A Bi-objective optimization model for the last train timetabling problem. (September 2022) - Ning, Jia; Peng, Qiyuan; Zhu, Yongqiu; Jiang, Yu; Nielsen, Otto Anker
Abstract: In cities where the urban rail transit (URT) systems do not provide 24-h services, passengers may not be able to reach their destinations if the last train services have closed by the time they arrive at the transfer stations. This paper aims to seek a well-coordinated last train timetable that can transport as many passengers as possible to their destinations (referred to as reachable passengers) and also transport those passengers who cannot reach their destinations (referred to as unreachable passengers) to the stations as close as possible to their destinations. A bi-objective mixed-integer linear programming (MILP) model is developed to maximize the number of reachable passengers and minimize the total remaining travel distance of all passengers. The augmented ε -constraint method is applied to generate all Pareto optimal solutions of the bi-objective MILP model. Numerical experiments were implemented in the Chengdu URT network. Results indicate that compared to the current-in-use timetable, the optimized timetable by our methods significantly increased the number of reachable passengers and meanwhile reduced the average remaining travel distance of unreachable passengers. In addition, we discussed two possible strategies to improve passengers' destination reachability, which are encouraging passengers to arrive early at their origin stations, and optimizing the timetable of last trains and non-last trains at the same time. Highlights: A bi-objective MILP model for last train timetabling considering both destination-reachable and unreachable passengers. An iterative algorithm based on the augmented epsilon-constraint method to obtain all Pareto optimal solutions. Discuss the impact of passenger arrival times at origin stations on their destination reachability. Optimizing both non-last and last train timetables simultaneously to improve passenger destination reachability. Provide practical suggestions for the last train operation based on numerical experiments of a real URT network.