Optimal Seat Movement Strategies Among Modular Bus Units
Shiyue Wang, Yuhao Liu, Zhibin Chen, Mingyang Pei, Changhong Lu
原文摘要
Movable seats enable passengers to transfer between coupled modular bus units while remaining seated, but require physical reconfiguration that existing modular transit models largely abstract away. We model seat reconfiguration as a colored generalized sliding-tile puzzle on the physical track graph, capturing simultaneous movements, seat indistinguishability within destination groups, and vertex, edge, and corner-following conflicts. A lexicographic objective minimizes makespan first and then the sum of costs (SoC), which penalizes movements and waiting at non-target positions. We develop an exact time-expanded mixed-integer linear programming formulation and a Boundary-Sequence Dynamic Programming (BSDP) algorithm. BSDP decomposes the problem at single-edge module interfaces and coordinates local schedules through compressed boundary-crossing sequences, provably preserving feasibility and optimal costs. On two- and three-module benchmarks, BSDP achieves mean per-instance speedups of 3.24x and 6.30x over Gurobi, respectively. In fixed-horizon tests with four to seven modules, both methods start from identical greedy schedules and receive a 300 s budget. BSDP obtains lower final SoC than Gurobi on 197 of 200 instances and ties on three, reducing mean final SoC by 17.93%-69.07% across the four size classes. Geometry sensitivity and ablation studies further clarify the contribution of boundary compression to computational performance. The framework links seat reconfiguration to the timing and operational cost of modular bus decoupling.
cs.CE · math.OC