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Railway transport becomes a more popular transportation in many countries due to its large transport capacity, low energy consumption, and benign environment. The passenger train service planning is the key of the rail operations system to balance the transport service and the passenger demand. In this paper, we propose a mixed binary linear programming formulation for the passenger train service planning to optimize the train route, frequency, stop schedule, and passenger assignment simultaneously. In addition, we analyze the computational complexities of the model and develop a Benders decomposition algorithm with valid inequalities to solve this problem. Finally, our model and algorithm are tested on a real-world instance of the Beijing-Shanghai high-speed railway line. The computational results show that our approach can solve these problems within reasonable solution time and small optimality gaps (less than 2.5%). [ABSTRACT FROM AUTHOR]

With the boom of big data, the Internet contains more and more personal behavior information, but it is difficult to extract effectively. A model involving multivariate processing capability must be constructed to deal with these time series with complex characteristics. In this paper, a novel hybrid model embedding Baidu Search Index is therefore proposed to implement multi-step ahead subway passenger flow forecasting. Firstly, we collect data from informative Baidu Search Index, reduce dimensionality, and screen out the powerful predictors by statistical analysis. Secondly, we extract matching common modes at similar time scales between the subway passenger flow and screened Baidu Search Index via multivariate mode decomposition being optimized by multi-objective algorithm. Furthermore, to eliminate pseudo statistical causality, we select the optimal combination of modal components between subway passenger flow and its corresponding Baidu Search Index at each time scale by an innovative multi–modal analysis strategy. Thirdly, we reconstruct the forecasting values of each selected optimal combination as the final results. The empirical results of Beijing, Shanghai and Guangzhou show that the proposed model can significantly outperform six benchmark models in both the level and directional accuracy. So introducing Baidu Search Index creates a sound opportunity to enhance the subway passenger flow forecasting ability. [ABSTRACT FROM AUTHOR]