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This study proposes a biobjective optimization method for timetable rescheduling during the end-of-service period of a subway network, taking all stakeholders' interests into consideration. We seek to minimize the total transfer waiting time for all transfer passengers, meanwhile minimizing the deviation to the scheduled timetable. The -constraint method and linearization techniques are utilized to obtain the approximate Pareto optimal solutions within limited seconds, allowing for figuring out the trade-off between the two objectives. The method is validated by numerical experiments for different delay scenarios based on a real-world case: the Beijing subway network.

The major objective of this work is to present a train rescheduling model with train capacity constraint from a passenger-oriented standpoint for a subway line. The model expects to minimize the average generalized delay time (AGDT) of passengers. The generalized delay time is taken into consideration with two aspects: the delay time of alighting passengers and the penalty time of stranded passengers. Based on the abundant automatic fare collection (AFC) system records, the passenger arrival rate and the passenger alighting ratio are introduced to depict the short-term characteristics of passenger flow at each station, which can greatly reduce the computation complexity. In addition, an efficient genetic algorithm with adaptive mutation rate and elite strategy is used to solve the large-scale problem. Finally, Beijing Subway Line 13 is taken as a case study to validate the method. The results show that the proposed model does help neutralize the effect of train delay, with a 9.47% drop in the AGDT in comparison with the train-oriented model.

A good timetable is required to not only be efficient, but also yield effectiveness in preventing and counteracting delays. When travelling via urban rail transit networks, transferring passengers may miss their scheduled connecting train because of a feeder train delay that results in them experiencing increased travel costs. Considering that running time supplements and transfer buffer times yield different effects on the travel plans of transferring and nontransferring passengers, we formulate an expected extra travel cost (EETC) function to appropriately balance efficiency and robustness, which is then implemented in the construction of a robust transfer optimization model with the objective of minimizing the total EETC. Next, to improve the computational efficiency, we propose an approximate linearization approach for the EETC function and introduce two types of binary variables and auxiliary substitution variables to convert the nonlinear model to a mixed-integer linear model. Experimental results show that our proposed method can yield practically applicable solutions with significant reductions in both EETC and probability of missing a transfer.

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