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Robust Optimal Discrete Arc Sizing for Tree-Shaped Potential Networks

Martin Robinius (m.robinius***at***fz-juelich.de)
Lars Schewe (lars.schewe***at***fau.de)
Martin Schmidt (mar.schmidt***at***fau.de)
Detlef Stolten (d.stolten***at***fz-juelich.de)
Johannes Thürauf (johannes.thuerauf***at***fau.de)
Lara Welder (l.welder***at***fz-juelich.de)

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

Category 1: Robust Optimization

Category 2: Integer Programming ((Mixed) Integer Linear Programming )

Category 3: Applications -- Science and Engineering

Citation:

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Entry Submitted: 02/01/2018
Entry Accepted: 02/01/2018
Entry Last Modified: 10/10/2018

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