PDF(3726 KB)
Collaborative optimization of modular bus routes and timetable for large residential areas
Zhaohui DING, Xiaoning ZHU, Liujiang KANG
Journal of Tsinghua University(Science and Technology) ›› 2026, Vol. 66 ›› Issue (3) : 627-637.
PDF(3726 KB)
PDF(3726 KB)
Collaborative optimization of modular bus routes and timetable for large residential areas
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.
bus route design / genetic algorithm / modular bus / timetable optimization
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