Schuster, Michael ; Strauch, Elisa ; Gugat, Martin ; Lang, Jens (2022)
Probabilistic constrained optimization on flow networks.
In: Optimization and Engineering, 23 (2)
doi: 10.1007/s11081-021-09619-x
Artikel, Bibliographie
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: | 2022 |
| Autor(en): | Schuster, Michael ; Strauch, Elisa ; Gugat, Martin ; Lang, Jens |
| Art des Eintrags: | Bibliographie |
| Titel: | Probabilistic constrained optimization on flow networks |
| Sprache: | Englisch |
| Publikationsjahr: | Juni 2022 |
| Verlag: | Springer |
| Titel der Zeitschrift, Zeitung oder Schriftenreihe: | Optimization and Engineering |
| Jahrgang/Volume einer Zeitschrift: | 23 |
| (Heft-)Nummer: | 2 |
| DOI: | 10.1007/s11081-021-09619-x |
| 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. |
| 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 |
| TU-Projekte: | DFG|TRR154|B01 Fr. Dr. Domschke |
| Hinterlegungsdatum: | 29 Nov 2022 06:46 |
| Letzte Änderung: | 13 Jun 2023 10:16 |
| PPN: | 368198278 |
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| Suche nach Titel in: | TUfind oder in Google |
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