考虑运行图抽线调整的城际铁路动车周转计划编制

Optimized Rolling Stock Circulation Planning for Intercity Railways with Train Diagram Adjustment by Routing

针对现有城际铁路动车组周转计划编制方法未考虑运行线客座率分布,导致抽线调整时难以单独停运低客座率车次而不影响高客座率车次的问题,本文提出一种适用于运行图抽线调整的动车组周转计划优化编制方法。以最小化动车组使用数量及交路中运行线客座率差异为目标,考虑满足一级修等约束条件,构建非线性整数规划模型;通过线性化处理并结合Hierholzer's算法筛选合格解的方式,高效求解模型。案例分析表明:相较于只考虑动车组使用数量的传统方法,该模型在不增加动车组使用数量的情况下,可以显著降低各交路中运行线客座率的差异。优化后的交路中运行线客座率极差提高了68.67%,交路中运行线客座率方差之和降低至对比方案的66.27%。抽线调整时,采用优化方案能够更精确地优先取消低客座率运行线,有效保留高客座率运行线。在抽线条数分别设定为1,2,3的情况下,优化方案停开的运行线中,客座率低于60%的运行线的占比均保持在77%以上,而对比方案中该比例均未超过45%;优化方案中被取消车次的平均客座率比对比方案分别降低了4.48%、5.88%和6.01%。

This paper proposes a method for formulating rolling stock circulation plans that takes into account routing adjustments,in response to the issue that existing intercity railway rolling stock circulation planning methods do not consider the distribution of seat occupancy rates on operating lines which makes it challenging to effectively suspend low-occupancy train services and retain high-occupancy ones during routing adjustments.The proposed method aims to minimize the number of Electric Multiple Units(EMUs)in service and reduce the disparity in seat occupancy rates along operating lines within each circulation route.A nonlinear integer programming model for rolling stock circulation plan formulation is developed with the constraints of primary maintenance.The model is solved through linearization and the Hierholzer's algorithm is used to search for feasible solutions.The case analysis demonstrates that,compared to traditional methods that only consider the number of EMUs used,the proposed model significantly reduces the disparity in load factors of different routings without increasing the number of EMUs.The optimized plan improves the extreme value of seat occupancy rates along optimized circulation routes by 68.67%and reduces the sum of the variances of seat occupancy rates along operational lines in circulation routes to 66.27%of the comparison plan.During routing adjustments,the optimized solutions accurately prioritize the cancellation of low-occupancy train services.When the number of adjusted routes is set to 1,2,or 3,the proportion of the operating lines with seat occupancy rates less than 60%in the optimized plan remains above 77%,whereas in the comparison plan,this proportion does not exceed 45%.In addition,the average seat occupancy rates of canceled train services in the optimized solution are reduced by 4.48%,5.88%,and 6.01%contrary to comparison plans.