面向大客流的城轨备用车投放车站选择与优化模型

为快速疏解城轨线路上车站的大客流，减少乘客的等待时间，研究了备用车投放问题; 在考虑列车追踪关系、列车停站时间等约束的基础上，建立了综合备用车投放时机确定、投放最佳车站选择和时刻表动态调整的多目标优化模型; 界定了城轨备用车开行条件，提出了城轨备用车投放时机的定量化判定方法; 用0-1变量表征车站是否具备备用车投放条件，并将其作为模型输入，以减小大客流车站乘客等待时间和降低运行图偏离时间(延误时间)为优化目标，构建了备用车投放的混合整数非线性规划模型，该模型通过比较不同的备用车投放方案效率得到最佳的备用车投放车站和后续开行计划; 为同时求解0-1变量与连续变量，设计了带惩罚函数的改进粒子群优化算法求解模型。研究结果表明:该方法可对所有符合备用车开行条件的车站制定投放方案，并进一步筛选出最优的备用车投放车站，最多可减少1 318 209 s的乘客等待时间，优化效率为21.9%，且改进的粒子群优化算法对混合整数非线性规划模型的适用性较好; 相比于既有城轨线路列车运行调整和时刻表优化方法，本文提出的方法在应对突发大客流的备用车投放时机上做出了更加定量化的判断，优先考虑了大客流车站的疏解能力和效率，并优化了备用车与后续列车的开行方案，可以有效解决高峰时段车站大客流问题。 

Selection and optimization model of standby train deployment stations on urban rail transit for large passenger flow

In order to quickly relieve the large passenger flow of stations on urban rail transit lines and reduce the total waiting time of passengers, the problem of standby train deployment was studied. Based on the consideration of train tracking relationship, train dwelling time, and other constraints, a multi-objective optimization model was established to determine the timing of standby train deployment, select the best station, and dynamically adjust the schedule. The conditions for the deployment of standby trains were defined and a quantitative determination method for the timing of the standby train operation was proposed. A 0-1 variable was used to characterize whether the station was equipped for standby trains, and it was used as the model input. Then, a mixed integer nonlinear programming (MINP) model of standby train deployment was established to minimize the waiting time of passengers at the station with large passenger flow, and the deviation time (delay time) of the timetable was constructed. The model compared the efficiency of different standby train deployment schemes to get the best standby train deployment station and the subsequent operation plan. An improved particle swarm optimization algorithm with a penalty function was designed to deal with the 0-1 variable and continuous variables simultaneously. Research results show that the method can make plans for all stations satisfying the conditions of standby train deployment, and further select the best standby train stations from the alternative stations. The maximum total passenger waiting time reduces by 1 318 209 s, and the optimization efficiency reduces about 21.9%. Moreover, the improved particle swarm optimization algorithm has good applicability to the MINP model. Compared to the existing urban rail line train operation adjustment and schedule optimization methods, the proposed method provides a more quantitative judgment on the timing of the standby train deployment in response to large passenger flow situations. It provides the evacuation capacity and efficiency of stations with large passenger flow stations and optimizes the operation plans of the standby and subsequent trains. The problem of large passenger flows at stations during peak hours can be relieve effectively. 4 tabs, 9 figs, 30 refs.