Limited Multistage Stochastic Programming for Water Distribution Systems Optimal Operation
Publication: Journal of Water Resources Planning and Management
Volume 142, Issue 10
Abstract
Least-cost operation of water distribution systems (WDS) is a well-known problem in water distribution systems optimization. The formulation of the problem started with deterministic modeling, and the problem was subsequently handled with more sophisticated stochastic models that incorporate uncertainties related to the problem’s parameters. This work applied a recently developed algorithm entitled limited multistage stochastic programming (LMSP) to deal with the stochastic formulation of the least-cost operation of WDS and serves merely as a proof of concept on an illustrative network. The demand is considered as the uncertain parameter in the problem formulation. This algorithm reduces the complexity of the classical multistage stochastic programming (MSP) by adding constraints which result in a linear growth of the problem, as opposed to an exponential growth in the MSP problem. This is accomplished by clustering decision variables based on a postanalysis of the implicit stochastic program of the problem. The clusters allow reduction of the number of decision variables, thus reducing the complexity of the optimization problem. The LMSP is expected to increase the cost because of the additional constraints imposed on the problem; however, a trade-off exists between the computational complexity and the optimality of the objective value to the number of clusters considered. An illustrative example application is provided for demonstrating the suggested methodology abilities.
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Acknowledgments
The Technion part of this study was supported by the U.S. Binational Science Foundation (BSF), the Technion Funds for Security research, the joint Israeli Office of the Chief Scientist (OCS) Ministry of Science, Technology and Space (MOST), and the Germany Federal Ministry of Education and Research (BMBF), under Project No. 02WA1298.
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© 2016 American Society of Civil Engineers.
History
Received: Dec 10, 2015
Accepted: Apr 4, 2016
Published online: May 25, 2016
Published in print: Oct 1, 2016
Discussion open until: Oct 25, 2016
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