Robustness Optimization Algorithm with Multi-Granularity Integration for Scale-Free Networks Against Malicious Attacks  

基于多粒度集成的无标度网络抵抗恶意攻击鲁棒性优化算法

作　　者：ZHANG Yiheng LI Jinhai 张毅恒;李金海(昆明理工大学数据科学研究中心,云南昆明650500;昆明理工大学理学院,云南昆明650500)

机构地区：[1]Data Science Research Center,Kunming University of Science and Technology,Kunming 650500,China [2]Faculty of Science,Kunming University of Science and Technology,Kunming 650500,China

出　　处：《昆明理工大学学报(自然科学版)》2025年第1期54-71,共18页Journal of Kunming University of Science and Technology(Natural Science)

基　　金：National Natural Science Foundation of China(11971211,12171388).

摘　　要：Complex network models are frequently employed for simulating and studyingdiverse real-world complex systems.Among these models,scale-free networks typically exhibit greater fragility to malicious attacks.Consequently,enhancing the robustness of scale-free networks has become a pressing issue.To address this problem,this paper proposes a Multi-Granularity Integration Algorithm(MGIA),which aims to improve the robustness of scale-free networks while keeping the initial degree of each node unchanged,ensuring network connectivity and avoiding the generation of multiple edges.The algorithm generates a multi-granularity structure from the initial network to be optimized,then uses different optimization strategies to optimize the networks at various granular layers in this structure,and finally realizes the information exchange between different granular layers,thereby further enhancing the optimization effect.We propose new network refresh,crossover,and mutation operators to ensure that the optimized network satisfies the given constraints.Meanwhile,we propose new network similarity and network dissimilarity evaluation metrics to improve the effectiveness of the optimization operators in the algorithm.In the experiments,the MGIA enhances the robustness of the scale-free network by 67.6%.This improvement is approximately 17.2%higher than the optimization effects achieved by eight currently existing complex network robustness optimization algorithms.复杂网络模型经常被用来模拟和研究现实世界中的各种复杂系统,其中无标度网络在面对恶意攻击时,通常表现得较为脆弱.因此,提升无标度网络鲁棒性成为了一个迫切需要解决的问题.针对这一问题,作者提出了一种多粒度集成算法(Multi-Granularity Integration Algorithm,MGIA),目的是在保持节点度值不变、确保网络连通性和避免产生重边的前提下,提升无标度网络鲁棒性.该算法首先由待优化的初始网络生成多粒度结构,再采用不同优化策略优化多粒度结构内不同粒层的网络,最后通过精英粒层迁移操作实现不同粒层之间的信息交流,进一步提升优化效果.本文设计了新的网络刷新操作、交叉操作和变异操作,以确保优化后的网络符合约束条件.同时,还提出了新的网络相似性和网络差异性评价指标,以提升算法内优化操作的效果.实验结果显示,多粒度集成算法成功将无标度网络的鲁棒性提高67.6%,在与目前存在的8种复杂网络鲁棒性优化算法的比较中,优化效果高出约17.2%.

关 键 词：complex network model MULTI-GRANULARITY scale-free networks ROBUSTNESS algorithm integration 

分 类 号：O157.5[理学—数学]