EURO Journal on Computational Optimization

, Volume 3, Issue 1, pp 53–78 | Cite as

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

  • Jesco Humpola
  • Armin FügenschuhEmail author
  • Thomas Lehmann
Original Paper


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.


Mixed-integer nonlinear programming Relaxations Heuristics Duality Nonlinear network design applications 

Mathematics Subject Classification

90-xx Mathematical Programming Operations Research 



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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Copyright information

© EURO - The Association of European Operational Research Societies 2014

Authors and Affiliations

  • Jesco Humpola
    • 1
  • Armin Fügenschuh
    • 2
    Email author
  • Thomas Lehmann
    • 1
  1. 1.Zuse Institute BerlinBerlinGermany
  2. 2.Helmut Schmidt University, University of the Federal Armed Forces HamburgHamburgGermany

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