Optimizing headways for urban rail transit services using adaptive particle swarm algorithms

Minimizing the passenger waiting times is an important aim of the rail companies to improve the service efficiency. The present study contributes to this aim by: (1) presenting novel mixed-integer nonlinear programming formulations for the train timetabling problem, (2) designing efficient algorithms to solve large instances of the problem. The model addresses the strict vehicle capacity constraint and the period-dependent arrival rate and alighting ratio. The basic model is then improved by embedding heuristic rules in the mathematical formulation. Due to the complexity of the problem, the sizes of the instances solved optimally are small and not practical for the real implementation. In order to tackle large-sized problem instances, different adaptive particle swarm algorithms are proposed. The solution methods are experimentally evaluated with respect to the real instances suggested by Tehran Metropolitan rail. The results demonstrate that the proposed adaptive particle swarm optimization algorithms could reduce the total passenger waiting times significantly compared to the current practice of using an even-headway timetable as well as the baseline schedule. For the given case study, the performance of the proposed adaptive particle swarm algorithm is about 9.4% and 64% better than the quality of the baseline timetable and the regular headway schedule, respectively