Central Force Optimization Method Used to Optimize Water Distribution Networks

Document Type : Research Paper


1 PhD Student of Hydraulic-Structures, Department of Water Engineering, Lorestan University, Khoramabad, Iran and Member of Young Researchers and Elite Club, Science and Research Branch, Islamic Azad University, Tehran, Iran

2 Assist. Prof., Department of Water Engineering, Lorestan University, Khoramabad, Iran

3 Assoc. Prof., Department of Water Engineering, Lorestan University, Khoramabad, Iran


Water supply networks account for a major portion of the urban infrastructure requiring sizable funds for their construction and operation.  This has encouraged many researchers to focus their efforts on optimizing water distribution networks. In most recent research in the field, stochastic meta-heuristic algorithms have been employed to address the problem. Given the many inadequacies of stochastic algorithms, the present study explored the application of a novel deterministic algorithm for minimizing pipe-sizing costs in water distribution systems (WDS). Methods: The algorithm used in this study is a modified version of the central force optimization algorithm called CFONet which is used for solving water distribution system problems. The performance of the proposed method was evaluated by optimizing pipe-sizing in two benchmark WDSs. For this purpose, both CFO and CFONet methods were written in MATLAB and interfaced with the hydraulic simulation model EPANET. Results and discussion: Application of the two methods mentioned above to two different water supply systems revealed the superior performance of the proposed CFOnet over its CFO counterpart. Thus, CFOnet yielded an optimum response for the deisgn of a double ringed system equal to US$419,000 after 12,432 runs of objective function estimations. Moreover, the optimum design of a CAdo system was obtained to cost 126,535,915 In. Ruppes after 259,476 runs of objective function estimations. Conclusion: Comparison of the results obtained in this study with those reported in the literature on other stochastic optimization algorithms showed that the proposed method yields satisfactory solutions for WDSs optimization problems while it also enjoys the merits of a deterministic optimization method.


Main Subjects

Afshar, M. H., Afshar, A., Marino, M. A. & Hon, M., 2009, "An iterative penalty method for the optimal design of pipe networks", International Journal of Civil Engineering, 7(2), 109-123.
Alperovits, E. & Shamir, U., 1977, "Design of optimal water distribution systems", Water Resource. Research, 13(6), 885-900.
Briere, F. G., 2014, Drinking-water distribution, sewage, and rainfall collection, Presses Internationales Polytechnique, Paris. 
Design Criteria of Urban and Rural Water Supply and Distribution Systems, 2013, Publication No. 117-3, 1st Ed., Vice Presidency for Strategic Planning and Supervision, A project to provide the guidelines and technical criteria of Iran's water industry, Ministry of Energy. 168 pages. (In Persian)
Ding, D., Qi, D., Luo, X., Chen, J., Wang, X., Du, P. & Guo, Y., 2012, "Convergence analysis and performance of an extended central force optimization algorithm", Journal of Applied Mathematiecs Computtation, 219(4), 2246-2259.
Eusuff, M. M., & Lansey, K. E., 2003, "Optimization of water distribution network design using the shuffled frog leaping algorithm", Journal of Water Resource Planning Management, 129(3), 210-225.
Formato, R. A., 2007, "Central force optimization: A new metaheuristic with applications in applied electromagnetic", Journal of Progress in. Electromagnetics Research, 77 (1), 425-491.
Formato, R. A., 2009, "Central force optimization: A new gradient-like metaheuristic for multidimensional search and optimization", International Journal of Bio-Inspired Computation, 1(4), 217-238.
Formato, R. A., 2010a, "Improved CFO algorithm for antenna optimization", Progress Electromagnetics Research,19, 405-425.
Formato, R. A., 2010b, "Central force optimization applied to the PBM suite of antenna benchmarks",  Computing Research Repository. http://arxiv.org/abs/1003.0221.
Haghighi, A. & Ramos, H. M., 2012, "Detection of leakage freshwater and friction factor calibration in drinking networks using central force Optimization", Water Resource Management, 26(8), 2347-2363.
Haghighi, A., Samani, M.V.H. & Samani, M.V. Z., 2011, "GA-ILP method for optimization of water distribution networks", Water Resource Management, 25, 1791-1808.
آب و فاضلاب                                                                                                                    شماره 2 سال 1396
Kadu, M. S., Gupta, R., & Bhave, P. R., 2008, "Optimal design of water networks using a modified genetic algorithm with reduction in search space", Journal of Water Resource Planing Management 134(2), 147-160.
Liong, S. & Atiquazzaman, M. D., 2004, "Optimal design of water distribution network using shuffled complex evolution", J. Inst Eng., 44(1), 93-107.
Liu, Y., & Tian, P., 2015, "A multi-start central force optimization for global optimization", Journal Applied Soft Computing, 27, 92-98.
Moghaddam, A. R., Alizadeh, A., Fardi Hoseini, A. R., Ziaei, A. N. & Fallah Heravi, D., 2013, "The application of an improved particle swarm optimization algorithm in design of water distribution systems", Iranian Journal of Irrigation and Drainage, 7(3), 389-401. (In Persian)
Mohammadi-Aghdam, K., Mirzaei, I., Pourmahmood, N. and Pourmahmood-Aghababa, M., 2015, "Application of dynamic mutated particle swarm optimization algorithm to design water distribution networks", Journal of Water and Wastewater, 26(4), 88-99. (In Persian)
Rossman, L.A., 2000, EPANET 2 User’s Manual, EPA/600/R-00/057.
Savic, D. A. & Walters, G. A., 1997, "Genetic algorithms for least-cost design of water distribution networks",
Journal of Water Resource Planning, Management, 123(2), 67-77.
Schaake, J. & Lai, D., 1969, Linear programming and dynamic programming –application of water distribution network design, Report 116. MIT Press: Cambridge, MA.
Suribabu, C. R., 2010, "Differential evolution algorithm for optimal design of water distribution networks", Journal of Hydroinform, 12(1), 66-82.
Swamee, P. K. & Sharma, A. K., 2008, Design of water supply pipe networks, John Wiley and Sons, Inc., Hoboken, N.T.