| Summary: | The research of vulnerability in complex network plays a key role in many real-world applications. However, most of existing work focuses on some static topological indexes of vulnerability and ignores the network functions. This paper addresses the network attack problems by considering both the topological and the functional indexes. Firstly, a network attack problem is converted into a multi-objective optimization network vulnerability problem (MONVP). Secondly to deal with MONVPs, a multi-objective evolutionary algorithm is proposed. In the new approach, a k-nearest-neighbor graph method is used to extract the structure of the Pareto set. With the obtained structure, similar parent solutions are chosen to generate offspring solutions. The statistical experiments on some benchmark problems demonstrate that the new approach shows higher search efficiency than some compared algorithms. Furthermore, the experiments on a subway system also suggests that the multi-objective optimization model can help to achieve better attach plans than the model that only considers a single index.
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