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As an extension of Genetic Algorithm (GA) and Genetic Programming (GP), a new approach named Genetic Network Programming (GNP) has been proposed in the evolutionary computation field. GNP uses multiple reusable nodes to construct directed-graph structures to represent its solutions. Recently, many research has clarified that GNP can work well in data mining area. In this paper, a novel evolutionary paradigm named GNP with Estimation of Distribution Algorithms (GNP-EDAs) is proposed and used to solve traffic prediction problems using class association rule mining. In GNP-EDAs, a probabilistic model is constructed by estimating the probability distribution from the selected elite individuals of the previous generation to replace the conventional genetic operators, such as crossover and mutation. The probabilistic model is capable of enhancing the evolution to achieve the ultimate objective. In this paper, two methods are proposed based on extracting the probabilistic information on the node connections and node transitions of GNP-EDAs to construct the probabilistic model. A comparative study of the proposed paradigm and the conventional GNP is made to solve the traffic prediction problems using class association rule mining. The simulation results showed that GNP-EDAs can extract the class association rules more effectively, when the number of the candidate class association rules increases. And the classification accuracy of the proposed method shows good results in traffic prediction systems.