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Robust optimal discrete arc sizing for tree-shaped potential networks


We consider the problem of discrete arc sizing for tree-shaped potential networks with respect to infinitely many demand scenarios. This means that the arc sizes need to be feasible for an infinite set of scenarios. The problem can be seen as a strictly robust counterpart of a single-scenario network design problem, which is shown to be NP-complete even on trees. In order to obtain a tractable problem, we introduce a method for generating a finite scenario set such that optimality of a sizing for this finite set implies the sizing’s optimality for the originally given infinite set of scenarios. We further prove that the size of the finite scenario set is quadratically bounded above in the number of nodes of the underlying tree and that it can be computed in polynomial time. The resulting problem can then be solved as a standard mixed-integer linear optimization problem. Finally, we show the applicability of our theoretical results by computing globally optimal arc sizes for a realistic hydrogen transport network of Eastern Germany.

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The authors thank the Deutsche Forschungsgemeinschaft for their support within Projects A05, B07, and B08 in the Sonderforschungsbereich/Transregio 154 “Mathematical Modelling, Simulation and Optimization using the Example of Gas Networks”. This research has been performed as part of the Energie Campus Nürnberg and is supported by funding of the Bavarian State Government and by the Emerging Field Initiative (EFI) of the Friedrich-Alexander-Universität Erlangen-Nürnberg through the project “Sustainable Business Models in Energy Markets”. Furthermore, this work has been supported by the Helmholtz Association under the Joint Initiative “EnergySystem 2050—A Contribution of the Research Field Energy”.

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Correspondence to Martin Schmidt.

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Robinius, M., Schewe, L., Schmidt, M. et al. Robust optimal discrete arc sizing for tree-shaped potential networks. Comput Optim Appl 73, 791–819 (2019).

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  • Discrete arc sizing
  • Network design
  • Potential networks
  • Scenario generation
  • Robust optimization
  • Mixed-integer linear optimization

Mathematics Subject Classification

  • 90-08
  • 90B10
  • 90C11
  • 90C35
  • 90C90