1. College of Mathematics and Computer Science,Fuzhou University,Fuzhou 350108 2.School of Computer,National University of Defense Technology,Changsha 410073
Abstract：An immunization strategy based on particle swarm optimization is presented to effectively solve the control of the virus spread in the weighted scale-free networks. Motivated by the idea of network partition,two optimization goals with the sub-network scale and the sum of the sub-network strength are simultaneously taken into account. Moreover,the mutation and the crossover operator of genetic algorithm are introduced to improve the population diversity and avoid the algorithm falling into a local optimal solution prematurely. Simulation results show that the proposed immunization strategy has better performance than the targeted immunization strategy which is generally considered to be highly efficient at present. Through immunizing the specified number of nodes,the network can be well divided into the sub-networks whose nodes number and sum of nodes strength are as small as possible.
[1] Niazi M,Hussain A. Agent-Based Tools for Modeling and Simulation of Self-Organization in Peer-to-Peer,Ad Hoc,and Other Complex Networks. IEEE Communications Magazine,2009,47(3): 166-173 [2] Hu Cheng,Yu Juan,Jiang Haijun,et al. Exponential Synchronization of Complex Networks with Finite Distributed Delays Coupling. IEEE Trans on Neural Networks,2011,22(12): 1999-2010 [3] Shi Chuan,Yan Zhenyu,Cai Yanan,et al. Multi-Objective Community Detection in Complex Networks. Applied Soft Computing,2012,12(2): 850-859 [4] Zhao Peng,Cai Qinsheng,Wang Qingyi,et al. An Automatic Keyword Extraction of Chinese Document Algorithm Based on Complex Network Features. Pattern Recognition and Artificial Intelligence,2007,20(6): 827-831 (in Chinese) (赵 鹏,蔡庆生,王清毅,等.一种基于复杂网络特征的中文文档关键词抽取算法.模式识别与人工智能,2007,20(6): 827-831) [5] Wang Xuesong,Gu Yangyang,Cheng Yuhu. Construction of Delay Gene Regulatory Network Based on Complex Network. Acta Electronica Sinica,2010,38(11): 2518-2522(in Chinese) (王雪松,谷阳阳,程玉虎.基于复杂网络的时延基因调控网络构建.电子学报,2010,38(11): 2518-2522) [6] Jin Di,Yang Bo,Liu Jie,et al. Ant Colony Optimization Based on Random Walk for Community Detection in Complex Networks. Journal of Software,2012,23(3): 451-464 (in Chinese) (金 弟,杨 博,刘 杰,等.复杂网络簇结构探测——基于随机游走的蚁群算法.软件学报,2012,23(3): 451-464) [7] Barab si A L,Albert R. Emergence of Scaling in Random Networks. Science,1999,286(5439): 509-512 [8] Callway D S,Newman M E J,Strogatz S H,et al. Network Robustness and Fragility: Percolation on Random Graphs[EB/OL]. [2012-02-01]. http://prl.aps.org/pdf/PRL/v85/i25/p5468_1 [9] Pastor-Satorras R,Vespignani A. Immunization of Complex Networks[EB/OL]. [2012-02-01]. http://pre.aps.org/pdf/PRE/v65/i3/e036106 [10] Cohen R,Ben-Avraham D,Havlin S. Efficient Immunization of Populations and Computers[EB/OL]. [2012-02-01]. http://prl.aps.org/pdf/PRL/v91/i24/e247901 [11] Bai Wenjie,Zhou Tao,Wang Binghong. Immunization of Susceptible-Infected Model on Scale-Free Networks. Physica A: Statistical Mechanics and Its Applications. 2007,384(2): 656-662 [12] Yang Shijie. Exploring Complex Networks by Walking on Them[EB/OL]. [2012-02-01]. http://arxiv.org/pdf/cond-mat/0406177.pdf [13] Eberhart R C,Kennedy J. A New Optimizer Using Particles Swarm Theory // Proc of the 6th International Symposium on Micro Machine and Human Science. Nagoya,Japan,1995: 39-43 [14] Kennedy J,Eberhart R C. Swarm Intelligence. San Mateo,USA: Morgan Kaufmann,2001 [15] Wang Wenxu,Wang Binghong,Hu Bo,et al. General Dynamics of Topology and Traffic on Weighted Technological Networks[EB/OL]. [2012-02-01]. http://prl.aps.org/pdf/PRL/v94/i18/e188702 [16] Bailey N T J. The Mathematical Theory of Infectious Diseases and Its Applications. 2nd Edition. London,UK: Griffin,1975 [17] Anderson R M,May R M. Infectious Diseases in Humans: Dynamics and Control. Oxford,UK: Oxford University Press,1992 [18] Hethcote H W. The Mathematics of Infectious Diseases. SIAM Review,2000,42(2): 599-653 [19] Xu Xinjian,Peng Haiou,Wang Xiaomei,et al. Epidemic Spreading with Time Delay in Complex Networks. Physica A: Statistical Mechanics and Its Application,2006,367: 525-530 [20] Earn D J D,Pejman R,Benjamin M B,et al. A Simple Model for Complex Dynamical Transitions in Epidemics. Science,2000,287(5453): 667-670 [21] Newman M E J. Threshold Effects for Two Pathogens Spreading on a Network[EB/OL]. [2012-02-01]. http://arxiv.org/pdf/cond-mat/0502373.pdf [22] Masuda N,Konno N. Multi-State Epidemic Processes on Complex Networks. Journal of Theoretical Biology,2006,243(1): 64-75 [23] Guo Wenzhong,Chen Guolong. Discrete Particle Swarm Optimization Algorithm and Its Application. Beijing,China: Tsinghua University Press,2012 (in Chinese) (郭文忠,陈国龙.离散粒子群优化算法及其应用.北京:清华大学出版社,2012) [24] Guo Wenzhong,Chen Guolong. An Efficient Discrete Particle Swarm Optimization Algorithm for Multi-Criteria Minimum Spanning Tree. Pattern Recognition and Artificial Intelligence,2009,22(4): 597-604 (in Chinese) (郭文忠,陈国龙.一种求解多目标最小生成树问题的有效离散粒子群优化算法.模式识别与人工智能,2009,22(4): 597-604) [25] Guo Wenzhong,Chen Guolong,Xiong Naixue,et al. Hybrid Particle Swarm Optimization Algorithm for VLSI Circuit Partitioning. Journal of Software,2011,22(5): 833-842 (in Chinese) (郭文忠,陈国龙,Xiong Naixue,等.求解VLSI电路划分问题的混合粒子群优化算法.软件学报,2011,22(5): 833-842) [26] Guo Wenzhong,Xiong Naixue,Chao H C,et al. Design and Analysis of Self-Adapted Task Scheduling Strategies in Wireless Sensor Networks. Sensors,2011,11(7): 6533-6554 [27] Chen Guolong,Guo Wenzhong,Chen Yuzhong. A PSO-Based Intelligent Decision Algorithm for VLSI Floor Planning. Soft Computing,2010,14(12): 1329-1337 [28] Shi Y,Eberhart R C. A Modified Particle Swarm Optimizer // Proc of the IEEE International Conference on Evolutionary Computation. Anchorage,USA,1998: 69-73
2013, Vol. 26 
