Robust Optimal Discrete Arc Sizing for Tree-Shaped Potential Networks

Submission Status:Published
  • 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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Author:Martin Robinius, Lars Schewe, Martin Schmidt, Detlef Stolten, Johannes Thürauf, Lara Welder
Parent Title (German):Computational Optimization and Applications
Document Type:Article
Date of Publication (online):2018/02/01
Date of first Publication:2018/02/01
Release Date:2018/02/01
Tag:Discrete arc sizing; Mixed-integer linear optimization; Potential networks; Robust optimization; Scenario generation
Page Number:29
First Page:791
Last Page:819
Institutes:Friedrich-Alexander-Universität Erlangen-Nürnberg
Forschungszentrum Jülich
Universität Trier
Licence (German):License LogoCreative Commons - CC BY - Namensnennung 4.0 International