Deterministic versus Stochastic Design of Water Distribution Networks
Publication: Journal of Water Resources Planning and Management
Volume 135, Issue 2
Abstract
The paper describes a procedure for the robust design of water distribution networks which incorporates the uncertainty of nodal water demands and pipe roughness in a multiobjective optimization scheme aimed at minimizing costs and maximizing hydraulic reliability. The methodology begins with a deterministic system design in order to generate a set of optimal networks that serves as the initial population for subsequent multiobjective stochastic design. This approach does not depend on the choice of multiobjective optimizer (for example, a multiobjective genetic algorithm is used here) and can drastically reduce the number of “stochastic” runs needed for searching robust solutions. A collection of probability density functions based on the function is introduced and applied to modeling variable uncertainty according to different physical requirements. The approach is tested in a case study involving a real network, illustrating its computational advantages.
Get full access to this article
View all available purchase options and get full access to this article.
References
Babayan, A. V., Kapelan, Z., Savic, D. A., and Walters, G. A. (2005). “Least cost design of robust water distribution networks under demand uncertainty.” J. Water Resour. Plann. Manage., 131(5), 375–382.
Bazin, H., and Darcy, H. (1865). Recherches hydrauliques, Enterprises par M. H. Darcy, Imprimerie Nationale, Paris (in French).
Benjamin, J. R., and Cornell, C. A. (1970). Probability, statistics, and decision for civil engineers, McGraw-Hill, New York.
Deb, K., Pratap, S., Agarwal, S., and Meyarivan, T. (2002). “A fast and elitist multiobjective genetic algorithm: NSGA-II.” IEEE Trans. Evol. Comput., 6(4), 182–197.
Devroye, L. (1986). Non-uniform random variate generation, Springer, New York.
Farmani, R., Walters, G. A., and Savic, D. A. (2005). “Trade-off between total cost and reliability for any-town water distribution network.” J. Water Resour. Plann. Manage., 131(3), 161–171.
Fishman, G. S. (1996). Monte Carlo: Concepts, algorithms and applications, Springer, New York.
Fonseca, C. M., and Fleming, P. J. (1993). “Genetic algorithms for multiobjective optimization: Formulation, discussion and generalization.” Proc., 5th Int. Conf. on Genetic Algorithms, S. Forrest, ed, Morgan Kaufmann, San Mateo, Calif., 416–423.
Giustolisi, O., Berardi, L., Doglioni, A., and Laucelli, D. (2005). “Automatic robust design of water distribution systems in an uncertain scenario.” Proc., 1st National Conf. on Urban Hydraulics, Centro Studi Drenaggio Urbano (CSDU), Milano, Italy, 65–66 (Abstract Volume and CD-ROM).
Giustolisi, O., Doglioni, A., Savic, D. A., and Laucelli, D. (2004). “A proposal for an effective multi-objective non-dominated genetic algorithm: The optimised multi-objective genetic algorithm—OPTIMOGA.” Research Rep. No. 2004/07, School of Engineering, Computer Science and Mathematics, Centre for Water Systems, Univ. of Exeter, Exeter, U.K.
Giustolisi, O., Laucelli, D., and Savic, D. A. (2006). “Development of rehabilitation plans for water mains replacement considering risk and cost-benefit assessment.” Civ. Eng. Environ. Syst., 23(3), 175–190.
Kapelan, Z. S., Savic, D. A., and Walters, G. A. (2005). “Multiobjective design of water distribution systems under uncertainty.” Water Resour. Res., 41(11), W11407-1–W11407-15.
Lansey, K. E., Ning Duan Mays, L. W., and Yeou-Kung, T. (1989). “Water distribution system design under uncertainties.” J. Water Resour. Plann. Manage., 115(5), 630–645.
Leonard, M., Zecchin, A., Roberts, A., and Berrisford, M. (2002). “Ant colony optimisation and risk-based assessment of water distribution systems.” Final Year Research Project Rep., School of Civil and Environmental Engineering, Univ. of Adelaide, Adelaide, Australia.
Manning, R. (1891). “On the flow of water in open channels and pipes.” Trans. Inst. Civ. Eng. Ireland, 20, 161–207.
McKay, M. D., Conover, W. J., and Beckman, R. J. (1979). “A comparison of three methods for selecting values of input variables in the analysis of output from a computer code.” Technometrics, 21(2), 239–245.
Mood, A. M., Graybill, F. A., and Boes, D. C. (1974). Introduction to the theory of statistics, McGraw-Hill, New York.
Savic, D. A. (2004). “Risk and robust strategic investment planning in the water industry, an optimisation approach.” Proc., 4th Int. Conf. on Decision Making in Urban and Civil Engineering (CD-ROM), University of Coimbra Press, Coimbra, Portugal.
Savic, D. A., and Walters, G. A. (1997). “Genetic algorithms for the least-cost design of water distribution networks.” J. Water Resour. Plann. Manage., 123(2), 67–77.
Todini, E., and Pilati, S. (1988). “A gradient algorithm for the analysis of pipe networks.” Computer applications in water supply, Vol. 1, Wiley, London, 1–20.
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., 130(1), 63–72.
Walski, T. M. (2001). “The wrong paradigm—Why water distribution doesn’t work?” J. Water Resour. Plann. Manage., 127(4), 203–205.
Xu, C., and Goulter, I. C. (1999). “Reliability-based optimal design of water distribution network.” J. Water Resour. Plann. Manage., 125(6), 352–362.
Information & Authors
Information
Published In
Journal of Water Resources Planning and Management
Volume 135 • Issue 2 • March 2009
Pages: 117 - 127
Copyright
© 2009 ASCE.
History
Received: Apr 12, 2007
Accepted: Aug 11, 2008
Published online: Mar 1, 2009
Published in print: Mar 2009
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.