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Sufficient pruning conditions for MINLP in gas network design

Author

Listed:
  • Jesco Humpola

    (Zuse Institute Berlin)

  • Felipe Serrano

    (Zuse Institute Berlin)

Abstract

One-quarter of Europe’s energy demand is provided by natural gas distributed through a vast pipeline network covering the whole of Europe. At a cost of 1 million Euros per kilometer the extension of the European pipeline network is already a multi-billion Euro business. Therefore, automatic planning tools that support the decision process are desired. We model the topology optimization problem in gas networks by a mixed-integer nonlinear program (MINLP). This gives rise to a so-called active transmission problem, a continuous nonlinear non-convex feasibility problem which emerges from the MINLP model by fixing all integral variables. We offer novel sufficient conditions for proving the infeasibility of this active transmission problem. These conditions can be expressed in the form of a mixed-integer program (MILP), i.e., the infeasibility of a non-convex continuous nonlinear program (NLP) can be certified by solving an MILP. This result provides an efficient pruning procedure in a branch-and-bound algorithm. Our computational results demonstrate a substantial speedup for the necessary computations.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:eurjco:v:5:y:2017:i:1:d:10.1007_s13675-016-0077-8
    DOI: 10.1007/s13675-016-0077-8
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    References listed on IDEAS

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    1. 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.
    2. 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).
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    4. 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).
    5. 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.
    6. Richard P. O'Neill & Mark Williard & Bert Wilkins & Ralph Pike, 1979. "A Mathematical Programming Model for Allocation of Natural Gas," Operations Research, INFORMS, vol. 27(5), pages 857-873, October.
    7. Ruth Misener & Christodoulos A. Floudas, 2014. "A Framework for Globally Optimizing Mixed-Integer Signomial Programs," Journal of Optimization Theory and Applications, Springer, vol. 161(3), pages 905-932, June.
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