为优化输水网络拓扑结构，量化网络抗毁性，建立以网络抗毁性最大化为目标的输水网络拓扑结构优化模型。首先，以输水网络拓扑结构为基础，从节点所处位置的中心程度和可替代程度出发，推求节点结构重要度，并以此表征网络抗毁度。其次，以网络边可连接数及边无交叉性为约束条件，建立以网络抗毁性最大化为目标函数的优化模型。最后，结合某输水网络算例，应用遗传算法求解该模型，寻求最优输水网络拓扑结构。算例计算结果表明：优化后网络中的节点结构重要度数值离散程度减小，网络抗毁性相较优化前得到了很大的提升，说明该模型能够为解决输水网络拓扑结构优化问题提供参考。

In order to optimize the topology of the water delivery network, the paper quantified the invulnerability of the network and established a topology optimization model for the water network with the goal of maximizing network invulnerability. Firstly, based on the topology of the water transport network, the importance of the node structure was derived from the central degree and the degree of substitutability of the location of the node, and the network invulnerability was characterized. Secondly, considering the number of connectable edges and the non-crossing of edges in a network as constraints, the optimization model with the maximization of network invulnerability was established. Finally, combined with a water delivery network example, the genetic algorithm was applied to solve the model, and the optimal water delivery network topology was sought. The calculation results showed that the degree of discreteness of the node structural importance in the network was reduced, and the network invulnerability was greatly improved compared with that before optimization. This indicated that the model could provide a reference for solving the problem of topology optimization of water delivery network.

国家自然科学基金项目（面上项目，重点项目，重大项目）