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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Abstract
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.
| Item Type: | Article |
|---|---|
| Erschienen: | 2024 |
| Creators: | Schuster, Michael ; Strauch, Elisa ; Gugat, Martin ; Lang, Jens |
| 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 |
| URL / URN: | https://tuprints.ulb.tu-darmstadt.de/23486 |
| Corresponding Links: | |
| Origin: | Secondary publication DeepGreen |
| Abstract: | 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) DFG-Collaborative Research Centres (incl. Transregio) > Transregios DFG-Collaborative Research Centres (incl. Transregio) > Transregios > TRR 154 Mathematical Modelling, Simulation and Optimization using the Example of Gas Networks 04 Department of Mathematics 04 Department of Mathematics > Numerical Analysis and Scientific Computing |
| Date Deposited: | 30 Apr 2024 12:49 |
| Last Modified: | 13 May 2024 09:09 |
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