipe Serrano, 2017. "Sufficient pruning conditions for MINLP in gas network design," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 5(1), pages 239-261, March.
    3. Conrado Borraz-Sánchez & Russell Bent & Scott Backhaus & Hassan Hijazi & Pascal Van Hentenryck, 2016. "Convex Relaxations for Gas Expansion Planning," INFORMS Journal on Computing, INFORMS, vol. 28(4), pages 645-656, November.
    4. Martin Robinius & Lars Schewe & Martin Schmidt & Detlef Stolten & Johannes Thürauf & Lara Welder, 2019. "Robust optimal discrete arc sizing for tree-shaped potential networks," Computational Optimization and Applications, Springer, vol. 73(3), pages 791-819, July.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Ralf Lenz & Kai Helge Becker, 2022. "Optimization of capacity expansion in potential-driven networks including multiple looping: a comparison of modelling approaches," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 44(1), pages 179-224, March.
    2. 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.
    3. Liang, Yingzong & Hui, Chi Wai, 2018. "Convexification for natural gas transmission networks optimization," Energy, Elsevier, vol. 158(C), pages 1001-1016.
    4. Conrado Borraz-Sánchez & Russell Bent & Scott Backhaus & Hassan Hijazi & Pascal Van Hentenryck, 2016. "Convex Relaxations for Gas Expansion Planning," INFORMS Journal on Computing, INFORMS, vol. 28(4), pages 645-656, November.
    5. Jingkuan Han & Yingjun Xu & Dingzhi Liu & Yanfang Zhao & Zhongde Zhao & Shuhui Zhou & Tianhu Deng & Mengying Xue & Junchi Ye & Zuo-Jun Max Shen, 2019. "Operations Research Enables Better Planning of Natural Gas Pipelines," Interfaces, INFORMS, vol. 49(1), pages 23-39, January.
    6. Daniel de Wolf, 2017. "Mathematical Properties of Formulations of the Gas Transmission Problem," Post-Print halshs-02396747, HAL.
    7. repec:cty:dpaper:1464 is not listed on IDEAS
    8. Hong, Sung-Pil & Kim, Taegyoon & Lee, Subin, 2019. "A precision pump schedule optimization for the water supply networks with small buffers," Omega, Elsevier, vol. 82(C), pages 24-37.
    9. Dieckhoener, Caroline, 2010. "Simulating security of supply effects of the Nabucco and South Stream projects for the European natural gas market," EWI Working Papers 2010-7, Energiewirtschaftliches Institut an der Universitaet zu Koeln (EWI), revised 21 Jan 2012.
    10. Daniel de Wolf & Yves Smeers, 2021. "Generalized derivatives of the optimal value of a linear program with respect to matrix coefficients," Post-Print halshs-02396708, HAL.
    11. Frédéric Babonneau & Yurii Nesterov & Jean-Philippe Vial, 2012. "Design and Operations of Gas Transmission Networks," Operations Research, INFORMS, vol. 60(1), pages 34-47, February.
    12. Olivier Massol, 2011. "A Cost Function for the Natural Gas Transmission Industry: Further Considerations," The Engineering Economist, Taylor & Francis Journals, vol. 56(2), pages 95-122.
    13. Jesco Humpola & Felipe Serrano, 2017. "Sufficient pruning conditions for MINLP in gas network design," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 5(1), pages 239-261, March.
    14. De Wolf, Daniel & Smeers, Yves, 2021. "Generalized derivatives of the optimal value of a linear program with respect to matrix coefficients," European Journal of Operational Research, Elsevier, vol. 291(2), pages 491-496.
    15. Jesco Humpola & Armin Fügenschuh & Thorsten Koch, 2016. "Valid inequalities for the topology optimization problem in gas network design," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 38(3), pages 597-631, July.
    16. repec:cty:dpaper:10.1080/0013791x.2011.573615 is not listed on IDEAS
    17. Mikolajková, Markéta & Haikarainen, Carl & Saxén, Henrik & Pettersson, Frank, 2017. "Optimization of a natural gas distribution network with potential future extensions," Energy, Elsevier, vol. 125(C), pages 848-859.
    18. Mikolajková, Markéta & Saxén, Henrik & Pettersson, Frank, 2018. "Linearization of an MINLP model and its application to gas distribution optimization," Energy, Elsevier, vol. 146(C), pages 156-168.
    19. Massol, Olivier & Tchung-Ming, Stéphane & Banal-Estañol, Albert, 2015. "Joining the CCS club! The economics of CO2 pipeline projects," European Journal of Operational Research, Elsevier, vol. 247(1), pages 259-275.
    20. André, Jean & Auray, Stéphane & Brac, Jean & De Wolf, Daniel & Maisonnier, Guy & Ould-Sidi, Mohamed-Mahmoud & Simonnet, Antoine, 2013. "Design and dimensioning of hydrogen transmission pipeline networks," European Journal of Operational Research, Elsevier, vol. 229(1), pages 239-251.
    21. 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.
    22. Mengying Xue & Tianhu Deng & Dingzhi Liu, 2016. "CNPC Uses an Iterative Two-Stage Convex Relaxation Approach to Operate Natural Gas Pipelines," Interfaces, INFORMS, vol. 46(6), pages 533-546, December.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:coopap:v:62:y:2015:i:3:p:717-759. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.