The Research Of Evolutionary Algorithms Based On Complex Network

With the continuous development and progress of science and moderntechnology, the optimization problem became the focus of thestudy.Evolutionary algorithms are a class of algorithms which simulate naturalbiological behavior,including Differential Evolution algorithm and ArtificialBee Colony algorithm.Themain characteristics of these algorithms areself-adaptive,self-organizing, self-learning.Themost important is that they areimmune to the search space of objective function(such as derivability anddifferentiability the objective function).In recent years, research of evolutionary algorithm has made greatdevelopment,mainly about the improvement of searching result and the measureof convergence efficiency.The key way to improve the searching result is thatimproving the algorithm mechanism to accelerate the convergence rate,enhanceglobal search ability and local search ability.There is no doubt that the rise of complex networks has opened new visionof study of evolutionary algorithm. Large number of real systems can becharacterized by a complex network,such as river networks,transportationnetworksand more complex scientific citation networks.The actual elements inthe system are assumed to be nodes, the relationships between the elements are assumed to be edges of nodes,then complex network is composed of the nodesand the edges between nodes.The visualization of system by usingcomplexnetwork upgrades the research of systems to network level,providesnew method to observe the topology of the system, analyze the impactsbetweenindividuals and characteristics of the system.The network topology is mostessential in the complex network study. The topologies of population during theevolutionary process is so complex that only text or statistical data to indicate itspopulation structure will lead to lack of information.It will be largelyconvenient to recognize the internal structure of the algorithmpopulation,observe information interaction between individuals with showingthe population structure in the form of network.For evolutionary algorithm, its population structure largely affectsconvergence rate of algorithm.In this paper, the population structures based onthe topology of the population after the end of the iteration of differentialevolution algorithm and artificial bee colony algorithm were analised by meansof complex network. The validity of analysing evolutionary algorithms usingcomplex network was verified by experiments in this paper:(1)Populationstructure can be visual by means of complex network.(2)The networks ofevolutionary algorithms possess some features of complex network.The main work ofthispaperis:(1)Under the conditions of specified criteria for modeling, the networks ofartificial bee colony algorithm, differential evolution algorithm are modelled. (2)After modeling,the information of population topology was recorded inthe form of network,then the information flux networks of these algorithmswere visualized by Pajek.(3)In this part,the information flux networks of these algorithms wereanalyzed from the point of statistics.Firstly,the adjacency matrix of network wasgraphed to show the mechanism of algorithm. Then the degree distribution wascalculated.Experiments show that the network of differential evolutionalgorithm is scale-freenetwork,the degree distribution follows a power lawdistribution.While the artificial bee colony algorithms are random networks,degree distribution is a Poisson distribution.(4)In the experiments, control parameters of each algorithm were selectedto test ten functions.The result indicates that the improvement of the searchingefficiency is accompanied by the increase of average degree of these algorithmsnetworks. To verify the results furthermore,the improved artificial bee algorithmand differential evolution algorithm are tested, the testing results are comparedwith the artificial bee algorithm and differential evolution algorithm.The finalcomparing results formulates the conclusion is reliable.