Multi-objective re-synchronizing of bus timetable: Model, complexity and solution

•Develop a multi-objective model for re-synchronizing of bus timetable.•Clarify its solution space and combinatorial complexity.•Prove it is NP-hard and the Pareto-optimal front is non-convex.•Propose a NSGA-II based algorithm to solve the multi-objective model. This work is originally motived by the re-planning of a bus network timetable. The existing timetable with even headways for the network is generated using line by line timetabling approach without considering the interactions between lines. Decision-makers (i.e., schedulers) intend to synchronize vehicle timetable of lines at transfer nodes to facilitate passenger transfers while being concerned with the impacts of re-designed timetable on the regularity of existing timetable and the accustomed trip plans of passengers. Regarding this situation, we investigate a multi-objective re-synchronizing of bus timetable (MSBT) problem, which is characterized by headway-sensitive passenger demand, uneven headways, service regularity, flexible synchronization and involvement of existing bus timetable. A multi-objective optimization model for the MSBT is proposed to make a trade-off between the total number of passengers benefited by smooth transfers and the maximal deviation from the departure times of the existing timetable. By clarifying the mathematical properties and solution space of the model, we prove that the MSBT problem is NP-hard, and its Pareto-optimal front is non-convex. Therefore, we design a non-dominated sorting genetic (NSGA-II) based algorithm to solve this problem. Numerical experiments show that the designed algorithm, compared with enumeration method, can generate high-quality Pareto solutions within reasonable times. We also find that the timetable allowing larger flexibility of headways can obtain more and better Pareto-optimal solutions, which can provide decision-makers more choice.