Variable and adaptive neighbourhood search algorithms for rail rapid transit timetabling problem

Supplying affordable and efficient transportation services to the users is one of the main tasks of the public transport systems. In this study, the objective is the minimization of the total and maximum waiting time of the passengers through optimization of the train timetables for urban rail transit systems. For this purpose, mixed-integer linear and non-linear programming models are developed which could solve the small to medium-sized test instances optimally. In order to tackle large instances, adaptive and variable neighbourhood search algorithms are designed based on different novel solution encoding schemes and decoding approaches. The effectiveness of the proposed models and solution methods are illustrated through the application to the Tehran intercity underground rail lines in IRAN. The outcomes demonstrate that the variable neighbourhood search algorithm outperforms the adaptive step-size neighbourhood search method in the different scenarios of the real case. Furthermore, the generated headway for the period of study result in a significant reduction in total waiting time of the passengers compared with the current baseline timetables. •We provide mixed-integer linear and non-linear programming models.•Novel solution encoding-decoding approaches are proposed.•VNS algorithm outperforms the adaptive neighbourhood search method.•A significant reduction in total waiting time of the passengers is achieved.•Results demonstrate the effectiveness of the frequency-based solution encoding.