Evolving Models And Topology Optimization On Complex Network

In the past few years,there has been increasing interest in studying complex network,especially after the models of small-world network and scale-free network were proposed.Researches on complex network, particularly on its topology structure,can help us know about and explain various network characteristics exhibited from the complex system,such as network congestion,network synchronization and network frangibility and so on;they can also help us deeply understand advantages and drawbacks of the existing network so as to take effective measures to avoid occurrence of risks or design a new network with good performance.This paper concentrates on evolving models and topology optimization of the complex network by using statistical theory,intelligent algorithms and computer simulation.These studies would provide some guides on network design.The main works are summarized as follow:1.Put forward a kind of complex network model with hierarchical structure.This work is done by referring to the formation mechanism of a real social network.The structure algorithm of the model and Matlab program are given.Characteristics of the model are also investigated from theoretical and numerical points of view.Comparison is performed with the WS network and NW network.The producing process of the proposed model simulates the formation mechanism of the real social network;its network topology is small-world,scale-free and with hierarchical structure;its statistic characteristics are consistent with the actual observation.2.Optimize the complex network by using an improved genetic algorithm.Based on the congestion and the cost,specifically the diameter and average degree of the complex network,the topology optimization is studied by using a genetic algorithm proposed in the paper.The algorithm has the following features:(1) population diversity is increased by using the transpose operator instead of the mutation operator;(2) the premature convergence of the algorithm is avoided by adaptively calculating the crossover operation rate and the transpose operation rate;(3) the evolution direction is determined by comparing the individual fitness after and before the genetic operator performs,the individual with high fitness remains;(4) the population size is adapted by an improved calculation of the individual 'lifetime',which decides the chromosome survival.The experiments show that the proposed genetic algorithm has better performance than the Genetic Algorithm with Varying Population Size.Next,the topology of the complex network is optimized by the improved algorithm.The coding scheme is based on the star-shaped network and the corresponding genetic rules are applied appropriately. Although some freedom of the network topology is lost,the optimization method avoids checking the individual connectivity after every operation of the genetic operator,which reduces the computational complexity and achieves better network topology in the relatively short time.