Optimizing public transport transfers by integrating timetable coordination and vehicle scheduling

Optimizing the Three-Dimensional Multi-Objective of Feeder Bus Routes Considering the Timetable

“…Recognizing the limitations of static timetables, Ai et al [16] introduced a dynamic optimization method for bus schedules using deep reinforcement learning, employing a deep Q network to produce more cost-effective and higher-quality timetables. Addressing the synchronization of bus timetables and schedules, Liu et al [17] formulated integer linear programming models, applying the ε-constraint method and solvers for small-scale issues, and devised a strategy to streamline constraints for larger problems. Dou et al [18] designed a mathematical model to reduce passenger wait times, transfer, and operational costs, solved via an artificial bee colony algorithm to mitigate the feeder bus scheduling challenges.…”

“…Constraint (10) indicates that when the feeder bus route m is included in the feeder bus network, passengers are able to choose the route m; Constraint (11) signifies that when feeder bus route m passes through a station, passengers can select route m to reach station s; Constraint (12) is the integrity constraint for feeder bus routes, indicating that each feeder bus route should include at least one rail transit station and bus station; Constraint (13) represents the requirement for the departure interval of feeder bus route m to meet actual conditions; Constraint (14) expresses the total number of buses required on the feeder bus route; Constraint (15) denotes the constraint on the capacity utilization rate of feeder buses; Constraint (16) specifies that the length of feeder bus routes should meet actual route limitations; Constraint (17) states the number of serviced bus stations required on feeder bus routes; Constraint (18) demonstrates that the service time for each bus trip on feeder bus route m should fall within a certain service level range; Constraint (19) indicates that the departure time for route m at station s should occur after route m passes through station s, where κ is a large positive number; Constraints (20)-( 22) refer to 0-1 integer decision variables.…”