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With multiple stations being built in the high-speed railway hub, how to schedule trains among stations is of great significance. This paper studies the integrated train routing and timetabling problem in a multi-station high-speed railway hub. Based on a specific bi-level network, a binary integer programming model using cumulative flow variables is proposed to minimize the total cost of trains and passengers. An extended Alternating Direction Method of Multipliers (ADMM) algorithm is developed to decompose the model into train and passenger subproblems. The performance of the algorithm is investigated on small-scale and large-scale networks. Compared with the commonly used Lagrangian Relaxation (LR) algorithm, the results indicate that the extended ADMM obtain better solutions with less iterations, where the lower bound decreases by 3.79% and iterations are reduced by 83.54%. Another comparative experiment shows the total cost of the optimization scheme is 16.22% lower than that of the current fixed scheme.

Integrated train routing and timetabling problem in a multi-station high-speed railway hub