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
Artikel, Zweitveröffentlichung, Verlagsversion
 | Es ist eine neuere Version dieses Eintrags verfügbar. |
Kurzbeschreibung (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.
| Typ des Eintrags: | Artikel |
|---|---|
| Erschienen: | 2024 |
| Autor(en): | Schuster, Michael ; Strauch, Elisa ; Gugat, Martin ; Lang, Jens |
| Art des Eintrags: | Zweitveröffentlichung |
| Titel: | Probabilistic constrained optimization on flow networks |
| Sprache: | Englisch |
| Publikationsjahr: | 30 April 2024 |
| Ort: | Darmstadt |
| Publikationsdatum der Erstveröffentlichung: | 2022 |
| Ort der Erstveröffentlichung: | Dordrecht |
| Verlag: | Springer Science |
| Titel der Zeitschrift, Zeitung oder Schriftenreihe: | Optimization and Engineering |
| Jahrgang/Volume einer Zeitschrift: | 23 |
| (Heft-)Nummer: | 2 |
| DOI: | 10.26083/tuprints-00023486 |
| URL / URN: | https://tuprints.ulb.tu-darmstadt.de/23486 |
| Zugehörige Links: | |
| Herkunft: | Zweitveröffentlichung DeepGreen |
| Kurzbeschreibung (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. |
| Freie Schlagworte: | Probabilistic constraints, Uncertain boundary data, Spheric radial decomposition, Kernel density estimation, Gas networks, Contamination of water |
| Status: | Verlagsversion |
| URN: | urn:nbn:de:tuda-tuprints-234866 |
| Sachgruppe der Dewey Dezimalklassifikatin (DDC): | 500 Naturwissenschaften und Mathematik > 510 Mathematik |
| Fachbereich(e)/-gebiet(e): | DFG-Sonderforschungsbereiche (inkl. Transregio) DFG-Sonderforschungsbereiche (inkl. Transregio) > Transregios DFG-Sonderforschungsbereiche (inkl. Transregio) > Transregios > TRR 154 Mathematische Modellierung, Simulation und Optimierung am Beispiel von Gasnetzwerken 04 Fachbereich Mathematik 04 Fachbereich Mathematik > Numerik und wissenschaftliches Rechnen |
| Hinterlegungsdatum: | 30 Apr 2024 12:49 |
| Letzte Änderung: | 13 Mai 2024 09:09 |
| PPN: | |
| Export: | |
| Suche nach Titel in: | TUfind oder in Google |
Verfügbare Versionen dieses Eintrags
- Probabilistic constrained optimization on flow networks. (deposited 30 Apr 2024 12:49) [Gegenwärtig angezeigt]
 |
Frage zum Eintrag |
Optionen (nur für Redakteure)
 |
Redaktionelle Details anzeigen |
Drucken
Impressum