为缓解区域灵活公交中, 车辆供需失衡导致的乘客等待焦虑和运营成本高等问题, 该文研究了考虑速度可变的模块化区域灵活公交路径优化问题。首先, 通过整合车辆速度调节、容量调节和路径规划3个维度的决策变量, 构建了最小化总成本(包括车辆成本和乘客时间成本)的混合整数非线性规划模型, 并通过引入辅助变量和构造非负整数数列等方法, 将非线性模型重构为线性模型, 以提高模型的求解效率; 其次, 采用嵌套速度优化算法的自适应大邻域搜索算法求解模型, 并借助Sioux Falls交通网络算例验证了模型和算法的有效性; 最后, 基于西安市实际区域道路网络案例进行了仿真分析, 并通过参数敏感性分析揭示了速度和最大运行时间对系统性能的影响规律。结果表明：与不考虑速度优化的模块化车辆的区域灵活公交优化模型相比, 该文所提模型可使系统总成本降低25.03%。该文研究结果可为未来城市公交自动驾驶车队的优化管理提供参考, 有助于推动城市公共交通的智慧化转型。

Objective: The mismatch between vehicle supply and passenger demand remains a persistent challenge in public transportation. Modular, zonal-based flexible bus services, as an innovative urban public transit mode, can adjust vehicle capacity and routes in response to passenger demand. However, the simultaneous optimization of vehicle speed, route, and capacity has not been adequately addressed, limiting the system's overall efficiency and flexibility. To address these challenges and minimize total system costs, this study aims to jointly optimize vehicle speed, route, and capacity allocation for modular zonal-based flexible bus services. Methods: First, a mixed-integer nonlinear programming (MINLP) model was developed to minimize total costs, integrating decisions across three interrelated dimensions: vehicle speed regulation, capacity allocation, and route planning. This model considers various constraints, including route generation, operating time, and adjustments to vehicle capacity. Furthermore, to improve computational efficiency, the MINLP model was linearized into a mixed-integer linear programming model by introducing auxiliary variables and constructing non-negative integer sequences. This linearization facilitated the use of standard optimization solvers for small-scale instances. Second, a hybrid heuristic algorithm combining adaptive large neighborhood search and speed optimization algorithms was designed to solve large-scale real-world problems. To validate the proposed model and algorithm, numerical experiments were conducted using the established Sioux Falls traffic network. Subsequently, a real-world case study of the Xi'an regional road network was performed, comparing the proposed model with a baseline that did not consider speed optimization, followed by a series of sensitivity tests. Results: The results revealed the following: First, compared with the baseline, the proposed model reduced total system costs by 25.03%, with vehicle and passenger time costs decreasing by 25.24% and 24.79%, respectively. These improvements primarily resulted from dynamic speed adjustment, which aligns vehicle arrivals with passenger time windows, thereby reducing waiting time and improving efficiency. Second, incorporating speed optimization reduced the number of deployed buses from 13 to 9 and shortened total travel distances from 90.28 to 75.54 km, demonstrating improved resource utilization. Third, the total costs and route numbers initially decreased and then stabilized as the maximum operating time increased. When the maximum operating time was short, more buses were required to meet demand, leading to higher total costs. Appropriately relaxing this parameter could effectively expand the service coverage of individual routes and improve vehicle utilization efficiency, thereby reducing total costs. However, once the parameter exceeded a certain threshold, further increases in the operating time would no longer yield optimization benefits due to constraints imposed by passenger time costs. Conclusions: The following conclusions can be drawn from the study's findings: (1) The proposed model demonstrates superior performance in minimizing total system costs compared with baseline models. (2) Integrating speed optimization significantly reduces passenger waiting times and operational expenses. (3) Sensitivity analysis reveals the diminishing marginal returns of maximum operating time, identifying a critical threshold for balanced service efficiency. These findings provide a validated theoretical framework to enhance the efficiency and sustainability of modular autonomous vehicle systems in flexible public transit.