旅行时间不确定的灵活线路公交调度优化

Robust flexible-route bus optimization model considering travel time uncertainty

乘客出行过程中,站点等待时间和车厢内拥挤程度会影响乘客满意度。传统的公交服务使用固定的路线和时刻表,无法动态响应乘客的实时请求。灵活线路公交在访问某些固定站点(检查点)的前提下,根据乘客提出的辅助运输请求,灵活制定公交运行路线,具有兼顾动态响应乘客出行需求和维持路线稳定性的特点。在制定灵活线路公交运行计划时,考虑公交运行过程中可能发生的时间扰动,可以提高计划的鲁棒性。本文考虑灵活线路公交运行过程中旅行时间的不确定性,以提升乘客乘车体验为出发点,建立鲁棒性较强的灵活线路公交车辆调度模型,尽可能减小站点的延迟成本和降低行程中的拥挤水平。本文使用旅行时间的平均绝对偏差作为不确定性的描述性统计量,构建了一个分布式鲁棒优化模型,通过对偶变换,将模型进一步转化为一个混合整数规划模型。数值实验的结果表明,提出的模型可以很好地降低站点延误水平和车内拥挤程度,提高乘客的乘车体验。模型提供更具鲁棒性的灵活线路公交运行方案能够提高灵活线路公交的服务水平,为运营和管理提供决策依据。

During travel,excessive waiting times at stations and congestion in carriages can negatively impact passenger satisfaction.However,traditional public transportation services use fixed routes and schedules that cannot respond dynamically to real-time passenger requests.Flexible Route Transit has the ability to strike a balance between dynamically responding to passenger travel demand and maintaining route stability by flexibly developing transit routes based on passenger requests for auxiliary transportation while visiting certain fixed stops(checkpoints).Considering possible time disturbances that may occur during operations in the development of flexible bus route operation plan can improve the robustness of the plans.With the objective of improving the passengers’riding experience,we considered the uncertainty of travel times during the operation of flexible bus routes,and established a robust flexible bus route vehicle scheduling model to minimize station delay costs and congestion levels during travel.Specifically,we construct a distributed robust optimization model using the average absolute deviation of travel time as a descriptive statistic of uncertainty,and transform the robust optimization model into a mixed-integer planning model through dual transformation.The results of numerical experiments indicate that the proposed model can provide a more robust and flexible bus route operation scheme,which can well reduce the level of station delays and in-ride crowding,and thereby improve the riding experience.Thus,the flexible route bus operation plan provided by the proposed model can improve the service level of flexible route buses and provide a decision-making basis for operation and management.