A novel multiple reservoirs network optimization (MRNO) model is proposed to provide referable diameters of pipes that can be applied in water distribution network (WDS) design. Firstly, the shortest path between reservoirs and junctions is solved by the Dijkstra algorithm. Then, pressure losses of all pipes are solved by extended period simulation (EPS) and the minimum pressure loss of each pipe is selected. Thirdly, the diameter of each pipe is updated according to Hazen-Williams (HW) equation and new diameter values are given to pipes. Diameters of pipes are re-calculated in the next iteration until convergence or up to the maximum iteration time. Then, NSGA-II is employed to optimize network reliability, and the initial population at the first generation is the result of MRNO. Objective functions contain unit pipe cost, pressure uniformity function, and leakage uniformity function. For verifying the effectiveness of this model, HDP-SGA, NSGA-II, and SGA are employed as comparisons. Finally, five cases are selected to verify the practicability of this model. The results demonstrate that the network reliability of all WDSs has improved and pipe costs are reduced after MRNO-NSGA-II optimization.

Graphical Abstract

中文翻译：

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配水系统水头损失的改进网络可靠性优化模型

提出了一种新颖的多水库网络优化模型（MRNO），以提供可用于配水管网（WDS）设计的参考管径。首先，通过Dijkstra算法求解储层与汇合点之间的最短路径。然后，通过延长周期仿真（EPS）解决所有管道的压力损失，并选择每条管道的最小压力损失。第三，根据Hazen-Williams（HW）公式更新每个管道的直径，并为管道指定新的直径值。在下一次迭代中将重新计算管道直径，直到收敛或直到最大迭代时间为止。然后，使用NSGA-II优化网络可靠性，第一代的初始填充是MRNO的结果。目标函数包含单位管道成本，压力均匀度函数和泄漏均匀度函数。为了验证该模型的有效性，将HDP-SGA，NSGA-II和SGA用作比较。最后，选择了五种情况来验证该模型的实用性。结果表明，优化MRNO-NSGA-II后，所有WDS的网络可靠性都得到了提高，管道成本降低了。

图形概要