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This paper investigates the robust collaborative train timetabling optimization problem by integrating short-turning strategy and train circulation plan while considering the uncertainty in passenger demand. The passenger dynamics equations are proposed to represent the relationship among headways, short-turning services, and passenger load. A mixed-integer nonlinear programming (MINLP) model is constructed to balance train utilization and stranded passengers. The extra variables are introduced to linearize the nonlinear constraints and convert the original model into a robust counterpart model according to the strong duality theory. Finally, two numerical experiments are carried out to verify the validity of the train timetabling model integrating with short-turning strategies. The study shows that the proposed strategy can better support the balance between stranded passengers and train utilization compared to other regular strategies. Moreover, the results indicate that robust strategies perform well in the trade-off between the optimality and the level of conservatism of the solutions.

Robust collaborative optimization for train timetabling and short-turning strategy in urban rail transit systems