Optimization method for modular bus systems combining cross-line scheduling, dynamic formation, and timetabling

Modular public transportation effectively mitigates urban transit spatiotemporal supply-demand imbalances through dynamic vehicle capacity adjustments. We propose a joint optimization framework integrating cross-line scheduling and timetabling, with decision variables encompassing departure times, modular unit formation quantities, and cross-line dispatch units. The model minimizes total costs comprising passenger waiting time, operational expenses, and unit reconfiguration penalties. To solve this mixed-integer nonlinear programming problem, we develop an adaptive large-neighborhood tabu search algorithm incorporating dynamic operator selection and constraint handling. Case studies demonstrate significant total cost reductions and vehicle utilization improvements compared to conventional and single-line modular scheduling models, validating the synergistic optimization value of cross-line scheduling and modular formations.