清华大学学报（自然科学版）2026，Vol.66Issue(3)：661-676,16.DOI:10.16511/j.cnki.qhdxxb.2026.26.018
考虑速度可变的模块化区域灵活公交路径优化
Route optimization for modular zonal-based flexible bus considering variable speeds
摘要
Abstract
[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.关键词
城市交通/区域灵活公交/模块化车辆系统/自适应大邻域搜索算法/速度优化Key words
urban traffic/zonal-based flexible bus/modular vehicle system/adaptive large neighborhood search algorithm/speed optimization分类
交通工程引用本文复制引用
高天洋,胡大伟..考虑速度可变的模块化区域灵活公交路径优化[J].清华大学学报（自然科学版）,2026,66(3):661-676,16.基金项目
陕西省自然科学基础研究计划重点项目(2021JZ-20) （2021JZ-20）
