Least-Cost Robust Design Optimization of Water Distribution Systems under Multiple Loading
Publication: Journal of Water Resources Planning and Management
Volume 142, Issue 9
Abstract
Least-cost design of water distribution system is a well-known problem in the literature. The formulation of the least-cost design problem started by deterministic modeling and later by more sophisticated stochastic models that incorporate uncertainties related to the problem’s parameters. Recently, a new nonprobabilistic modeling, titled the robust counterpart (RC) approach, has been developed for the least-cost design problem to incorporate the uncertainty without the need for full stochastic information. These nonprobabilistic methods, developed in the field of robust optimization, were shown to be advantageous over classical stochastic methods in the following aspects: tractability and computation time, nonnecessity of full probabilistic information, and the ability to integrate correlation of uncertain parameters aspects without adding complexity. Former studies have considered the RC approach for a special case of the least-cost problem with a single load demand uncertainty, and single gravitational source to simplify the problem formulation and facilitate the use of the method. This special case does not handle the joint temporal and spatial correlations between the problem uncertainties and does not include components such as pumping stations and storage facilities. These new components require trading off capital and operation (i.e., energy) costs in the objective function, as the design cost is explicitly influenced by the demand uncertainty, unlike the situation where only capital cost is considered. In this study, the RC approach is expanded to cover the general least-cost design problem, including (1) multiload patterns, (2) pumping stations, and (3) storage facilities. The unknowns are the pipe diameters, pump and tank capacities, and the heads added by the pumping stations. The problem is solved using the cross-entropy method for several possible protection levels, which are defined by the size of the uncertainty set. The results are demonstrated on two examples to show the trade-off between cost and reliability and test the network’s ability to cope with unexpected scenarios.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The Technion part of this study was supported by the United States—Binational Science Foundation (BSF), by the Technion Funds for Security research, by the joint Israeli Office of the Chief Scientist (OCS) Ministry of Science, Technology and Space (MOST), and by the Germany Federal Ministry of Education and Research (BMBF), under project no. 02WA1298. We would also like to acknowledge the two reviewers, and especially reviewer 1, for their valuable comprehensive comments during the manuscript revision process.
References
Alperovits, E., and Shamir, U. (1977). “Design of optimal water distribution systems.” J. Water Resour. Res., 13(6), 885–900.
Babayan, A. V., Kapelan, Z., Savic, D. A., and Walters, G. A. (2005). “Least cost design of water distribution networks under demand uncertainty.” J. Water Resour. Plann. Manage., 375–382.
Babayan, A. V., Savic, D. A., Walters, G. A., and Kapelan, Z. S. (2007). “Robust least-cost design of water distribution networks using redundancy and integration-based methodologies.” J. Water Resour. Plann. Manage., 67–77.
Ben-Tal, A., and Nemirovski, A. (1999). “Robust solutions of uncertain linear programs.” J. Oper. Res. Lett., 25(1), 1–13.
Boulos, P. F., Lansey, K. E., and Karney, B. W. (2006). Comprehensive water distribution systems analysis handbook for engineers and planners, MWH Soft, Broomfield, CO.
De Maesschalck, R., Jouan-Rimbaud, D., and Massart, D. L. (2000). “The Mahalanobis distance.” Chemom. Intell. Lab. Syst., 50(1), 1–18.
Fu, G., and Kapelan, Z. (2011). “Fuzzy probabilistic design of water distribution networks.” J. Water Resour. Res., 47(5), W05538.
Housh, M., Ostfeld, A., and Shamir, U. (2011). “Optimal multiyear management of a water supply system under uncertainty: Robust counterpart approach.” J. Water Resour. Res., 47(10), W10515.
Julier, S. J., and Uhlmann, J. K. (1997). “New extension of the Kalman filter to nonlinear systems.” AeroSense'97: Signal Processing, Sensor Fusion, and Target Recognition, International Society for Optics and Photonics, Bellingham, WA, 182–193.
Kapelan, Z. S., Savic, D. A., and Walters, G. A. (2005). “Multi-objective design of water distribution systems under uncertainty.” J. Water Resour. Res., 41(11), W11407.
Kullback, S., and Leibler, R. A. (1951). “On information and sufficiency.” Ann. Math. Stat., 22(1), 79–86.
Lan, F., Lin, W. H., and Lansey, K. (2015). “Scenario-based robust optimization of a water supply system under risk of facility failure.” J. Environ. Modell. Software, 67, 160–172.
Lansey, K. E., Duan, N., Mays, L. W., and Yeou-Kung, T. (1989). “Water distribution system design under uncertainties.” J. Water Resour. Plann. Manage., 630–645.
Perelman, L., Housh, M., and Ostfeld, A. (2013a). “Least cost design of water distribution systems under demand uncertainty: The robust counterpart approach.” J. Hydroinf., 15(3), 737–750.
Perelman, L., Housh, M., and Ostfeld, A. (2013b). “Robust optimization for water distribution systems least cost design.” J. Water Resour. Res., 49(10), 6795–6809.
Prasad, T. D., and Park, N. S. (2004). “Multi-objective genetic algorithms for design of water distribution networks.” J. Water Resour. Plann. Manage., 73–82.
Rubinstein, R. Y. (1999). “The cross-entropy method for combinatorial and continuous optimization.” Method. Comput. Appl. Probab., 1(2), 127–190.
Tanyimboh, T. T., and Templeman, A. B. (1993). “Calculating maximum entropy flows in networks.” J. Oper. Res. Soc., 44(4), 383–396.
Todini, E. (2000). “Looped water distribution networks design using a resilience index based heuristic approach.” J. Urban Water, 2(2), 115–122.
Todini, E., and Pilati, S. (1987). “A gradient method for the analysis of pipe networks.” Proc., Int. Conf. on Computer Applications for Water Supply and Distribution, Leicester Polytechnic, Leicester, U.K.
Tolson, B. A., Maier, H. R., Simpson, A. R., and Lence, B. J. (2004). “Genetic algorithms for reliability-based optimization of water distribution systems.” J. Water Resour. Plann. Manage., 63–72.
Xu, C., and Goulter, I. C. (1999). “Reliability-based optimal design of water distribution network.” J. Water Resour. Plann. Manage., 352–362.
Information & Authors
Information
Published In
Journal of Water Resources Planning and Management
Volume 142 • Issue 9 • September 2016
Copyright
© 2016 American Society of Civil Engineers.
History
Received: Oct 27, 2015
Accepted: Feb 9, 2016
Published online: May 11, 2016
Published in print: Sep 1, 2016
Discussion open until: Oct 11, 2016
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.