A dynamic multi-objective optimization approach for integrated timetabling and vehicle scheduling

Dynamic integrated timetabling and vehicle scheduling (D-ITVS) is essential for mitigating the negative impacts of service disruptions arising from the stochastic nature of traffic flow and passenger demand fluctuations in public transit. Existing optimization approaches for the D-ITVS problem typically conduct optimization independently at each rescheduling stage. In contrast, this paper proposes a novel dynamic multi-objective optimization approach that considers evolving patterns across different rescheduling stages from a holistic perspective. This approach formulates the optimization problem for all rescheduling stages during a day’s operation as a dynamic multi-objective optimization problem, modeled using a dynamic time-space network flow framework. To leverage these evolving patterns for achieving optimal solutions throughout, a dynamic multi-objective optimization approach for the D-ITVS problem (DMO-TVS) is introduced. The DMO-TVS approach learns the evolving patterns, and incorporates a dynamic solution representation alongside three key mechanisms: (1) change detection mechanism, (2) change response mechanism, and (3) multi-objective optimization mechanism. These mechanisms work in tandem to dynamically adjust the initial solution set at each rescheduling stage based on predicted optimal solutions derived from learned evolving patterns, balance conflicting objectives in the D-ITVS problem, and select optimal solutions with diversity throughout the optimization process. Experimental results demonstrate that the dynamic multi-objective optimization approach is capable of generating timetables and vehicle schedules with reduced costs, enhanced robustness, and improved convergence and diversity across all rescheduling stages. By balancing operational costs and passenger service quality, these improvements benefit transit operators, and during daily operations, passengers enjoy reduced travel costs and enhanced service reliability.