Sufficient pruning conditions for MINLP in gas network design

  • Jesco Humpola
  • Felipe Serrano
Original Paper


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.


Network design Mixed-integer nonlinear programming Infeasibility detection 

Mathematics Subject Classification

90C11 90C26 90C30 90C90 



The authors thank two anonymous referees for carefully reading the manuscript and their various comments helping to improve its quality. They thank all members of the Forschungskooperation Netzoptimierung (ForNe) for supporting this work. Jesco Humpola was supported by Open Grid Europe GmbH (OGE, Essen/Germany). Felipe Serrano was supported by the Research Campus Modal “Mathematical Optimization and Data Analysis Laboratories” funded by the German Ministry of Education and Research (BMBF Grant 05M14ZAM).


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Copyright information

© EURO - The Association of European Operational Research Societies 2016

Authors and Affiliations

  1. 1.Zuse Institute BerlinBerlinGermany

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