基于列车运行图优化的动车组周转接续问题的研究
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摘要
动车组周转接续问题是编制动车组运用计划的重要部分,其方案的优劣不仅关系到动车组的运用数量,而且对车站作业计划的质量与可实施性有着重要的影响。在旅客列车运行计划的编制过程中,动车组列车之间的周转接续必须以列车运行图为基础,运行图的编制质量直接影响着动车组列车之间的周转接续方案,由此可见,旅客列车运行计划中的三大问题之间具有密切的联系。从运输组织一体化的思想出发,研究基于运行图优化的动车组周转接续问题具有重要的研究价值和现实意义。
本文在借鉴国内外已有研究成果的基础上,运用运筹学方法,研究了基于通过式客运站的运行图编制方法以及动车组列车之间的周转接续问题,并以动车组列车之间的周转接续优化为目标对运行图进行了反馈调整,在运行图的编制和反馈调整模型中,初步考虑了车站能力的约束问题。论文主要工作包括以下3个方面：
1.分析了周期性列车运行图的优点,研究评述了国外基于PESP(周期事件规划问题,Periodic event scheduling problem)的周期性列车运行图的编制模型及存在的问题。基于我国客运专线的特点,建立了适合我国客运专线路情的基于定序的周期性列车运行图的线性规划模型。进一步地,研究了基于通过式客运站的网络化运行图的编制问题,将上述模型拓展到线路双向及路网上,通过考虑进路冲突约束初步考虑了车站咽喉区的能力问题,提出了基于路网的周期运行图的编制流程和方法。
案例结果表明：以1h为周期的周期性列车运行图在一定程度上减小了运行图铺划问题的规模,运用Lingo软件能快速得到问题的解；基于定序的列车运行图是在列车在各车站的到发顺序已知的情况下建模,因此仅需考虑运行线本身和相邻运行线之间的关系,与基于PESP的模型相比,减少了Lingo建模的工作量。
2.为了编制基于通过式客运站的动车周转计划,提出了部分环形运转的概念,并基于部分环形运转的动车组运用方式分析了动车组周转接续问题的特点。从使动车组列车之间尽可能多地发生顺向接续的角度考虑,提出时间容忍值σ的概念,构建了动车组周转接续模型,并设计了基于σ的紧凑接续算法。
案例分析表明,在尽端式客运站列车运行成对的条件下,考虑运行图的均衡性铺划保证了动车组列车之间的周转接续质量,尽端式客运站A站7对列车、E站6对列车均发生了折返接续,接续率为100%；在通过式客运站,运用基于σ的紧凑接续算法可使D站动车组列车之间的顺向接续在一个周期内增加2次,有利于增强进路分配计划的鲁棒性,缓解车站咽喉区的压力,但在编制运行图时, D站列车到发均衡性约束不强,且各条线路上运行的列车数量不等,动车组周转接续的效果不甚理想,在13对列车中仅10对列车发生了接续,且均为顺向接续,接续率为76.9%。
3.研究了基于冗余时间分布的运行图调整方法,提出了关联运行线群的概念,针对顺向接续和逆向接续,分别给出了各类调整方法下列车运行线的最大可调整量；针对关联运行线群不存在调整量的情况,建立了运行图反馈调整模型,尽量使动车组列车之间均能发生周转接续以及最多的顺向接续,并以后验的方式考虑了车站到发线的数量问题。
案例结果表明,当运行线需要的调整量较小时,可利用基于冗余时间分布的运行图调整方法对运行图进行调整,先对具有拟接续关系的运行线自身进行调整,然后再对其关联运行线群进行调整；当关联线群不存在调整量或需调整的运行线过多而难以统计调整量时,运用数学模型的方法进行建模调整；运行图调整完毕后,在车站的能力约束得到保证,且运行图的周期性结构不变,运行图的调整量较小的前提下明显提高了动车组周转接续的质量,A站7对列车、E站6对列车以及D站13对列车全部发生了接续,接续率为100%,且D站13次周转接续中,有12次顺向接续,顺向接续率达到了92.3%,为车站作业计划的可实施性创造了条件。
本文致力于周期性列车运行图的编制、基于周期运行图的动车组周转接续问题以及基于动车组周转接续质量优化的运行图反馈调整等方面的研究,并初步考虑了进路计划的鲁棒性和车站到发线的运用数量等问题,为车站作业计划的质量和可实施性奠定了基础,也为运行计划一体化的平台建设提供了理论支持。
The scheme of railway train-set circulation is an important part in operation, which not only determines the number of needed rain-sets, but also influences the enablement of the yard operational plan seriously. During the process of drawing-up train operational scheme, timetable is a critical input data of planning train-set circulation. Train scheduling, train-set circulation and the yard operational are interdependent. Based on the all-in-one of transportation organization, it is essential to study the circulation of train-set while considering timetable optimization.
Based on the well-known research achievements at home and abroad, this paper study the flow of timetabling based on "through" station and the circulation of train-set. To get optimal connection between train lines, the adjustment method and model for timetable based on feedback are proposed. During the process of timetabling, optimizing and adjusting, the station capacity is considerd roughly. The following components are involved:
1. The character of cyclic train timetable is analyzed in detail. The mathematical model about working out cyclic train timetable based on periodic event scheduling problem (PESP) is analyzed. In China, some passenger dedicated lines with complex operation need more adaptable model. An ameliorated line programming model based on fixed departure/ arrival order is put forward for such situation. Further, the model was extended for the up-down line with the constraint of route conflict to take the capacity of throat into account. The flow of the railway network cyclic train timetable based on "through" station is proposed. And then, a case study is given out.
The result demonstrates that the timetable with one hour as cycle time can partially reduce the scale of scheduling, Lingo can solve the problem quickly; Compared with timetable based on PESP, the model based on fixed departure/ arrival order which only considers the relationship between adjacent lines, needs fewer modeling time.
2. To plan the circulation of train-sets based on railway "through" station with two lines at least, the characteristics of circulation for train-set is discussed in term of semicircle of train-sets'turnaround. Time tolerance a is defined to get more connection between train lines without a direction change. The model of train-set circulation is put forward and a compact connection algorithm based on time toleranceσis then designed.
The result of case demonstrates that the connections between trains at terminal station is guaranteed because of timetable's equilibrium when the train lines is in pair, there are 7 connections and 6 connections at terminal station A and E separately, the connection rate is 100%; At through station D, there is 2 more connection between train lines without a direction change while the usage of compact connection algorithm based on time tolerance, but the result is not so satisfactory as a whole because of weakness of the timetable's equilibrium and the difference in quantity between railway lines, there are only 10 connections in 13 pairs without direction change, the connection rate is only 76.9%.
3. The adjustment method of timetable based on the distribution of superfluous time is studied. To get the maximum adjusted quantity of train line while considering the adjustment method based on the connection with or without direction change, the related train line group is defined. If there is no adjusted space or it is hard to get the adjusted quantity when using the adjustment method, the model which can describe all the constraints between related train lines based on the feedback of train-set's circulation is more important. Then the model for feedback and adjustment is proposed to attain most connections, especially without direction change in through station between train lines. The number of arrival-departure track is also considered in the model as a posterior way.
The result of the case shows that if there is no need to get big adjusted quantity, choose the adjustment method, then adjust the train lines which are the planned connection firstly; After the ultimate adjustment, there is no change for the timetable's structure and slight adjustment of travel time about train lines, and most important of all, the quality of circulation plan is improved obviously based on the station capacity satisfied, there are 7,6 connections at terminal station A and E separately, there are 13 connections, the rate of connection is 100%, especially 12 connections without direction change at through station D, and the rate reaches up to 92.3%.
This paper makes efforts to study the cyclic train diagram establishment, train-set circulation and their feedback and optimization, while considering the robustnessof route assighment and the number constraint of station tracks. Hopefully, it can lay the foundation for the actionability to station working plan, and provide theoretical support to integrated train operational scheme.
本文在借鉴国内外已有研究成果的基础上,运用运筹学方法,研究了基于通过式客运站的运行图编制方法以及动车组列车之间的周转接续问题,并以动车组列车之间的周转接续优化为目标对运行图进行了反馈调整,在运行图的编制和反馈调整模型中,初步考虑了车站能力的约束问题。论文主要工作包括以下3个方面：
1.分析了周期性列车运行图的优点,研究评述了国外基于PESP(周期事件规划问题,Periodic event scheduling problem)的周期性列车运行图的编制模型及存在的问题。基于我国客运专线的特点,建立了适合我国客运专线路情的基于定序的周期性列车运行图的线性规划模型。进一步地,研究了基于通过式客运站的网络化运行图的编制问题,将上述模型拓展到线路双向及路网上,通过考虑进路冲突约束初步考虑了车站咽喉区的能力问题,提出了基于路网的周期运行图的编制流程和方法。
案例结果表明：以1h为周期的周期性列车运行图在一定程度上减小了运行图铺划问题的规模,运用Lingo软件能快速得到问题的解；基于定序的列车运行图是在列车在各车站的到发顺序已知的情况下建模,因此仅需考虑运行线本身和相邻运行线之间的关系,与基于PESP的模型相比,减少了Lingo建模的工作量。
2.为了编制基于通过式客运站的动车周转计划,提出了部分环形运转的概念,并基于部分环形运转的动车组运用方式分析了动车组周转接续问题的特点。从使动车组列车之间尽可能多地发生顺向接续的角度考虑,提出时间容忍值σ的概念,构建了动车组周转接续模型,并设计了基于σ的紧凑接续算法。
案例分析表明,在尽端式客运站列车运行成对的条件下,考虑运行图的均衡性铺划保证了动车组列车之间的周转接续质量,尽端式客运站A站7对列车、E站6对列车均发生了折返接续,接续率为100%；在通过式客运站,运用基于σ的紧凑接续算法可使D站动车组列车之间的顺向接续在一个周期内增加2次,有利于增强进路分配计划的鲁棒性,缓解车站咽喉区的压力,但在编制运行图时, D站列车到发均衡性约束不强,且各条线路上运行的列车数量不等,动车组周转接续的效果不甚理想,在13对列车中仅10对列车发生了接续,且均为顺向接续,接续率为76.9%。
3.研究了基于冗余时间分布的运行图调整方法,提出了关联运行线群的概念,针对顺向接续和逆向接续,分别给出了各类调整方法下列车运行线的最大可调整量；针对关联运行线群不存在调整量的情况,建立了运行图反馈调整模型,尽量使动车组列车之间均能发生周转接续以及最多的顺向接续,并以后验的方式考虑了车站到发线的数量问题。
案例结果表明,当运行线需要的调整量较小时,可利用基于冗余时间分布的运行图调整方法对运行图进行调整,先对具有拟接续关系的运行线自身进行调整,然后再对其关联运行线群进行调整；当关联线群不存在调整量或需调整的运行线过多而难以统计调整量时,运用数学模型的方法进行建模调整；运行图调整完毕后,在车站的能力约束得到保证,且运行图的周期性结构不变,运行图的调整量较小的前提下明显提高了动车组周转接续的质量,A站7对列车、E站6对列车以及D站13对列车全部发生了接续,接续率为100%,且D站13次周转接续中,有12次顺向接续,顺向接续率达到了92.3%,为车站作业计划的可实施性创造了条件。
本文致力于周期性列车运行图的编制、基于周期运行图的动车组周转接续问题以及基于动车组周转接续质量优化的运行图反馈调整等方面的研究,并初步考虑了进路计划的鲁棒性和车站到发线的运用数量等问题,为车站作业计划的质量和可实施性奠定了基础,也为运行计划一体化的平台建设提供了理论支持。
The scheme of railway train-set circulation is an important part in operation, which not only determines the number of needed rain-sets, but also influences the enablement of the yard operational plan seriously. During the process of drawing-up train operational scheme, timetable is a critical input data of planning train-set circulation. Train scheduling, train-set circulation and the yard operational are interdependent. Based on the all-in-one of transportation organization, it is essential to study the circulation of train-set while considering timetable optimization.
Based on the well-known research achievements at home and abroad, this paper study the flow of timetabling based on "through" station and the circulation of train-set. To get optimal connection between train lines, the adjustment method and model for timetable based on feedback are proposed. During the process of timetabling, optimizing and adjusting, the station capacity is considerd roughly. The following components are involved:
1. The character of cyclic train timetable is analyzed in detail. The mathematical model about working out cyclic train timetable based on periodic event scheduling problem (PESP) is analyzed. In China, some passenger dedicated lines with complex operation need more adaptable model. An ameliorated line programming model based on fixed departure/ arrival order is put forward for such situation. Further, the model was extended for the up-down line with the constraint of route conflict to take the capacity of throat into account. The flow of the railway network cyclic train timetable based on "through" station is proposed. And then, a case study is given out.
The result demonstrates that the timetable with one hour as cycle time can partially reduce the scale of scheduling, Lingo can solve the problem quickly; Compared with timetable based on PESP, the model based on fixed departure/ arrival order which only considers the relationship between adjacent lines, needs fewer modeling time.
2. To plan the circulation of train-sets based on railway "through" station with two lines at least, the characteristics of circulation for train-set is discussed in term of semicircle of train-sets'turnaround. Time tolerance a is defined to get more connection between train lines without a direction change. The model of train-set circulation is put forward and a compact connection algorithm based on time toleranceσis then designed.
The result of case demonstrates that the connections between trains at terminal station is guaranteed because of timetable's equilibrium when the train lines is in pair, there are 7 connections and 6 connections at terminal station A and E separately, the connection rate is 100%; At through station D, there is 2 more connection between train lines without a direction change while the usage of compact connection algorithm based on time tolerance, but the result is not so satisfactory as a whole because of weakness of the timetable's equilibrium and the difference in quantity between railway lines, there are only 10 connections in 13 pairs without direction change, the connection rate is only 76.9%.
3. The adjustment method of timetable based on the distribution of superfluous time is studied. To get the maximum adjusted quantity of train line while considering the adjustment method based on the connection with or without direction change, the related train line group is defined. If there is no adjusted space or it is hard to get the adjusted quantity when using the adjustment method, the model which can describe all the constraints between related train lines based on the feedback of train-set's circulation is more important. Then the model for feedback and adjustment is proposed to attain most connections, especially without direction change in through station between train lines. The number of arrival-departure track is also considered in the model as a posterior way.
The result of the case shows that if there is no need to get big adjusted quantity, choose the adjustment method, then adjust the train lines which are the planned connection firstly; After the ultimate adjustment, there is no change for the timetable's structure and slight adjustment of travel time about train lines, and most important of all, the quality of circulation plan is improved obviously based on the station capacity satisfied, there are 7,6 connections at terminal station A and E separately, there are 13 connections, the rate of connection is 100%, especially 12 connections without direction change at through station D, and the rate reaches up to 92.3%.
This paper makes efforts to study the cyclic train diagram establishment, train-set circulation and their feedback and optimization, while considering the robustnessof route assighment and the number constraint of station tracks. Hopefully, it can lay the foundation for the actionability to station working plan, and provide theoretical support to integrated train operational scheme.
引文
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