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Time related association rule mining is a kind of sequence pattern mining for sequential databases. In this paper, a generalized class association rule mining is proposed using genetic network programming (GNP) in order to find time related sequential rules more efficiently. GNP has been applied to generate the candidates of the time related association rules as a tool. For fully utilizing the potential ability of GNP structure, the mechanism of Generalized GNP with Multi-Branchesmiddot Full-Paths mechanism is proposed for class association data mining. The aim of this algorithm is to better handle association rule extraction from the databases with high efficiency in a variety of time-related applications, especially in the traffic volume prediction problems. The algorithm capable of finding the important time related association rules is described and experimental results are presented using a traffic prediction problem.