Water supply is one of the most recognizable and important public services contributing to
quality of life. Water distribution networks WDNs are extremely complex assets. A number of
complex tasks, such as design, planning, operation, maintenance, and management, are inherently
associated with such networks. In this paper, we focus on the design of a WDN, which is a
wide and open problem in hydraulic engineering. This problem is a large-scale combinatorial,
nonlinear, nonconvex, multiobjective optimization problem, involving various types of decision
variables and many complex implicit constraints. To handle this problem, we provide a synergetic
association between swarm intelligence and multiagent systems where human interaction is also
enabled. This results in a powerful collaborative system for finding solutions to such a complex
hydraulic engineering problem. All the ingredients have been integrated into a software tool that
has also been shown to efficiently solve problems from other engineering fields.This work has been developed with the support of the project IDAWAS, DPI2009-11591, of the Direccion General de Investigacion of the Ministerio de Educacion y Ciencia, and ACOMP/2010/146 of the Conselleria d'Educacio of the Generalitat Valenciana. The first author is also indebted to the Universitat Politecnica de Valencia for the sabbatical leave granted during the first semester of 2011. The use of English in this paper was revised by John Rawlins.Izquierdo Sebastián, J.; Montalvo Arango, I.; Pérez García, R.; Matías, A. (2012). On the Complexities of the Design of Water Distribution Networks. Mathematical Problems in Engineering. 2012:1-25. https://doi.org/10.1155/2012/9479611252012Goulter, I. C., & Coals, A. V. (1986). Quantitative Approaches to Reliability Assessment in Pipe Networks. Journal of Transportation Engineering, 112(3), 287-301. doi:10.1061/(asce)0733-947x(1986)112:3(287)Goulter, I. C., & Bouchart, F. (1990). Reliability‐Constrained Pipe Network Model. Journal of Hydraulic Engineering, 116(2), 211-229. doi:10.1061/(asce)0733-9429(1990)116:2(211)Kleiner, Y., Adams, B. J., & Rogers, J. S. (2001). Water Distribution Network Renewal Planning. Journal of Computing in Civil Engineering, 15(1), 15-26. doi:10.1061/(asce)0887-3801(2001)15:1(15)Dandy, G. C., & Engelhardt, M. O. (2006). Multi-Objective Trade-Offs between Cost and Reliability in the Replacement of Water Mains. Journal of Water Resources Planning and Management, 132(2), 79-88. doi:10.1061/(asce)0733-9496(2006)132:2(79)Izquierdo, J., Pérez, R., & Iglesias, P. L. (2004). Mathematical models and methods in the water industry. Mathematical and Computer Modelling, 39(11-12), 1353-1374. doi:10.1016/j.mcm.2004.06.012Giustolisi, O., Savic, D., & Kapelan, Z. (2008). Pressure-Driven Demand and Leakage Simulation for Water Distribution Networks. Journal of Hydraulic Engineering, 134(5), 626-635. doi:10.1061/(asce)0733-9429(2008)134:5(626)Montalvo, I., Izquierdo, J., Pérez, R., & Tung, M. M. (2008). Particle Swarm Optimization applied to the design of water supply systems. Computers & Mathematics with Applications, 56(3), 769-776. doi:10.1016/j.camwa.2008.02.006Montalvo, I., Izquierdo, J., Pérez, R., & Iglesias, P. L. (2008). A diversity-enriched variant of discrete PSO applied to the design of water distribution networks. Engineering Optimization, 40(7), 655-668. doi:10.1080/03052150802010607Montalvo, I., Izquierdo, J., Pérez-García, R., & Herrera, M. (2010). Improved performance of PSO with self-adaptive parameters for computing the optimal design of Water Supply Systems. Engineering Applications of Artificial Intelligence, 23(5), 727-735. doi:10.1016/j.engappai.2010.01.015Martínez, J. B. (2010). Cost and reliability comparison between branched and looped water supply networks. Journal of Hydroinformatics, 12(2), 150-160. doi:10.2166/hydro.2009.080Goulter, I. C. (1992). Systems Analysis in Water‐Distribution Network Design: From Theory to Practice. Journal of Water Resources Planning and Management, 118(3), 238-248. doi:10.1061/(asce)0733-9496(1992)118:3(238)Park, H., & Liebman, J. C. (1993). Redundancy‐Constrained Minimum‐Cost Design of Water‐Distribution Nets. Journal of Water Resources Planning and Management, 119(1), 83-98. doi:10.1061/(asce)0733-9496(1993)119:1(83)Khomsi, D., Walters, G. A., Thorley, A. R. D., & Ouazar, D. (1996). Reliability Tester for Water-Distribution Networks. Journal of Computing in Civil Engineering, 10(1), 10-19. doi:10.1061/(asce)0887-3801(1996)10:1(10)Tanyimboh, T. T., Tabesh, M., & Burrows, R. (2001). Appraisal of Source Head Methods for Calculating Reliability of Water Distribution Networks. Journal of Water Resources Planning and Management, 127(4), 206-213. doi:10.1061/(asce)0733-9496(2001)127:4(206)Kalungi, P., & Tanyimboh, T. T. (2003). Redundancy model for water distribution systems. Reliability Engineering & System Safety, 82(3), 275-286. doi:10.1016/s0951-8320(03)00168-6Morgan, D. R., & Goulter, I. C. (1985). Optimal urban water distribution design. Water Resources Research, 21(5), 642-652. doi:10.1029/wr021i005p00642Walters, G. A., & Knezevic, J. (1989). Discussion of «
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