Journal
COMPUTATIONAL OPTIMIZATION AND APPLICATIONS
Volume 73, Issue 3, Pages 791-819Publisher
SPRINGER
DOI: 10.1007/s10589-019-00085-x
Keywords
Discrete arc sizing; Network design; Potential networks; Scenario generation; Robust optimization; Mixed-integer linear optimization; 90-08; 90B10; 90C11; 90C35; 90C90
Funding
- Deutsche Forschungsgemeinschaft [Sonderforschungsbereich/Transregio 154]
- Bavarian State Government
- Emerging Field Initiative (EFI) of the Friedrich-Alexander-Universitat Erlangen-Nurnberg through the project Sustainable Business Models in Energy Markets
- Helmholtz Association under the Joint Initiative EnergySystem 2050-A Contribution of the Research Field Energy
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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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