北京交通大学学报2026，Vol.50Issue(3)：40-51,12.DOI:10.11860/j.issn.1673-0291.20250129
考虑客流时空分布的公交非均匀发车时刻优化方法
Optimization method of non-uniform bus departure times considering spatiotemporal distribution of passenger flow
摘要
Abstract
To alleviate the misallocation of capacity resources caused by the mismatch between passen-ger demand fluctuations and bus headways,and to balance service quality and operating costs of the transit system,this paper proposes an intelligent scheduling method for fixed-route bus timetables that considers the spatiotemporal distribution characteristics of passenger flow.First,bus passenger flow data are utilized to extract information on passengers'boarding and alighting stations.A Gaussian mix-ture model is then employed to describe the spatiotemporal distribution of the passenger flow and fit the distribution of passenger arrivals at stations.Second,by comprehensively considering passenger travel time costs and transit enterprise operating costs,an integrated optimization model for bus timeta-bling is constructed based on a non-uniform departure time strategy,with the objective of minimizing the total system cost.Key indicators,such as the arrival passenger volume and waiting time cost at each station along the route,are calculated using the fitting results of the spatiotemporal passenger flow distribution.Third,tailored to the model's characteristics,a Genetic Algorithm(GA)is utilized as the underlying framework,integrating two temporal-difference-based reinforcement learning meth-ods,Q-learning and State-Action-Reward-State-Action(SARSA),to enable the adaptive adjustment of key algorithm parameters and enhance solution quality.Finally,a single route within the fixed-route transit network of Beijing is used as a case study to validate the proposed scheduling procedure.The re-sults indicate that the improved GA incorporating reinforcement learning outperforms the traditional GA in minimizing the total system cost.For the single-route scenario,when the maximum number of departures is set to 10 and 15,the non-uniform scheduling strategy reduces passenger waiting costs by approximately 26.7%and 14.5%,respectively,and decreases total system costs by approximately 25.5%and 13.1%,respectively,compared to a fixed-headway strategy.Furthermore,the proposed scheduling strategy effectively balances the load factor,aligns well with passenger flow fluctuation trends,and enhances overall operational efficiency.关键词
城市交通/公交时刻表编制/高斯混合模型/遗传算法/强化学习Key words
urban transportation/bus timetabling/Gaussian mixture model/genetic algorithm/rein-forcement learning分类
交通工程引用本文复制引用
陈汐,吕佳雯,王健宇,谭二龙,焦朋朋..考虑客流时空分布的公交非均匀发车时刻优化方法[J].北京交通大学学报,2026,50(3):40-51,12.基金项目
国家自然科学基金(52172301) （52172301）
教育部人文社会科学研究青年基金(24YJC630017) （24YJC630017）
北京市博士后科研活动经费资助(ZZ-2024-56) National Natural Science Foundation of China(52172301) （ZZ-2024-56）
Humanities and Social Sciences Youth Foundation,Ministry of Education of China(24YJC630017) （24YJC630017）
Beijing Postdoctoral Research Foundation(ZZ-2024-56) （ZZ-2024-56）
