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Public transportation is a common passenger transportation system widely used all over the world. The system includes buses, trolley-buses, shuttles, rapid transit (Metro, Subway, undergrounds) and other vehicles to provide the best service. Determining optimal routes (lines) for such vehicles can highly affect the costs and efficiency of the transportation system. In this paper, a mathematical model for clustering the multiple routes of the bus transportation system is proposed in order to optimize the total transportation cost over the routes. The model is implemented in Lingo 11.0 software. Due to the complexity of the model, a Genetic Algorithm meta-heuristic is also developed for solving the model, and four examples are solved using this approach. The computational results show the effectiveness of the proposed model.