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城市生命线系统中存在2个重要问题,一个是面对自然灾害时的脆弱性,另一个是极高的建造成本。针对这2个问题,用具有边权重迭代的级联效应脆弱性和基于最短路径数目的构建成本等2个指标,建立基于复杂网络的优化模型。设计多目标的启发式优化算法,求解针对这2个指标的网络最优拓扑结构。从得到的最优网络中,用网络模体侦测方法求得模体的相对密度,发现其中的模体的相对密度能保持稳定。最后用美国电网的数据进行对比分析,发现相似的相对密度,表明美国电网的设计在级联脆弱性和建造成本上符合最优的拓扑结构。
There are two important problems in the urban lifeline system, one is the vulnerability in the face of natural disasters and the other is the extremely high construction cost. In view of these two problems, we build the optimization model based on complex network using two indexes: the cascade effect vulnerability with edge weight iteration and the construction cost based on the shortest path number. A multi-objective heuristic optimization algorithm is designed to solve the optimal network topology for these two indicators. From the obtained optimal network, the relative density of the mold body is obtained by the network mold detection method, and the relative density of the mold body therein is found to be stable. Finally, the comparative analysis of the data of the United States power grid and the finding of similar relative density show that the design of the United States power grid conforms to the optimal topology in terms of cascading vulnerability and construction cost.