Robust optimal discrete arc sizing for tree-shaped potential networks

Martin Robinius, Lars Schewe, Martin Schmidt (), Detlef Stolten, Johannes Thürauf and Lara Welder
Additional contact information
Martin Robinius: Forschungszentrum Jülich GmbH
Lars Schewe: Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU)
Martin Schmidt: Energie Campus Nürnberg
Detlef Stolten: Forschungszentrum Jülich GmbH
Johannes Thürauf: Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU)
Lara Welder: Forschungszentrum Jülich GmbH

Computational Optimization and Applications, 2019, vol. 73, issue 3, No 3, 819 pages

Abstract: Abstract 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.

Keywords: Discrete arc sizing; Network design; Potential networks; Scenario generation; Robust optimization; Mixed-integer linear optimization; 90-08; 90B10; 90C11; 90C35; 90C90 (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (12)

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DOI: 10.1007/s10589-019-00085-x

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