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A primal heuristic for optimizing the topology of gas networks based on dual information

  • Original Paper
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EURO Journal on Computational Optimization

Abstract

We present a novel heuristic to identify feasible solutions of a mixed-integer nonlinear programming problem arising in natural gas transportation: the selection of new pipelines to enhance the network’s capacity to a desired level in a cost-efficient way. We solve this problem in a linear programming based branch-and-cut approach, where we deal with the nonlinearities by linear outer approximation and spatial branching. At certain nodes of the branching tree, we compute a KKT point of a nonlinear relaxation. Based on the information from the KKT point we alter some of the binary variables in a locally promising way exploiting our problem-specific structure. On a test set of real-world instances, we are able to increase the chance of identifying feasible solutions by some order of magnitude compared to standard MINLP heuristics that are already built in the general-purpose MINLP solver SCIP.

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Acknowledgments

We are grateful to Open Grid Europe GmbH (OGE, Essen/Germany) for supporting our work. Armin Fügenschuh conducted parts of this research under a Konrad-Zuse-Fellowship. We thank two anonymous referees for carefully reading our manuscript and their various comments helping us to improve its quality.

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Authors and Affiliations

  1. Zuse Institute Berlin, Takustr. 7, 14195, Berlin, Germany

    Jesco Humpola & Thomas Lehmann

  2. Helmut Schmidt University, University of the Federal Armed Forces Hamburg, Holstenhofweg 85, 22043, Hamburg, Germany

    Armin Fügenschuh

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  1. Jesco Humpola
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  2. Armin Fügenschuh
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  3. Thomas Lehmann
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Correspondence to Armin Fügenschuh.

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Humpola, J., Fügenschuh, A. & Lehmann, T. A primal heuristic for optimizing the topology of gas networks based on dual information. EURO J Comput Optim 3, 53–78 (2015). https://doi.org/10.1007/s13675-014-0029-0

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  • DOI: https://doi.org/10.1007/s13675-014-0029-0

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