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Probabilistic constrained optimization on flow networks

Schuster, Michael ; Strauch, Elisa ; Gugat, Martin ; Lang, Jens (2024)
Probabilistic constrained optimization on flow networks.
In: Optimization and Engineering, 2022, 23 (2)
doi: 10.26083/tuprints-00023486
Article, Secondary publication, Publisher's Version

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Item Type: Article
Type of entry: Secondary publication
Title: Probabilistic constrained optimization on flow networks
Language: English
Date: 30 April 2024
Place of Publication: Darmstadt
Year of primary publication: 2022
Place of primary publication: Dordrecht
Publisher: Springer Science
Journal or Publication Title: Optimization and Engineering
Volume of the journal: 23
Issue Number: 2
DOI: 10.26083/tuprints-00023486
Corresponding Links:
Origin: Secondary publication DeepGreen

Uncertainty often plays an important role in dynamic flow problems. In this paper, we consider both, a stationary and a dynamic flow model with uncertain boundary data on networks. We introduce two different ways how to compute the probability for random boundary data to be feasible, discussing their advantages and disadvantages. In this context, feasible means, that the flow corresponding to the random boundary data meets some box constraints at the network junctions. The first method is the spheric radial decomposition and the second method is a kernel density estimation. In both settings, we consider certain optimization problems and we compute derivatives of the probabilistic constraint using the kernel density estimator. Moreover, we derive necessary optimality conditions for an approximated problem for the stationary and the dynamic case. Throughout the paper, we use numerical examples to illustrate our results by comparing them with a classical Monte Carlo approach to compute the desired probability.

Uncontrolled Keywords: Probabilistic constraints, Uncertain boundary data, Spheric radial decomposition, Kernel density estimation, Gas networks, Contamination of water
Status: Publisher's Version
URN: urn:nbn:de:tuda-tuprints-234866
Classification DDC: 500 Science and mathematics > 510 Mathematics
Divisions: DFG-Collaborative Research Centres (incl. Transregio) > Transregios > TRR 154 Mathematical Modelling, Simulation and Optimization using the Example of Gas Networks
04 Department of Mathematics > Numerical Analysis and Scientific Computing
Date Deposited: 30 Apr 2024 12:49
Last Modified: 30 Apr 2024 12:50
SWORD Depositor: Deep Green
URI: https://tuprints.ulb.tu-darmstadt.de/id/eprint/23486
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