Multi Objective Design of Water Distribution System Using Todini’s Resilience Index and Improving the Strength Pareto Evolutionary Algorithm

Document Type : Research Paper


1 PhD Student of Water Resources Engineering, Dept. of Water Engineering, College of Agriculture, Ferdowsi University, Mashhad, Iran

2 Assoc. Prof., Dept. of Water Engineering, College of Agriculture, Ferdowsi University, Mashhad, Iran

3 Prof., Dept. of Water Engineering, College of Agriculture, Ferdowsi University, Mashhad, Iran


Water distribution network one of the most important and most sensitive urban infrastructures which can be recently with regard to population growth and consumers '' needs to increase with challenges such as reducing the pressure and discharge that are all due to unsuitable design and based on economic goals. In order to overcome these problems when designing an urban water distribution system should always be considered reliability of the network. In this research, to optimize the water distribution networks, two main objectives of cost minimization and maximization of network reliability were considered. To calculate network reliability, the Tondini''s Resilience Index and its hydraulic simulation EPANET 2.0 model were used. Then using the second edition of the evolutionary algorithm based on the strength of the Pareto (SPEA2) and creating a dynamic connection with the EPANET 2.0 hydraulic model in the MATLAB software environment, optimizing the multi-objective of the four water distribution networks including Two-Loop, Kadu, Hanoi networks and D zone of Mashhad. Simultaneous optimization of two main objectives including cost minimization and maximization of the Tondini''s Resilience Index led to the production of optimal solutions in the form of the Pareto front. An optimal solution, called Point C, was introduced using Young''s bargaining method from the final Pareto front of in each of the networks. Selected C solution in two-loop,Hanoi and Kadu networks increased 22.91, 17.13 and 7.41 precent, of the network average pressure compared to its lowest cost in this study (point A). Also, the selected C solution in D-zone network of Mashhad, with an increase of 4.23 precent of the network average pressure compared to the initial design of the consulting company (point D), illustrate that the solution designed by the consulting company would be a dominated solution under the final Pareto front of this study. In this research, the Tondini''s Resilience Index illustrate that, based on increasing nodal pressure, it has the ability to increase the reliability of the network, which This causes the network to be in critical condition or failure of the pipes, with high reliability, providing adequate pressure and discharge in other nodes. Also, the satisfactory performance of the SPEA2 multi-objective algorithm in providing the optimal Pareto front for the issues indicated showed that the design pattern developed in this study could be to provide an optimal set of solutions to the employer to select the points in which each two factors of cost and reliability are combined in a favorable situation.


Alperovits, E. & Shamir, U. 1977. Design of optimal water distribution systems. Water Resources Research, 13, 885-900.
Creaco, E., Franchini, M. & Todini, E. 2016. Generalized resilience and failure indices for use with pressure-driven modeling and leakage. Journal of Water Resources Planning and Management, 142, 04016019.
Fujiwara, O. & Khang, D. B. 1990. A two‐phase decomposition method for optimal design of looped water distribution networks. Water Resources Research, 26, 539-549.
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 Resources Planning and Management, 134, 147-160.
Ostfeld, A., Oliker, N. & Salomons, E. 2013. Multiobjective optimization for least cost design and resiliency of water distribution systems. Journal of Water Resources Planning and Management, 140, 04014037.
Reca, J., Martínez, J. & López, R. 2017. A hybrid water distribution networks design optimization method based on a search space reduction approach and a genetic algorithm. Water, 9, 845.
Surco, D. F., Vecchi, T. P. & Ravagnani, M. A. 2018. Optimization of water distribution networks using a modified particle swarm optimization algorithm. Water Science and Technology: Water Supply, 18, 660-678.
Todini, E. 2000. Looped water distribution networks design using a resilience index based heuristic approach. Urban Water, 2, 115-122.
Young, H. P. 1993. An evolutionary model of bargaining. Journal of Economic Theory,59, 145-168.
Zitzler, E., Laumanns, M. & Thiele, L. 2001. SPEA2: improving the strength pareto evolutionary algorithm. TIK-Report, 103, Swiss Federal Intitute of Technology, Zurich.