An Interior Point Method Applied to Flow Constraints in a Pressure-Dependent Water Distribution System
Publication: Journal of Water Resources Planning and Management
Volume 148, Issue 1
Abstract
This paper used the fusion of an active-set method (ASM) and an interior point method (IPM), with a Newton method, to solve for the steady-state flows, heads, and outflows of a pressure-dependent water distribution system. The outflow constraints which arise from the pressure dependency are handled by an ASM, and the linkflow constraints are handled by an IPM. The authors believe that this is the first time an ASM and an IPM have been used together in this way to solve a real-world optimization problem. Including flow constraints in a network model allows a variety of flow control devices (flow control valves, check valves, pumps) to be modeled efficiently. The new method does not require damping. The separate treatment methods for the two constraint sets mean that the linear inequality constraint qualification condition cannot be violated during iteration, unlike the case in which all the constraints are handled by an ASM. The method was shown to converge quickly on nine case study networks, the largest of which had more than 157,000 links, 150,000 nodes, and 6,000 linkflow constraints. When tested on those same nine networks, an interior point optimizer software package took about 2–4 times longer than the new method for five of the networks, 7 and 9 times as long for two of the networks, and about an equal amount of time for the remaining two networks. For the largest network, the software package took 34 min, whereas the method presented here took 4 min. The generality of the method makes it applicable to network design and management, capacity analysis, and self-cleaning networks.
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Data Availability Statement
Some or all data, models, or code generated or used during the study are proprietary or confidential in nature and may be provided only with restrictions. The four networks , , , and are not available either because they are proprietary or because of security concerns. Some or all data, models, or code used during the study were provided by a third party (Network ). Direct request for these materials may be made to the provider as indicated in the Acknowledgments. EPANET.inp files for the network in Fig. 4 and Networks , , , and are available from the ASCE library (www.ascelibrary.org) as material that is supplementary to Deuerlein et al. (2019). In addition, EPANET.inp files for the network in Fig. 3 and Networks , , , and with the flow constraints used in the tests reported here (flow control valves and check valves) are available from the ASCE library as Supplemental Materials for this paper.
Acknowledgments
The authors thank Dr. Robert Sitzenfrei who provided the authors with the virtRom network, . This network is available from https://www.uibk.ac.at/umwelttechnik/softwareanddatasets/. One author gratefully thanks Dr. J. Kautsky for useful discussions. One author of this paper was supported in part by the German Ministry for Education and Research (BMBF Project W-Net 4.0 02WIK1477C).
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Published In
Journal of Water Resources Planning and Management
Volume 148 • Issue 1 • January 2022
Copyright
© 2021 American Society of Civil Engineers.
History
Received: Feb 25, 2021
Accepted: Aug 20, 2021
Published online: Oct 21, 2021
Published in print: Jan 1, 2022
Discussion open until: Mar 21, 2022
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