Researches On Modelling Scale-free And Small World Networks By Multi-objective Optimization

Complex networks often have the traits of scale-free,small world,ultra small world,community structure,fractal and so on.Modelling and Researching on these traits has always been the focus and difficulty in the field of complex network research.Nowadays,many domestic and foreign experts and scholars have established a lot of models to elaborate the traits of complex networks.However,these models often explain the traits of complex networks from different mechanisms,often can not be unified with the same mechanism to explain a variety of traits of a single complex network,they can not explain the various traits of complex networks and their relationships,and they often do not have the compatibility.This thesis explores a mechanism to explain the scale-free trait of complex networks and the small world effect,so as to establish a unified basis for the interpretation of the two traits.In this thesis,a multi-objective optimization modelling method is proposed,the complex network constructed by this method has the traits of scale-free and small world effect,thus,the two traits are attributed to the optimization mechanism of the network.The specific work and innovative points of this thesis are briefly introduced as follows:(1)Using the optimization theory to model the scale-free trait and the small world effect of complex networks.Firstly,the thesis generates a scale-free sample network and initialize the optimal model,then optimize the model which the paper construct to achieve that its node degrees match the sample.(2)The network model is optimized by setting multiple objectives.In the thesis,the average shortest path length is the first optimal objective and the similarity of the degree distribution that the optimal network matches the sample network is the second optimal objective,the average clustering coefficient of all the nodes of the network is the third optimal objective and the optimal model supplies to the constraint of the value which is the degree of the node of the network.(3)Drawing the topological maps of the networks which are generated by the optimization model,through the observation of the topological map to find the gradient of the law.In the simulation experiment,using the simulation software to write the simulation code and run the simulation experiment.In the 18 groups of simulation experiments,by setting different parameter values in the optimization model,many scale-free and small world networks with a variety of parameters are generated and their degree distributions of the networks are obtained.Using the drawing software to process the network datas which are obtained by the simulation experiments,the topological maps of the networks which are generated by the optimization model are drawn.Through the observation of topological maps,some gradual change rules of the topological maps are found.By observing the degree distributions of the networks,it is concluded that the degree distributions of the networks follow the power law distribution,the networks which are generated by the optimization model have the scale-free trait.Through the statistics and calculation,the values of average shortest path length of the network which are generated by the optimization model are approximately equal to ln(N),and the values of the clustering coefficient are relatively high,the networks which are generated by the optimization model have small world effect.The research of this thesis proves that the scale-free and small world network is likely to be built on the multi-objective optimization mechanism.