Trip reservation and train operation plan optimization method of urban rail transit under demand responsive mechanism
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摘要: 轨道交通供给侧的计划性与需求侧的时变性相互冲突，为更好地协同供需双方，提出了需求响应机制下城市轨道交通列车运行计划的优化方法，包括出行预约和需求响应2个环节；建立了需求响应与列车运行计划协同优化模型，以最小化乘客出行成本和列车运行成本为目标，重点关注乘客由于预约行为产生的延误时间成本；考虑列车运行、运输能力、编组情况、客流分布等因素，设计了基于乘客优先级的自适应大规模邻域搜索算法，外层优化列车运行计划，内层优化客流分配方案，最终实现客流的供需匹配；以北京地铁八通线为例，按照需求响应机制对该线路全天的需求处理与运输组织进行数值试验，并对试验结果从车底运用、乘客等待时间和满载率分布三方面进行分析。研究结果表明：该优化方法可使开行的列车数降低13.8%，同时采用多编组模式，使用车辆数减少了29.8%，这能够有效压缩列车走行公里数，削减企业开支；能够在保证乘客基本出行的前提下，最高可将乘客平均在站等待时间缩短约35.3%，并且预约比例的提升对等待时间的削减效果明显；优化后的运行计划能控制列车满载率维持在设定水平，有效降低人员密度，避免人群大规模聚集，对城市轨道交通疫情的有效防控做出有益探索。Abstract: In rail transit systems, the planning of the supply side conflicts with the time-varying characteristics of the demand side. Therefore, an optimization method of trian operation plan for urban rail transit under a demand responsive mechanism was proposed to coordinate the supply and demand relationship. The optimization method includes two steps: trip reservation and demand response. A collaborative optimization model of demand response and train operation plan was established to minimize passenger trip cost and train operation cost, and the delay cost of passengers due to trip reservation was emphasized. The factors such as train operation, transport capacity, train marshalling and passenger distribution were considered, and an adaptive large-scale neighborhood search algorithm based on passenger priority was designed. It was featured with an outer layer optimizing the train operation plan and an inner layer optimizing the passenger allocation, which realizes the matching between the supply and demand of passenger flows. With Beijing Subway Batong Line as an example, a numerical experiment was carried out on its all-day demand management and transportation organization based on the demand responsive mechanism. The results were analyzed from three aspects including locomotive application, passenger waiting time and load rate distribution. Analysis results show that the optimization method can reduce the number of operation trains by 13.8%, and 29.8% of units can be saved by the multi-group mode, which can effectively reduce the operating miles of trains and cut down corporate expenses. Furthermore, the method can shorten the average passenger waiting time at stations by up to 35.3% while ensuring the basic trip of passengers, and the increase in the proportion of reservations has an obvious effect on the reduction of passenger waiting time. The optimized operation plan can make the train load rate maintain at a set level and effectively reduce personnel density to avoid large-scale gathering of passengers, which is a useful exploration and can effectively prevent and control the pandemic appearing in urban rail transit. 2 tabs, 8 figs, 31 refs.
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图 1 “预约-响应”机制下供需双方耦合关系
Figure 1. Coupling relationship between supply and demand under reservation-responsive mechanism
图 3 不同类型乘客延误时间成本的分布
Figure 3. Distribution of delay time costs for different types of passengers
图 4 自适应大规模邻域搜索算法流程
Figure 4. Flow of adaptive large scale neighborhood search algorithm
图 6 高峰期不同场景下乘客平均等待时间
Figure 6. Passenger average waiting times under different scenarios during peak hours
图 7 需求响应机制对列车满载率的影响
Figure 7. Effect of demand responsive mechanism on train load rate
图 8 不同预约比例下乘客平均等待时间
Figure 8. Passenger average waiting times under different reservation rates
表 1 其他参数取值
Table 1. Values of remaining parameters
参数 取值 参数 取值 U/min 5 θ/min 1 Imin/min 3 T 1 080 Imax/min 10 λ 2 σ1 1 ξ1 1.2 σ2 20 ξ2 0.6 
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表 2 不同场景下的试验结果
Table 2. Experimental results under different scenarios
运营场景 服务人数 开行列车数 使用车数 乘客平均等待时间/min 原有运行图-无预约(场景1) 41 496 216 1 296 5.53 优化运行图-无预约(场景2) 41 496 186 910 5.61 优化运行图-有预约(场景3) 41 496 186 910 3.58
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