A robust train timetable optimization approach for reducing the number of waiting passengers in metro systems

Timetable optimization in metro systems has been an active research topic for a long time. Traditional studies often ignore some uncertainties of passenger characteristics to simplify the model formulation and solution algorithm. In this paper, we present a robust optimization approach for the timetable optimization problem with consideration of the uncertainties of passenger arrival times and alighting passenger number for each station. Firstly, the uncertain properties of passengers are analyzed, and the scenarios are designed to reveal the impact of the uncertainties. Secondly, a robust optimization model with two phases is developed: the first phase is to obtain the minimum number of waiting passengers for each scenario, and the second phase is to decide on a robust solution with the minimax regret value. Furthermore, two heuristic algorithms are designed to search the robust optimal solutions. Finally, a practical example is presented based on the real-life operation data from the Beijing Metro Yizhuang Line. The results on the basis of 20 new scenarios show that the relative regret value of the robust timetable is less than 15%, which illustrates that the obtained timetable is strongly robust.