为解决大型居住区居民出行的“最后一公里”问题, 该文协同优化了大型居住区内接驳地铁的模块化微循环公交线路与时刻表。该文首先考虑线路生成、乘客分配和车辆运用等多重约束, 构建了最小化总成本(包括公交线路运营成本和乘客出行时间成本)的混合整数非线性规划模型; 其次, 为高效求解上述模型, 引入辅助变量降次了目标函数和约束条件的高次项; 最后, 基于真实的区域道路网和随机生成的乘客需求进行了算例分析和灵敏度测试。由于商业求解器难以求解大规模问题的精确解, 因此该文设计了一种改进的混合遗传算法, 在遗传算法中嵌入乘客分配和线路修复算子, 以加速算法求解进程, 确保子代个体可行; 采用精英保留策略, 将模拟退火算子融入遗传算法, 在提高算法寻优效率的同时避免过早陷入局部最优。该文算例求解结果表明：模块化公交的行驶速度对运营成本影响显著, 在一定范围内提升行驶速度可降低运营成本; 超过阈值后继续提升行驶速度, 成本降低效应减弱且安全风险增加。在预约时间误差容忍度方面, 严格的容忍度能降低乘客平均预约时间误差, 但会增加公交线路运营成本和乘客在车时间。应合理设置行驶速度和预约时间误差容忍度, 以实现模块化微循环公交系统的效益最大化。该文研究结果可为后续模块化公交的大规模应用提供参考。

Objective: In public transportation, the "last mile" challenge encountered by residents of large residential communities remains a persistent issue. Existing feeder-bus systems operating within such areas often encounter issues, such as high rates of empty vehicles, traffic congestion, and inadequate capacity during peak hours, primarily stemming from suboptimal route designs and inflexible scheduling. To address these challenges, this study aims to optimize the route design and timetable of modular microcirculation buses that shuttle passengers to subways within large residential areas. Methods: First, a mixed-integer nonlinear programming model considering various constraints, such as route generation, passenger assignment, and vehicle utilization, is constructed to minimize total cost, which encompasses the operating expenses of the company, the reservation time of the passengers, and the in-transit time. To increase the efficiency of the constructed model in obtaining solutions, auxiliary variables are introduced to minimize the degree of high-order terms in the objective function and constraint conditions. Second, an improved hybrid genetic algorithm is designed to overcome the shortcomings of commercial solvers in obtaining exact solutions for large-scale problem models. This improved algorithm comprises the following features: passenger-assignment operators and route-repair operators are embedded in the algorithm to accelerate the process of obtaining solutions and ensure the feasibility of offspring individuals, and the elitism preservation strategy is adopted, followed by the integration of simulated annealing operators into the genetic algorithm. These features improve the optimization efficiency of the algorithm and prevent premature convergence to local optima. Finally, a case study is conducted on real regional road networks and generated passenger demands, followed by a series of sensitivity tests. Results: The results of the case study revealed the following: (1) The driving speed of the modular buses had a significant effect. As the bus driving speed increased from 33.00 to 36.00km/h, the total system cost decreased significantly owing to the reduced number of deployed vehicles. Conversely, as the driving speed exceeded 39.00km/h, the total system cost exhibited diminished sensitivity to further variations in speed. (2) The total system cost generally decreased linearly with the relaxation of the tolerance for reservation-time errors. When the tolerance for reservation-time errors was relaxed from 10.00 to 13.00min, the number of deployed vehicles decreased from eight to five. (3) When the fixed costs were set at ￥1100.00, ￥1050.00, ￥850.00, and ￥800.00, the numbers of deployed modular buses in all the cases exceeded five, and the average reservation-time errors of the passengers in all four experiments were significantly smaller than those in the other experiments. Conclusions: The following conclusions can be drawn from the case study results: (1) Increasing speed within a certain range can lead to reduced operational costs. However, beyond this range, the cost-reduction effect diminishes and safety risks increase, requiring a balance between efficiency and risk. (2) Strict tolerance of reservation time errors reduces passengers' average reservation errors but increases operational costs and passengers' in-transit time. Therefore, setting an appropriate driving speed and error tolerance is crucial for maximizing system benefits. (3) Flexible parameter settings help maintain greater population diversity during the early and middle stages of algorithm execution, thereby enriching the types of individuals in the system and creating favorable conditions for the algorithm to obtain improved solutions.