基于模块化车辆的跨区域需求响应式公交动态调度优化研究

doi:10.3976/j.issn.1002-4026.2025044

摘要/Abstract

摘要： 为解决传统容量固定的需求响应式公交满载率较低的问题，引入模块车系统，提出一种基于模块化公交的跨区域通勤需求响应式公交动态调度优化方法，建立了以乘客出行成本和企业运营成本最小化的目标函数，引入耦合站点概念，设计了考虑耦合站点的模块化车队动态编组模型，实现了两条线路上的车队重组和乘客交换。使用大M法将模型线性化为混合整数线性规划（MILP）并进行求解，以北京市九棵树至王府井的两条通勤线路为案例进行验证。试验结果表明与传统固定容量的需求响应式公交相比，引入模块化公交能够有效增加车辆的满载率，降低企业运营成本，乘客出行成本也得到了一定的降低但是影响较小。由此可见，在城市通勤场景下，引入模块化公交系统可以为乘客出行企业运营提供更加灵活高效的模式。

关键词: 城市交通, 模块化公交系统, 混合整数线性规划, 需求响应式公交

Abstract: To address the issue of low load factors associaated with conventional demand-responsive buses with fixed capacity, this study introduces a modular vehicle system and proposes a cross-regional demand-responsive bus dynamic scheduling optimization method based on modular vehicles. An objective function is established to minimize travel and operational costs for passengers and enterprises, respectively. The concept of coupling stations is introduced, and a dynamic fleet formation model considering coupling stations is designed, which allows for fleet reorganization and passenger transfer across two routes. Using the Big-M method, the model is linearized into a mixed-integer linear programming (MILP) problem for solutions, and the model is validated through a case study of two commuting routes from Jiukeshu to Wangfujing in Beijing. The experimental results show that compared to the introduction of conventional demand-responsive buses with fixed capacity, the introduction of modular buses effectively increases vehicle load factors, reduces operational costs for enterprises, and slightly reduces passenger travel costs. This indicates that the introduction of modular bus systems in urban commuting scenarios can provide a more flexible and efficient operational model for passenger travel and enterprise operations.

Key words: urban transportation, modular bus system, mixed-integer nonlinear programming, demand-responsive bus

中图分类号:

U491.1

张艾霖, 贾顺平. 基于模块化车辆的跨区域需求响应式公交动态调度优化研究[J]. 山东科学, 0, (): 1-.

ZHANG Ailin, JIA Shunping. Cross-regional demand-responsive bus dynamic scheduling optimization based on modular vehicles[J]. Shandong Science, 0, (): 1-.

参考文献

[1] 张文波, 左玙璠, 王岳平, 等. 定制公交居民出行方式选择的影响因素[J]. 山东科学, 2021, 34(6): 97-105.

[2] HUANG A L, DOU Z Q, QI L Z, et al. Flexible route optimization for demand-responsive public transit service[J]. Journal of Transportation Engineering, Part A: Systems, 2020, 146(12): 04020132. DOI: 10.1061/jtepbs.0000448.

[3] 孙继洋, 黄建玲, 陈艳艳, 等. 面向多目标站的灵活型公交路径优化调度模型[J]. 交通运输系统工程与信息, 2019, 19(6): 105-111. DOI: 10.16097/j.cnki.1009-6744.2019.06.016.

[4] SUN Q, CHIEN S, HU D W, et al. Optimizing multi-terminal customized bus service with mixed fleet[J]. IEEE Access, 2020, 8: 156456-156469.

[5] 曹宏, 任华玲. 双模式下考虑碳税的定制公交站点位置与票价优化研究[J]. 山东科学, 2023, 36(4): 69-79.

[6] DAI Z, LIU X C, CHEN X, et al. Joint optimization of scheduling and capacity for mixed traffic with autonomous and human-driven buses: A dynamic programming approach[J]. Transportation Research Part C: Emerging Technologies, 2020, 114: 598-619. DOI: 10.1016/j.trc.2020.03.001.

[7] PEI M Y, LIN P Q, DU J, et al. Vehicle dispatching in modular transit networks: A mixed-integer nonlinear programming model[J]. Transportation Research Part E: Logistics and Transportation Review, 2021, 147: 102240. DOI: 10.1016/j.tre.2021.102240.

[8] LIU X H, QU X B, MA X L. Improving flex-route transit services with modular autonomous vehicles[J]. Transportation Research Part E: Logistics and Transportation Review, 2021, 149: 102331. DOI: 10.1016/j.tre.2021.102331.

[9] 高天洋, 胡大伟, 姜瑞森, 等. 基于模块化车辆的区域灵活接驳公交线路优化[J]. 吉林大学学报(工学版), 2025, 55(2): 537-545. DOI: 10.13229/j.cnki.jdxbgxb.20230515.

[10] SHI X W, CHEN Z W, PEI M Y, et al. Variable-capacity operations with modular transits for shared-use corridors[J]. Transportation Research Record: Journal of the Transportation Research Board, 2020, 2674(9): 230-244. DOI: 10.1177/0361198120928077.

[11] CHEN Z W, LI X P. Designing corridor systems with modular autonomous vehicles enabling station-wise docking: Discrete modeling method[J]. Transportation Research Part E: Logistics and Transportation Review, 2021, 152: 102388. DOI: 10.1016/j.tre.2021.102388.

[12] LIU Z K, HOMEM DE ALMEIDA CORREIA G, MA Z L, et al. Integrated optimization of timetable, bus formation, and vehicle scheduling in autonomous modular public transport systems[J]. Transportation Research Part C: Emerging Technologies, 2023, 155: 104306. DOI: 10.1016/j.trc.2023.104306.

[13] 高虹, 刘锴, 姚恩建. 站点需求响应的电动模块公交车重组调度优化[J]. 中国公路学报, 2024, 37(4): 24-36. DOI: 10.19721/j.cnki.1001-7372.2024.04.003.

[14] TIAN Q Y, LIN Y H, WANG D Z W, et al. Planning for modular-vehicle transit service system: Model formulation and solution methods[J]. Transportation Research Part C: Emerging Technologies, 2022, 138: 103627. DOI: 10.1016/j.trc.2022.103627.

[15] 易洪波, 刘昱岗, 王童语. 考虑空间需求不均的模块化公交线路运行方案优化研究[J]. 交通运输系统工程与信息, 2024, 24(4): 166-175. DOI: 10.16097/j.cnki.1009-6744.2024.04.016.

[16] YI H B, LIU Y G, MENÉNDEZ M, et al. Charging scheduling and route planning for modular bus systems considering non-linear charging profile[J]. Transportation Research Part C: Emerging Technologies, 2025, 179: 105292. DOI: 10.1016/j.trc.2025.105292.