**References**

- H.M. Lee, D.G. Yoo, A. Sadollah, J.H. Kim, Optimal cost design of water distribution networks using a decomposition approach, Eng. Optim., 48 (2016) 2141–2156.
- E. Alperovits, U. Shamir, Design of optimal water distribution systems, Water Resour. Res., 13 (1977) 885–900.
- A. Kessler, U. Shamir, Analysis of the linear programming gradient method for optimal design of water supply networks, Water Resour. Res., 25 (1989) 1469–1480.
- O. Fujiwara, D.B. Khang, A two‐phase decomposition method for optimal design of looped water distribution networks, Water Resour. Res., 26 (1990) 539–549.
- J.C. Schaake, F.H. Lai, Linear Programming and Dynamic Programming Application to Water Distribution Network Design, MIT Hydrodynamics Laboratory, Cambridge, 1969.
- I.C. Goulter, B.M. Lussier, D.R. Morgan, Implications of head loss path choice in the optimization of water distribution networks, Water Resour. Res., 22 (1986) 819–822.
- G.E. Quindry, J.C. Liebman, E.D. Brill, Optimization of looped water distribution systems, J. Environ. Eng. Div., 107 (1981) 665–679.
- L.W. Mays, Water Distribution Systems Handbook, McGraw- Hill, New York, 2000.
- D.J. Wood, Computer Analysis of Flow in Pipe Networks Including Extended Period Simulations, User’s Manual, Office of Continuing Education and Extension of the College of Engineering of the University of Kentucky, Lexington, KY, 1980.
- D.A. Savic, G.A. Walters, Genetic algorithms for least-cost design of water distribution networks, J. Water Resour. Plann. Manage., 123 (1997) 67–77.
- M.d.C. Cunha, J. Sousa, Water distribution network design optimization: simulated annealing approach, J. Water Resour. Plann. Manage., 125 (1999) 215–221.
- M.B. Johns, E. Keedwell, D. Savic, Adaptive locally constrained genetic algorithm for least-cost water distribution network design, J. Hydroinf., 16 (2013) 288–301.
- W. Bi, G.C. Dandy, H.R. Maier, Improved genetic algorithm optimization of water distribution system design by incorporating domain knowledge, Environ. Modell. Software, 69 (2015) 370–381.
- E. Creaco, M. Franchini, T. Walski, Accounting for phasing of construction within the design of water distribution networks, J. Water Resour. Plann. Manage., 140 (2014) 598–606.
- A. Ostfeld, N. Oliker, E. Salomons, Multiobjective optimization for least cost design and resiliency of water distribution systems, J. Water Resour. Plann. Manage., 140 (2014) 04014037, doi: 10.1061/(ASCE)WR.1943-5452.0000407.
- H.R. Maier, A.R. Simpson, A.C. Zecchin, W.K. Foong, K.Y. Phang, H.Y. Seah, C.L. Tan, Ant colony optimization for design of water distribution systems, J. Water Resour. Plann. Manage., 129 (2003) 200–209.
- A.C. Zecchin, A.R. Simpson, H.R. Maier, M. Leonard, A.J. Roberts, M.J. Berrisford, Application of two ant colony optimisation algorithms to water distribution system optimisation, Math. Comput. Modell., 44 (2006) 451–468.
- D. Mora-Melia, P.L. Iglesias-Rey, F.J. Martínez-Solano, P. Muñoz- Velasco, The efficiency of setting parameters in a modified shuffled frog leaping algorithm applied to optimizing water distribution networks, Water, 8 (2016) 182.
- S.-Y. Liong, M. Atiquzzaman, Optimal design of water distribution network using shuffled complex evolution, J. Inst. Eng. Singapore, 44 (2004) 93–107.
- A. Shibu, M.J. Reddy, Optimal design of water distribution networks considering fuzzy randomness of demands using cross entropy optimization, Water Resour. Manage., 28 (2014) 4075–4094.
- M. da Conceição Cunha, L. Ribeiro, Tabu search algorithms for water network optimization, Eur. J. Oper. Res., 157 (2004) 746–758.
- M.-D. Lin, Y.-H. Liu, G.-F. Liu, C.-W. Chu, Scatter search heuristic for least-cost design of water distribution networks, Eng. Optim., 39 (2007) 857–876.
- I. Montalvo, J. Izquierdo, R. Pérez, P.L. Iglesias, A diversityenriched variant of discrete PSO applied to the design of water distribution networks, Eng. Optim., 40 (2008) 655–668.
- R. Ezzeldin, B. Djebedjian, T. Saafan, Integer discrete particle swarm optimization of water distribution networks, J. Pipeline Syst. Eng. Pract., 5 (2013) 04013013, doi: 10.1061/(ASCE) PS.1949-1204.0000154.
- X. Qi, K. Li, W.D. Potter, Estimation of distribution algorithm enhanced particle swarm optimization for water distribution network optimization, Front. Environ. Sci. Eng., 10 (2016) 341–351.
- Z.W. Geem, Optimal cost design of water distribution networks using harmony search, Eng. Optim., 38 (2006) 259–277.
- Z.W. Geem, Harmony search optimisation to the pumpincluded water distribution network design, Civ. Eng. Environ. Syst., 26 (2009) 211–221.
- A. Bolognesi, C. Bragalli, A. Marchi, S. Artina, Genetic heritage evolution by stochastic transmission in the optimal design of water distribution networks, Adv. Eng. Software, 41 (2010) 792–801.
- A. Vasan, S.P. Simonovic, Optimization of water distribution network design using differential evolution, J. Water Resour. Plann. Manage., 136 (2010) 279–287.
- H. Fallah, S. Ghazanfari, C. Suribabu, E. Rashedi, Optimal pipe dimensioning in water distribution networks using gravitational search algorithm, J. Hydraul. Eng., 15 (2019) 1–14, doi: 10.1080/09715010.2019.1624630.
- H. Fallah, O. Kisi, S. Kim, M. Rezaie-Balf, A new optimization approach for the least-cost design of water distribution networks: improved crow search algorithm, Water Resour. Manage., 33 (2019) 3595–3613.
- R. Thangaraj, M. Pant, A. Abraham, P. Bouvry, Particle swarm optimization: hybridization perspectives and experimental illustrations, Appl. Math. Comput., 217 (2011) 5208–5226.
- A. Gálvez, A. Iglesias, A new iterative mutually coupled hybrid GA–PSO approach for curve fitting in manufacturing, Appl. Soft Comput., 13 (2013) 1491–1504.
- C.-F. Juang, A hybrid of genetic algorithm and particle swarm optimization for recurrent network design, IEEE Trans. Syst. Man Cybern. Part B, 34 (2004) 997–1006.
- K. Premalatha, A. Natarajan, Hybrid PSO and GA for global maximization, Int. J. Open Problems Compt. Math., 2 (2009) 597–608.
- A.A. Esmin, S. Matwin, HPSOM: a hybrid particle swarm optimization algorithm with genetic mutation, Int. J. Innovative Comput. Inf. Control, 9 (2013) 1919–1934.
- A. Moghaddam, A. Alizadeh, A. Faridhosseini, A.N. Ziaei, D.F. Heravi, Optimal design of water distribution networks using simple modifed particle swarm optimization approach, Desal. Water Treat., 104 (2018) 1–12 (in press).
- R.P. Minaee, M. Mokhtari, A. Moghaddam, A.A. Ebrahimi, M. Askarishahi, M. Afsharnia, Wall decay coefficient estimation in a real-life drinking water distribution network, Water Resour. Manage., 33 (2019) 1557–1569.
- D.E. Goldberg, C.H. Kuo, Genetic algorithms in pipeline optimization, J. Comput. Civ. Eng., 1 (1987) 128–141.
- J.H. Holland, Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence, MIT Press, Cambridge, Massachusetts, London, England, 1992.
- R. Eberhart, J. Kennedy, Eds., A New Optimizer Using Particle Swarm Theory, MHS’95, Proceedings of the Sixth International Symposium on Micro Machine and Human Science, IEEE, Nagoya, Japan, 1995.
- A. Moghaddam, J. Behmanesh, A. Farsijani, Parameters estimation for the new four-parameter nonlinear Muskingum model using the particle swarm optimization, Water Resour. Manage., 30 (2016) 2143–2160.
- W. Peng, A. Maleki, M.A. Rosen, P. Azarikhah, Optimization of a hybrid system for solar-wind-based water desalination by reverse osmosis: comparison of approaches, Desalination, 442 (2018) 16–31.
- M. Clerc, Ed., The Swarm and the Queen: Towards A Deterministic and Adaptive Particle Swarm Optimization, CEC 99, Proceedings of the 1999 Congress on Evolutionary Computation, IEEE, Washington, DC, 1999.
- K.E. Parsopoulos, M.N. Vrahatis, Recent approaches to global optimization problems through particle swarm optimization, Nat. Comput., 1 (2002) 235–306.
- Y. Shi, R. Eberhart, Eds., A Modified Particle Swarm Optimizer, The 1998 IEEE International Conference on Evolutionary Computation Proceedings, IEEE World Congress on Computational Intelligence, Anchorage, AK, IEEE, 1998.
- Y. Shi, R.C. Eberhart, Parameter Selection in Particle Swarm Optimization, V.W. Porto, N. Saravanan, D. Waagen, A.E. Eiben, Eds., International Conference on Evolutionary Programming, Springer, Berlin, Heidelberg, 1998.
- F. Van den Bergh, A.P. Engelbrecht, A cooperative approach to particle swarm optimization, IEEE Trans. Evol. Comput., 8 (2004) 225–239.
- Guidelines for Design of Urban and Rural Water Supply and Distribution Systems, 117–3 (First Review Edition), Islamic Republic of Iran Vice Presidency For Strategic Planning and Supervision Press, Tehran, Iran, 2011.
- E. Todini, Looped water distribution networks design using a resilience index based heuristic approach, Urban Water J., 2 (2000) 115–122.
- A. Haghighi, A.E. Bakhshipour, Optimization of sewer networks using an adaptive genetic algorithm, Water Resour. Manage., 26 (2012) 3441–3456.