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A Bi-Objective Optimization Model for Coordinated Train Timetabling in Rail Transit Networks

In large-cities, urban rail networks usually involve more than two connected lines and passengers mostly transfer several times to reach their destinations. Thus, the coordination of train timetables in different lines has become a key issue in recent years for improving the transfer convenience of passengers. In this paper, we first propose a synchronization quality index (SQI) to qualitatively evaluate the transfer convenience of passengers, and we develop a bi-objective optimization approach for the coordination of train timetables, where the objectives are to optimize both SQI and average waiting time of passengers. We also construct a mixed integer nonlinear programming formulation by considering the time-dependent properties of passenger demand and their transfers among multiple transit lines. Further, we adopt a local search, a simulated annealing algorithm and a genetic algorithm to solve the proposed model. A real-world instance based on the passenger demand data in Beijing Metro Network is conducted to verify the effectiveness of our approach. By comparing with the current (uncoordinated) timetable in Beijing Metro, our solution can improve the value of SQI by 31.28% and reduce the passenger waiting time by 3.49 %.