Mathematical Model Of Node Matching And Evolutionary Solutions

Recently, more and more scholars pay attention to complex network, which plays an important part in many areas, such as transportation, communication, biology,physics, computer, control and so on. What’s more, there have been outstanding research results in these areas.Due to universal connections among substances in the world, not only does there exist a connection among different individuals in the same network system, but also there is a close interaction and association among different systems. A common interaction is that an individual may exist in several different networks at the same time(Such an individual is called a multi-identity individual one). When we are to analyze associated networks, a very important task is to find out the corresponding relations among different identities, which is called the node matching problem. The task plays an important part in identification and pattern matching problems. However,the existing node matching method of matching accuracy remains to be improved. As a result, this paper mainly studied how to use the topology of networks to establish a mathematical model of network node matching problems. What’s more, the corresponding evolutionary algorithm is presented.Above all, this paper studied the matching theory and method of network nodes based on adjacency matrix that is the perfect embodiment of network topology.Therefore, in order to realize the match among the nodes, this paper is to measure the degree of match network through the similarity among the network adjacency matrix.First, set up a optimization model of node matching based on the graph adjacency matrix of the network; Then, solve the mentioned model by presenting a relevant evolutionary algorithm. Finally, do experiments and get the result that the proposed method can achieve satisfactory matching accuracy compared with the traditional random algorithm.Secondly, this paper studied the node matching theory and method based on multi-objective optimization. It is probable to get more partial results by using only a single objective function to evaluate the degree of match about two networks. In fact,in addition to the adjacency matrix, we can also use other ways to express the topology of a network. Only in this way can we use multiple indicators to measure the degree of match between networks. First, employ many optimization in-dices to establish the multi-objective optimization model of node matching networks; Then,use the multi-objective evolutionary algorithm for a solution. Finally, applyexperimental results to show that the method can be better matching precision than single objective methods.The research achievements of this paper offers a new way to solve node matching problems as well as improve the efficiency and accuracy of node matching.Therefore, it has important theoretical significance and practical application value.