Optimizing Complex Network Topology For Robustness Based On Natural Connectivity

The complex networks in real world such as the Internet,power networks,transportation networks,social networks,etc.,plays an important role in our life.In order to make sure that our living and production are always in a normal status,these network systems should be able to resist the external attacks or internal failures.The robustness of a network is the ability of the network to maintain its connectivity after a random failure or an intentional attack,meaning that the nodes(or links)deletions.Therefore,how can we model the optimization for robustness of these network systems? What kind of structural features the best robust network has? These questions can be solved by the optimization for robustness on network topology.The results of complex network robustness optimization can be utilized to design the network topology to improve the robustness of networks.With the development of complex network theory,more and more scholars began to focus on complex network optimization research for robustness.The paper considers a new network's robustness measure based on spectral properties,natural connectivity,as the objective of optimization.We comprehensively utilize multi-field knowledge like the theory of combination graph,probability theory,statistical physics and intelligent computing,and study the robustness optimization problems on complex network topology based on natural connectivity for the further modeling analysis.(1)Modeling the optimization of complex network topology for robustness based on natural connectivity.Natural connectivity is based on the spectrum of network,and has a specific physical meaning and a concise and straightforward math.Thus it received more and more attentions from international and domestic scholars.The research of robustness optimization of complex network topology based on natural connectivity is still a theory blank,which inspires us to study.The paper mainly study on the modeling and optimization for network robustness by building reasonable assumptions and selecting suitable optimization algorithm.We aim to find out the network structure with a maximum value of natural connectivity and discuss the topological information of optimal network.(2)Proposing the optimization algorithm of complex network topology for robustness based on tabu search.As the optimization of complex network topology for robustness is clearly a classic combinational optimization problem,it is impossible to obtain the global optimal solution of the optimization problem.The satisfactory solution of this problem can be gained only if a heuristic method is employed.Therefore,the paper utilizes a tabu search algorithm to solve the optimization problem,and verifies its effectiveness.The paper study the change of significant structural properties of network to help us analyze the structural features of optimal robust network(3)Modeling the tradeoff problem for optimizing the robustness and efficiency of network.In the process of optimization for robustness,we found the conflicting relation between robustness and efficiency of network.Therefore,we further prove the conflicting relation by mean of the optimization on the model network and real network,and finally build the multi-objective optimization model.We adopt a multi-objective evolutionary algorithm to solve the model,and get a compromised network structure with high robustness and high efficiency.We use a degree correlation analysis method based on null model to analyze the tradeoff results.