病毒传播的网络结构度量及其多目标优化控制

In order to control network epidemic propogation and enhance the network security ability, the network structure based measurement method is proposed to describe the characteristics of the epidemic propagation, such as epidemic threshold, speed and scale, and the multi-objective optimization strategies for network structure are developed to control the epidemic propogation in the project. The main contents are as follows: The mathematical and simulation models are constructed by using Markov Chain and Cellular Automata theory, in which the network structure is completely included in the two models. Then we study the measurement relations between the epidemic propogation and network structure, and develop the network structure based multi-objective optimization functions for controlling virus propogation in the network. Based on the proposed optimal functions, we present the corresponding network structure based heuristic optimal strategies, such as node protection, link deleting and rewiring, in order to optimize the network structure and improve the ability of controlling epidemic propogation. Through the study of the project, we can obtain the network structural metric for epidemic propogation and the multi-objective optimization functions with network structure, and develop the corresponding optimal strategies for some networks with different structures. The study of the project has important significance for optimally designing the network structure and improving network security and efficiency, and can be applied to fault cascading and rumor spreading in complex networks.

本项目从对抗网络病毒传播、增强网络系统安全出发，研究用网络结构特征准确表征病毒传播阈值、传播速度和稳态规模等病毒传播特性，通过对网络结构进行多目标优化来达到对抗病毒传播的目的。主要研究内容包括：使用马尔科夫链和元胞自动机理论，建立复杂网络病毒传播的数学模型和仿真模型，将网络结构完全表征在这两种传播模型中，研究网络病毒传播特性与网络结构的度量关系，建立控制病毒传播的网络结构多目标优化函数；基于该多目标优化函数，提出节点保护、边删除和边重写等启发式优化算法，对任意结构网络进行结构优化和免疫保护，增强网络对抗病毒传播的能力。通过本项目研究，将获得病毒传播的网络结构度量，得到网络结构多目标优化函数，建立多种网络结构优化策略。本项目研究对优化网络结构设计、提高网络安全和网络运行效率具有重要意义，该研究成果也能够推广到网络相继故障和谣言传播等复杂网络研究领域。

本项目研究复杂网络中网络结构复杂性与传播行为之间的关系，采用马尔科夫链和元胞自动机理论，建立复杂网络病毒传播的数学模型和仿真模型，研究网络结构特征与传播行为演化的相互作用和度量关系。寻找有效的网络结构优化策略和传播免疫策略，达到抑制病毒和谣言传播的目的。本项目在社交网络谣言传播、网络中节点发现等方面进一步拓展研究，并就公共交通网络、无线传感网络等进行了一定的应用研究。项目组分别在均匀、异质、加权、自适应网络中研究了网络结构参数对病毒传播特性影响并建立一系列的传播模型，提出了几个重要节点发现算法，提出了几种抑制病毒和谣言传播的免疫策略；在结构优化方面也提出了相应的而优化策略。项目组成员在已在Physic A，The European Physical Journal B，Chin. Phys. B ，Journal of Networks，物理学报，武汉大学学报等权威学术期刊以及International Conference on IEEE 、CCDC 等国际知名会议发表高水平论文40余篇，其中 SCI 检索论文10余篇，EI检索论文18篇。本项目按照预定计划执行，实现了预期目标。在研究领域取得了一定的创新成果，也通过广泛的国际学术交流提升了团队影响力，培养了一批高水平人才。