Robust optimal discrete arc sizing for tree-shaped potential networks

Robinius M, Schewe L, Schmidt M, Stolten D, Thürauf J, Welder L (2019)

Publication Language: English

Publication Type: Journal article

Publication year: 2019

Journal

Computational Optimization and Applications Springer Verlag (Germany)

DOI: 10.1007/s10589-019-00085-x

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.

Authors with CRIS profile

Lars Schewe Economics - Discrete Optimization - Mathematics (EDOM) Martin Schmidt Juniorprofessur für Optimierung von Energiesystemen Johannes Thürauf Economics - Discrete Optimization - Mathematics (EDOM)

Related research project(s)

Energiemarktdesign (EMD) Energie Campus Nürnberg (EnCN2) Jan. 1, 2017 - Dec. 31, 2021 Welfare optimal nominations in gas networks and associated equilibria SFB TRR 154 “Mathematische Modellierung, Simulation und Optimierung am Beispiel von Gasnetzen” Oct. 1, 2016 - June 30, 2018 Adaptive MIP-Relaxations for MINLPs (B07) (2014 - 2018) TRR 154: Mathematical Modelling, Simulation and Optimisation Using the Example of Gas Networks (TRR 154) Oct. 1, 2014 - Oct. 1, 2017

Involved external institutions

Forschungszentrum Jülich / Research Centre Jülich (FZJ) DE Germany (DE)

How to cite

APA:

Robinius, M., Schewe, L., Schmidt, M., Stolten, D., Thürauf, J., & Welder, L. (2019). Robust optimal discrete arc sizing for tree-shaped potential networks. Computational Optimization and Applications. https://doi.org/10.1007/s10589-019-00085-x

MLA:

Robinius, Martin, et al. "Robust optimal discrete arc sizing for tree-shaped potential networks." Computational Optimization and Applications (2019).

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