Fuzzy Programming Approach for Multiobjective Optimization of Water Distribution Systems
Publication: Journal of Water Resources Planning and Management
Volume 143, Issue 7
Abstract
This paper proposes a fuzzy multiobjective programming model for meeting competing objectives in the optimal design of water distribution systems (WDSs). Fuzzy membership functions for minimizing the pipe network cost and maximizing a number of reliability surrogates are defined, and the model maximizes the degree of satisfaction of these membership functions. Reliability surrogates investigated include: (1) the sum over all nodes of the relative surplus of energy at each node; (2) the minimum surplus head at a critical node; (3) the sum over all nodes of the relative surplus of energy at each node modified by the degree of uniformity of its associated loop; and (4) the minimum uniformity of the associated loops over all nodes. The model is applied to various combinations of objective functions, to identify the design pipe diameters of the water-main network of Farhadgerd, Iran. Optimal solutions of the various model variations, based on inclusion of one or more reliability surrogate(s), show that for this WDS the third surrogate (3) may be a reasonable substitute for the first surrogate (1), and that while the inclusion of the last surrogate (4) may be beneficial, the inclusion of the second surrogate (2) may not. Based on postoptimization cut-set analyses, the model that minimizes cost and maximizes surrogates (3) and (4) exhibits the highest level of mechanical reliability, while the model that minimizes cost and maximizes the second surrogate (2) exhibits the lowest level of mechanical reliability.
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References
Amirabdollahian, M., Asghari, K., and Chamani, M. R. (2011). “Type 2 fuzzy logic system in water network optimal design procedure.” Int. Conf. on Information and Intelligent Computing IPCSIT, IACSIT Press, Singapore.
Ang, W., and Jowitt, P. (2003). “Some observations on energy loss and network entropy in water distribution networks.” Eng. Optim., 35(4), 375–389.
Atiquzzaman, M., Liong, S., and Yu, X. (2006). “Alternative decision making in water distribution network with NSGA-II.” J. Water Resour. Plann. Manage., 122–126.
Atkinson, S., Farmani, R., Memon, F., and Butler, D. (2014). “Reliability indicators for water distribution system design: Comparison.” J. Water Resour. Plann. Manage., 160–168.
Babayan, A., Kapelan, Z., Savic, D., and Walters, G. (2005). “Least-cost design of water distribution networks under demand uncertainty.” J. Water Resour. Plann. Manage., 375–382.
Baños, R., Gil, C., Reca, J., and Ortega, J. (2010). “A Pareto-based memetic algorithm for optimization of looped water distribution systems.” Eng. Optim., 42(3), 223–240.
Bhave, P. R., and Gupta, R. (2007). “Optimal design of water distribution networks for fuzzy demands.” Civ. Eng. Environ. Syst., 21(4), 229–245.
Cohen, J. L. (1978). Multiobjective programming and planning, Academic Press, London.
Creaco, E., Franchini, M., and Todini, E. (2014). “The combined use of resilience and loop diameter uniformity as a good indirect measure of network reliability.” Urban Water J., 13(2), 167–181.
Damelin, E., Shamir, U., and Arad, N. (1972). “Engineering and economic evaluation of the reliability of water supply.” Water Resour. Res., 8(4), 861–877.
Farmani, R., Walters, G., and Savic, D. (2006). “Evolutionary multiobjective optimization of the design and operation of water distribution network: Total cost versus reliability versus water quality.” J. Hydroinf., 8(3), 165–179.
Farmani, R., Walters, G. A., and Savic, D. A. (2005). “Trade-off between total cost and reliability for Anytown water distribution network.” J. Water Resour. Plann. Manage., 161–171.
Fu, G., and Kapelan, Z. (2011). “Fuzzy probabilistic design of water distribution networks.” Water Resour. Res., 47(5), .
Geem, Z. W. (2015). “Multiobjective optimization of water distribution networks using fuzzy theory and harmony search.” Water, 7(7), 3613–3625.
Giustolisi, O., Laucelli, D., and Colombo, A. (2009). “Deterministic versus stochastic design of water distribution networks.” J. Water Resour. Plann. Manage., 117–127.
Giustolisi, O., and Moosavian, N. (2014). “Testing linear solvers for global gradient algorithm.” J. Hydroinf., 16(5), 1178–1193.
Goulter, I. C., and Bouchart, F. (1988). “Fuzzy programming in water distribution network design.” Proc., 1st Int. Conf. on Computer Methods and Water Resources, Vol. 2, Computational Mechanics Publications, Southampton, U.K., 33–44.
Greco, R., Di Nardo, A., and Santonastaso, G. (2012). “Resilience and entropy as indices of robustness of water distribution networks.” J. Hydroinf., 14(3), 761–771.
Jaramillo, A., et al. (2016). “Solving the set covering problem with the Soccer League Competition algorithm.” Trends in applied knowledge-based systems and data science, Springer, Switzerland, 884–891.
Jayaram, N., and Srinivasan, K. (2008). “Performance-based optimal design and rehabilitation of water distribution networks using life cycle costing.” Water Resour. Res., 44(1), .
Liu, H., Savić, D., Kapelan, Z., Zhao, M., Yuan, Y., and Zhao, H. (2014). “A diameter-sensitive flow entropy method for reliability consideration in water distribution system design.” Water Resour. Res., 50(7), 5597–5610.
MATLAB [Computer software]. MathWorks, Natick, MA.
Mays, L. W., and Cullinane, M. J. (1986). “A review and evaluation of reliability concepts for design of water distribution systems.”, U.S. Army Corps of Engineers, Waterwayy Experiment Station, MS Environmental Lab, Vicksburg, MS.
Moosavian, N. (2015). “Soccer league competition algorithm for solving knapsack problems.” Swarm Evol. Comput., 20, 14–22.
Moosavian, N., and Jaefarzadeh, R. (2014). “Hydraulic analysis of water supply networks using a modified Hardy Cross method.” Int. J. Eng., 27(9), 1331–1338.
Moosavian, N., and Lence, B. (2016). “Non-dominated sorting differential algorithms for multi-objective optimization of water distribution systems.” J. Water Resour. Plann. Manage., in press.
Moosavian, N., and Roodsari, B. K. (2014a). “Soccer league competition algorithm, a new method for solving systems of nonlinear equations.” Int. J. Intell. Sci., 4(1), 7–16.
Moosavian, N., and Roodsari, B. K. (2014b). “Soccer league competition algorithm: A novel meta-heuristic algorithm for optimal design of water distribution networks.” Swarm Evol. Comput., 17, 14–24.
Ostfeld, A., Oliker, N., and Salomons, E. (2014). “Multiobjective optimization for least cost design and resiliency of water distribution systems.” J. Water Resour. Plann. Manage., .
Prasad, T., and Park, N. (2004). “Multiobjective genetic algorithms for design of water distribution networks.” J. Water Resour. Plann. Manage., 73–82.
Prasad, T. D., Hong, S. H, and Park, N. (2003). “Reliability based design of water distribution networks using multi-objective genetic algorithms.” KSCE J. Civ. Eng., 7(3), 351–361.
Raad, D., Sinske, A., and Van Vuuren, J. (2009). “Robust multi-objective optimization for water distribution system design using a meta-metaheuristic.” Int. Trans. Oper. Res., 16(5), 595–626.
Saleh, S. H. A., and Tanyimboh, T. T. (2014). “Optimal design of water distribution systems based on entropy and topology.” Water Resour. Manage., 28(11), 3555–3575.
Schwartz, R., Housh, M., and Ostfeld, A. (2016). “Limited multistage stochastic programming for water distribution systems optimal operation.” J. Water Resour. Plann. Manage., .
Shamir, U., and Howard, C. D. D. (1981). “Water supply reliability theory.” J. Am. Water Works Assoc., 73(7), 379–384.
Todini, E. (2000). “Looped water distribution networks design using a resilience index based heuristic approach.” Urban Water J., 2(2), 115–122.
Vamvakeridou, L. S., Savic, D. A., and Walters, G. A. (2006). “Fuzzy hierarchical decision support system for water distribution network optimization.” Civ. Eng. Environ. Syst., 23(3), 237–261.
Xu, C., and Goulter, I. C. (1999). “Optimal design of water distribution networks using fuzzy optimization.” Civ. Eng. Environ. Syst., 16(4), 243–266.
Xu, T. Y., and Qin, X. S. (2013). “Applying an extended fuzzy parametric approach to the problem of water allocations.” Math. Prob. Eng., 2013, 1–10.
Yu, P. L. (1973). “A class of decisions for group decision problems.” Manage. Sci., 19(8), 936–946.
Zadeh, L. A. (1965). “Fuzzy sets.” Inf. Control, 8(3), 338–353.
Zeleny, M. (1974a). Linear multi-objective programming, Springer, New York.
Zeleny, M. (1974b). “A concept of compromise solutions and the method of the displaced ideal.” Comput. Oper. Res., 1(3–4), 479–496.
Zimmermann, H. J. (1991). Fuzzy set theory and its applications, Kluwer Academic, Boston.
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Published In
Journal of Water Resources Planning and Management
Volume 143 • Issue 7 • July 2017
Copyright
©2017 American Society of Civil Engineers.
History
Received: Apr 7, 2016
Accepted: Dec 21, 2016
Published online: Mar 10, 2017
Published in print: Jul 1, 2017
Discussion open until: Aug 10, 2017
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