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In recent decades, due to the high cost of running a water supply network, designers have been trying to design networks with the least cost and maximum reliability. Networks that are able to provide good services in the face of demand changes or failure of the pipeline. Several indexes for reliability measurements were introduced and used as one of the objective functions along with cost in water distribution systems design problem. One of the issues that has been highlighted in recent years is which of these indicators are more successful in measuring the reliability of a water supply network. In this study, six famous reliability indicator entitled Minimum surplus head (MSH), total surplus head (TSH), resilience index (RI), network resilience index (NRI) and modified resilience index (MRI), entropy reliability indicator (ERI) and a new presented reliability indicator entitled Ratio of surplus head (MSH) described and used as one of the objective functions of a water distribution system design optimization problem. For this purpose, a multi-objective differential evolution algorithm has been developed in Matlab software and linked to the Epanet as the hydraulic solver. The generated algorithm applied on two different sample networks with different nature (gravitational feeding and feeding with pumping stations). To analysis of real hydraulic and mechanical reliability of obtained networks in optimization processes, a large number of abnormal operating conditions such as water demand uncertainty or pipes burst scenarios have been generated and applied on obtained Pareto Fronts of each optimization process. Then, the percentage of scenarios that each network could not satisfy the design’s constraints or failed in response to them has been calculated. The over demand’s scenarios were sampled using the general normal distribution method. The percentage of scenarios that each answer (water network in Pareto Front) cannot satisfy the design constraint has been measured and called Hydraulic Failure Percentage (HFP). Also, for modeling the abnormal mechanical conditions, lot of scenarios were produced with broken pipes. In each of these scenarios, there is a possibility of one to ten different pipes break. The locations of burst pipes are selected randomly. The percentage of scenarios that each case cannot satisfy the design constraint has been measured and called Mechanical Failure Percentage (MFP). These scenarios would remain constant for all of members of Pareto Fronts. The lower value of HFP and MFP demonstrate the greater ability of the network to deal with changes in nodal demand and the pipe bursts respectively. For deeper analysis, the conditions of failing (Not satisfying the constraints) divides into three sub-state as flowing: State A: Pressure of all nodes is more than the minimum acceptable pressure in all time. State B: Pressure of all nodes is more than 95% of the minimum acceptable pressure in all time. State C: Pressure of 95% of nodes is more than the minimum acceptable pressure in all time. The results of calculations summarized and have been shown in the diagrams. Results show that MSH and RI are the best indicators for optimal design of water supply networks without pumping station and include it.

Keywords: Urban Water Distribution Networks, Optimization, Reliability Indicators, Differential Evolution Algorithms

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