Pareto optimal train scheduling for urban rail transit using generalized particle swarm optimization

In urban rail transport, train timetable plays a crucial role, whose quality determines the whole system's performance to a large extent. In practical urban rail operation, two contradictive aspectsservice quality and operation costshould be considered during train scheduling. A good train timetable should achieve considerable service quality with as little operation cost as possible. Previously, many studies have been conducted specific to urban rail train scheduling, although most of them do not put enough emphasis on its multi-objective nature. In this article, therefore, Pareto optimal urban rail train scheduling which can give more instruction to practical operation is studied. First, referring to some existing studies, the problem is reasonably defined, which takes time-dependent origin-destination demand as the input and aims at minimizing the passengers' total travel time and the number of used train stocks. Then, an efficient iteration algorithm and a valid train stock assignment procedure are designed to calculate the passengers' total travel time and required train stock number, respectively. On that basis, the studied problem is reasonably formulated as a bi-objective optimization model and a Pareto-based particle swarm optimization procedure is designed to solve it. Finally, with two different scaled urban rail lines, the whole methodology is illustrated and the algorithm is tested.