客运专线网络列车开行方案与运行图综合优化模型及算法
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摘要
客运专线网络列车开行方案与运行图综合优化指在一定客运专线网络结构和运输设施条件下,以铁路客运网络上各起讫点之间旅客出行需求量为基础,以旅客运输市场为导向,以提高旅客出行服务水平以及方便车站客运组织作业为目的,科学合理地安排旅客列车开行等级、数量、编组结构、开行起终点、经由线路以及各旅客列车在所经车站的到达、出发或者通过作业时间等内容,体现从客流到列车流的组织方案。由于长期的运输能力紧张,我国铁路的旅客运输组织侧重于满足旅客运输的数量需求,而对旅客出行质量方面的要求并不能给予很好的满足。随着我国铁路客运专线的建设,以“四纵四横”铁路快速通道和四个城际快速客运系统为主的客运专线网的形成极大地提高了铁路运输能力。因此,对如今面对旅客高质量的出行服务需求以及其它旅客运输方式的激烈竞争的铁路企业而言,进一步优化客运专线网络上开行旅客列车,提供高质量的旅客出行服务水平是其旅客运输组织中迫切需要解决的关键问题,具有较强的现实意义。
论文首先分别对旅客列车开行方案和列车运行图进行单独优化研究,设计基于弹性需求的客运专线网络列车开行方案优化方法和基于定序优化的网络列车运行图铺划方法；然后以客运专线网络列车开行方案和列车运行图整体作为研究对象进行综合优化,设计两者的综合优化方法,主要研究内容如下：
(1)考虑客运专线网络上旅客列车开行质量对路网上各起终点之间旅客出行需求量的影响,在分析铁路旅客运输出行需求的主要影响因素,建立客运专线旅客运输出行需求量与其影响因素之间的弹性需求函数关系的基础上,通过描述旅客列车开行效益和旅客出行效益,利用铁路运输企业与旅客之间的Stackelberg博弈关系,建立了基于弹性需求的旅客列车开行方案的双层规划模型。
(2)结合旅客列车开行方案及其双层规划模型的特点,以模拟退火算法作为整个求解算法的基本框架,用于求解上层规划模型中的旅客列车开行方案,而以基于弹性需求的GP算法作为给定旅客列车开行方案条件下客流分配算法嵌套其中,用于求解下层规划模型,设计了旅客列车开行方案双层规划模型的模拟退火求解算法。
(3)在考虑旅客列车始发时间域和维修天窗的基础上,以旅客列车旅行时间最少为优化目标,建立客运专线列车运行图优化模型；通过扩展客运专线松弛列车运行图的多平行四边形和有向图表示形式,进而在生成初始松弛旅客列车运行图的基础上,利用其有向图以平移列车作业时间、交换列车作业顺序、变更列车停站方案和调整列车始发时间域等冲突化解策略优化列车运行图,构建基于定序优化的客运专线列车运行图的铺划方法。
(4)结合客运专线列车运行图优化模型和网络列车运行图中作业间隔的衔接区间属性,以旅客列车旅行时间最少为优化目标,建立客运专线网络列车运行图优化模型；通过扩展网络松弛列车运行图的有向图表示形式,建立网络松弛列车运行图的定序优化线性规划模型,组合平移列车作业时间、交换列车作业顺序、变更列车停站方案以及调整列车始发时间域等冲突化解策略,设计基于定序优化的客运专线网络列车运行图铺划方法。
(5)在构造基于旅客列车运行图旅客换乘网络,准确描述旅客出行过程中各项出行费用的基础上,以客运专线网络列车开行方案和列车运行图整体作为优化对象,结合客运专线网络列车开行方案双层规划模型和网络运行图优化模型,以铁路企业运营效益最大为优化目标,以车站整备能力、车辆总数和列车编组辆数等能力资源限制以及列车到发作业相容性为约束,建立旅客列车开行方案和运行图综合优化的双层规划模型。
(6)通过基于客运专线线路网络、旅客列车开行方案以及旅客列车运行图等不同信息层次换乘网络的客流分配将旅客列车开行方案和旅客列车运行图的优化有效结合起来,设计了基于模拟退火的旅客列车开行方案与运行图综合优化算法。
Integrated optimization of train plan and train diagram on dedicated passenger network is to arrange the grade, number, marshalling structure, starting and terminal station, running route, arrive and depart time at passed station scientifically and rationally for each train, which is based on the railway transportation facilities and passenger travel demands, oriented by passenger transport market, aims to improve the passenger travel services level and facilitate the passenger station organization operation. It can reflect the organization plan from passenger flows to train flows. Due to the intense capacity of railway transport, the railway passenger transportation organization focuses to meet the demand quantity of passenger travel, while the demand quality of passenger travel can not be satisfied in our country for long time. With the construction of dedicated passenger railway, the conformation of dedicated passenger network mainly constituted by four-vertical-and-four-horizontal fast-track railway and four inter-city fast passenger transport system, which can improve the capacity of railway transport greatly. Therefore, it is a key issue in railway passenger transportation organization for railway enterprise to further optimize the running trains on dedicated passenger network and provide high quality travel service level for passengers, when confronting with high quality travel service demand and fierce competition with other passenger transport modes nowadays. It has practical significance to integrated optimize of train plan and train diagram on dedicated passenger network.
Firstly, the passenger train plan and train diagram are optimized respectively in this paper. A method for optimizing the passenger train plan on dedicated passenger network with elastic demands is designed and a method for drawing train diagram on dedicated passenger network based on fixed order optimization is proposed. Then an integrated optimization method for passenger trains plan and train diagram on dedicated passenger network is put forward. The main contents are as follows.
(1) Considering the fluctuation of passenger travel demand caused by the quality varying of passenger train plan on dedicated passenger network, based on analyzing the influence factors of railway passenger travel demand, establishing the railway passenger travel elastic demand function and calculating the train running profit and passenger travel benefit, the bi-level programming model for the passenger train plan with elastic demands is set up by utilizing the stackelberg game relation between railway enterprise and passengers.
(2) Combining the characteristics of passenger train plan and its bi-level programming model, the optimal algorithm based on the simulated annealing algorithm is designed to optimize the passenger train plan. The simulated annealing algorithm, which is regarded as the basic framework of the whole algorithm, is used to solve the upper programming model for passenger train plan, while the adjusted GP algorithm based on elastic demand is used to solve the lower programming model for flow distribution in conditions of certain passenger train plan.
(3) Considering the passenger train departure time domain and comprehensive window maintenance, the model for drawing the passenger train diagram for dedicated passenger lines is built to minimize the travel time of passenger train. Through extending the multi-parallelogram and diagraph of the relaxation train diagram, the method for drawing train diagram of dedicated passenger line based on fixed order optimization is designed, which applies the diagraph to optimize the train diagram by moving operation time, exchanging operation order, changing stop plan and adjusting passenger train departure time domain on the basis of drawing relaxation train diagram.
(4) Considering the time interval constraint among all direction train operation of the station, the model for drawing the passenger train diagram for dedicated passenger network is built to minimize train travel time based on the train diagram optimization model of dedicated passenger line. Through extending network diagram's digraph and building order optimization linear programming model of network relaxation diagram, the model's solution method based on fixed order optimization is designed combining with moving operation time, exchanging operation order, changing stop plan and adjusting passenger train departure time domain.
(5) Through accurately describing the passenger travel costs based on the passenger train diagram, Combining the bi-level programming model of passenger train plan and the optimization model of train diagram on dedicated passenger network, the bi-level programming model for integrated optimizing the passenger train plan and train diagram is established to maximize the passenger train operating benefit with the constraint of preparedness capacity of the station, total number of vehicles, number of train vehicles and compatibility of train running time.
(6) The optimization of passenger train plan and train diagram are combined effectively by the flow distribution based on different transfer network with different levels of information such as passenger railway network, passenger train plan and train diagram. The integrated optimization algorithm of train plan and diagram is designed on the basis of simulated annealing algorithm.
论文首先分别对旅客列车开行方案和列车运行图进行单独优化研究,设计基于弹性需求的客运专线网络列车开行方案优化方法和基于定序优化的网络列车运行图铺划方法；然后以客运专线网络列车开行方案和列车运行图整体作为研究对象进行综合优化,设计两者的综合优化方法,主要研究内容如下：
(1)考虑客运专线网络上旅客列车开行质量对路网上各起终点之间旅客出行需求量的影响,在分析铁路旅客运输出行需求的主要影响因素,建立客运专线旅客运输出行需求量与其影响因素之间的弹性需求函数关系的基础上,通过描述旅客列车开行效益和旅客出行效益,利用铁路运输企业与旅客之间的Stackelberg博弈关系,建立了基于弹性需求的旅客列车开行方案的双层规划模型。
(2)结合旅客列车开行方案及其双层规划模型的特点,以模拟退火算法作为整个求解算法的基本框架,用于求解上层规划模型中的旅客列车开行方案,而以基于弹性需求的GP算法作为给定旅客列车开行方案条件下客流分配算法嵌套其中,用于求解下层规划模型,设计了旅客列车开行方案双层规划模型的模拟退火求解算法。
(3)在考虑旅客列车始发时间域和维修天窗的基础上,以旅客列车旅行时间最少为优化目标,建立客运专线列车运行图优化模型；通过扩展客运专线松弛列车运行图的多平行四边形和有向图表示形式,进而在生成初始松弛旅客列车运行图的基础上,利用其有向图以平移列车作业时间、交换列车作业顺序、变更列车停站方案和调整列车始发时间域等冲突化解策略优化列车运行图,构建基于定序优化的客运专线列车运行图的铺划方法。
(4)结合客运专线列车运行图优化模型和网络列车运行图中作业间隔的衔接区间属性,以旅客列车旅行时间最少为优化目标,建立客运专线网络列车运行图优化模型；通过扩展网络松弛列车运行图的有向图表示形式,建立网络松弛列车运行图的定序优化线性规划模型,组合平移列车作业时间、交换列车作业顺序、变更列车停站方案以及调整列车始发时间域等冲突化解策略,设计基于定序优化的客运专线网络列车运行图铺划方法。
(5)在构造基于旅客列车运行图旅客换乘网络,准确描述旅客出行过程中各项出行费用的基础上,以客运专线网络列车开行方案和列车运行图整体作为优化对象,结合客运专线网络列车开行方案双层规划模型和网络运行图优化模型,以铁路企业运营效益最大为优化目标,以车站整备能力、车辆总数和列车编组辆数等能力资源限制以及列车到发作业相容性为约束,建立旅客列车开行方案和运行图综合优化的双层规划模型。
(6)通过基于客运专线线路网络、旅客列车开行方案以及旅客列车运行图等不同信息层次换乘网络的客流分配将旅客列车开行方案和旅客列车运行图的优化有效结合起来,设计了基于模拟退火的旅客列车开行方案与运行图综合优化算法。
Integrated optimization of train plan and train diagram on dedicated passenger network is to arrange the grade, number, marshalling structure, starting and terminal station, running route, arrive and depart time at passed station scientifically and rationally for each train, which is based on the railway transportation facilities and passenger travel demands, oriented by passenger transport market, aims to improve the passenger travel services level and facilitate the passenger station organization operation. It can reflect the organization plan from passenger flows to train flows. Due to the intense capacity of railway transport, the railway passenger transportation organization focuses to meet the demand quantity of passenger travel, while the demand quality of passenger travel can not be satisfied in our country for long time. With the construction of dedicated passenger railway, the conformation of dedicated passenger network mainly constituted by four-vertical-and-four-horizontal fast-track railway and four inter-city fast passenger transport system, which can improve the capacity of railway transport greatly. Therefore, it is a key issue in railway passenger transportation organization for railway enterprise to further optimize the running trains on dedicated passenger network and provide high quality travel service level for passengers, when confronting with high quality travel service demand and fierce competition with other passenger transport modes nowadays. It has practical significance to integrated optimize of train plan and train diagram on dedicated passenger network.
Firstly, the passenger train plan and train diagram are optimized respectively in this paper. A method for optimizing the passenger train plan on dedicated passenger network with elastic demands is designed and a method for drawing train diagram on dedicated passenger network based on fixed order optimization is proposed. Then an integrated optimization method for passenger trains plan and train diagram on dedicated passenger network is put forward. The main contents are as follows.
(1) Considering the fluctuation of passenger travel demand caused by the quality varying of passenger train plan on dedicated passenger network, based on analyzing the influence factors of railway passenger travel demand, establishing the railway passenger travel elastic demand function and calculating the train running profit and passenger travel benefit, the bi-level programming model for the passenger train plan with elastic demands is set up by utilizing the stackelberg game relation between railway enterprise and passengers.
(2) Combining the characteristics of passenger train plan and its bi-level programming model, the optimal algorithm based on the simulated annealing algorithm is designed to optimize the passenger train plan. The simulated annealing algorithm, which is regarded as the basic framework of the whole algorithm, is used to solve the upper programming model for passenger train plan, while the adjusted GP algorithm based on elastic demand is used to solve the lower programming model for flow distribution in conditions of certain passenger train plan.
(3) Considering the passenger train departure time domain and comprehensive window maintenance, the model for drawing the passenger train diagram for dedicated passenger lines is built to minimize the travel time of passenger train. Through extending the multi-parallelogram and diagraph of the relaxation train diagram, the method for drawing train diagram of dedicated passenger line based on fixed order optimization is designed, which applies the diagraph to optimize the train diagram by moving operation time, exchanging operation order, changing stop plan and adjusting passenger train departure time domain on the basis of drawing relaxation train diagram.
(4) Considering the time interval constraint among all direction train operation of the station, the model for drawing the passenger train diagram for dedicated passenger network is built to minimize train travel time based on the train diagram optimization model of dedicated passenger line. Through extending network diagram's digraph and building order optimization linear programming model of network relaxation diagram, the model's solution method based on fixed order optimization is designed combining with moving operation time, exchanging operation order, changing stop plan and adjusting passenger train departure time domain.
(5) Through accurately describing the passenger travel costs based on the passenger train diagram, Combining the bi-level programming model of passenger train plan and the optimization model of train diagram on dedicated passenger network, the bi-level programming model for integrated optimizing the passenger train plan and train diagram is established to maximize the passenger train operating benefit with the constraint of preparedness capacity of the station, total number of vehicles, number of train vehicles and compatibility of train running time.
(6) The optimization of passenger train plan and train diagram are combined effectively by the flow distribution based on different transfer network with different levels of information such as passenger railway network, passenger train plan and train diagram. The integrated optimization algorithm of train plan and diagram is designed on the basis of simulated annealing algorithm.
引文
[1]我国中长期铁路网规划,http://www.china-mor.gov.cn.
[2]未来20年我国支线航空运输,http://www.southcn.com/news/china/zgkx/.
[3]杨月芳.旅游列车开行方案及相关问题研究[J].铁道经济研究,2001(6)：39-41.
[4]罗玉屏,叶怀珍,陈继红.确定直通旅客列车开行的效益原则[J].西南交通大学学报,1998,33(4)：405-410.
[5]叶怀珍,杨永兰,王彦.铁路旅客列车开行方案问题的探讨[J].西南交通大学学报,2000,35(2)：230-234.
[6]贾俊芳.旅游列车开行方案经济效益评价方法研究[J].北方交通大学学报,2002,26(2)：87-90.
[7]汪波,杨浩,张志华.基于周期运行图的京津城际铁路列车开行方案研究[J].铁道学报,2007,29(2)：8-13.
[8]夏阳,周让.引入客运专线后旅客列车停车方案研究[J].四川建筑,2005(4)：39-40.
[9]陈慧.客运专线周期运行图列车开行方案的研究[J].铁道运输与经济,2006,28(12)：80-83.
[10]徐行方,季令.既有线快速列车开行方案的研究[J].铁道运输与经济,1996,18(7)：7-9.
[11]史峰,邓连波,黎新华,方琪根.客运专线相关旅客列车开行方案研究[J].铁道学报,2004(2).
[12]史峰,邓连波,霍亮.旅客列车开行方案的双层规划模型和算法[J].中国铁道科学,2007,28(3)：110-116.
[13]闫海峰.客运专线列车开行方案优化思路综述[J].铁道运输与经济,2008,30(5)：66-69.
[14]雷蕾.城际客运专线列车开行方案分析[J].现代商贸工业,2009,(5)：259-259.
[15]赵钢,彭其渊.城际铁路列车开行方案优化分析[J].交通科技与经济,2008,(6)：104-105.
[16]何宇强,张好智,毛保华等.客运专线旅客列车开行方案的多目标双层规划模型[J],铁道学报,2006,28(5)：6-10.
[17]肖龙文,史峰.铁路公交化旅客列车开行方案优化[J],湖南大学学报(自然科学版),2009,36(1)：85-88.
[18]徐瑞华,邹晓磊.客运专线列车开行方案的优化方法研究[J],同济大学学报(自然科学版),2005,33(12)：1699-1703.
[19]查伟雄,符卓.直通旅客列车开行方案优化方法的研究[J],铁道学报,2000,22(5)：1-5.
[20]吴柏青.城际客运专线运输组织相关问题研究：[硕士学位论文].成都：西南交通大学,2008.
[21]徐行方,向劲松.区域性城际列车开行方案的研究[J],同济大学学报(自然科学版),2008,36(5)：650-654.
[22]张玉召,张红伟.旅客列车开行方案的DEA分析与评价[J],兰州交通大学学报,2008,27(6)：83-86.
[23]陈军团,吕红霞.旅客列车运输成本测算及盈亏分析[J],铁道运输与经济,2006,28(9)：5-9.
[24]宋伟,吕红霞.铁路旅客列车开行绩效评价研究[J],铁道运输与经济,2009,31(1)：16-19.
[25]李剑,刘会林.铁路旅客列车开行方案经济效益评价系统的开发[J],铁道运输与经济,2008,30(5)：26-28.
[26]陶诗宇,查伟雄.旅客列车开行方案经济效益的评价方法[J].中国铁路,2005,(8)：42-45.
[27]邓连波,史峰.旅客列车开行方案评价指标体系[J].中国铁道科学,2006,27(3).106-110.
[28]Assad A. A. Models for rail transportation [J]. Transportation Research 14A, 205-220,1980.
[29]Harker, PT. The use of ATCS in scheduling and operating railroads:Models, algorithms and applications [J]. Transportation Research Record 1263,101-110,1990.
[30]Higgins, A., Kozan, E., Ferreira, L. Optimal scheduling of trains on a single line track[J]. Transportation Research B,147-161,1996.
[31]Michael R. Bussieck,Peter Kreuzer,Uwe T. Zimmermann. Optimal lines for railway systems [J]. European Journal of Operational Research,1996(96), 54-63.
[32]Current, J., Min, H. Multiobjective design of transportation networks: taxonomy and annotation [J]. European Journal of Operational Research 26, 187-201,1986.
[33]Salzborn, EJ. M. Timetables for a suburban rail transit system [J].
Transportation Science3,279-316,1969.
[34]Assad, A. A. A class of train-scheduling problems [J]. Transportation Science 16, 281-310,1982.
[35]Ghoneim N. S. A., Wirasinghe S. C. Optimum zone structure during peak periods for existing urban rail lines [J]. Transportation Research 20B,7-18, 1986.
[36]Sone S. Novel train stopping patterns for high-frequency, high-speed train scheduling [A]. In:Murthy, T. K. S., Allan, J., Hill, R. J., Sciutto, G., Sone,5. (Eds.), Computers in Railways 111, Technology, vol.2. Computational Mechanics Publications, Southampton, UK, pp.107-118,1992.
[37]Sone,S. High-speed, high-density train allocation [A]. In:Murthy, T. K. S., Mellitt, B., Brebbia, C.A., Sciutto, G., Sone, S. (Eds.), Computers in Railways IV, Railway Operations, vol.2. Computational Mechanics Publications, Southampton, UK, pp.11-18,1994.
[38]Claessens, M. T. A mathematical programming model to determine a set of operation lines at minimal costs [A]. In:Murthy T. K. S., Mellitt B., Brebbia C. A., Sciutto G., Sone S. (Eds.), Computers in Railways IV, Railway Operations, vol.2. Computational Mechanics Publications, Southampton, UK, pp.117-123,1994.
[39]Salzborn, EJ. M. The minimum fleet size for a suburban railway system [J]. Transportation Science4,383-402,1970.
[40]Eisele, D. O. Application of zone theory to a suburban rail transit network [J]. Traffic Quarterly 22,49-67,1968.
[41]Anthony, R. N. Planning and control systems:a framework for analysis[J]. Harvard University, Boston,1965.
[42]Hooghiemstra, J. S. Design of regular interval time tables for strategic and tactical railway planning [A]. In:Allan J., Brebbia C. A., Hill R. J., Sciutto G.., Sone S. (Eds.),Computers in railways V, vol.1. Computational Mechanics Publications, Southampton, UK, pp.393-402,1996.
[43]M. T. Claessens, N. M. van Dijk, P. J. Zwaneveld. Cost optimal allocation of rail passenger lines [J]. European Journal of Operational Research,1998(110): 474-489.
[44]Yu-Hern Chang, Chung-Hsing Yeh, Ching-Cheng Shen. A multiobjective model for passenger train services planning:application to Taiwan's high-speed
rail line [J]. Transportation Research Part B,2000(34),91-106.
[45]MASHFORD J.S., MARKSJO B.S. Airline base schedule optimisation by flight network annealing [J]. Annals of Operations Research 108,293-313, 2001.
[46]Carlos Martins, Margarida Pato. Search strategies for the feeder bus network design problem [J]. European Journal of Operational Research, 1998(106):325-340.
[47]贾永刚,杜旭生.我国客运专线列车运行图编制的有关问题[J].铁道运输与经济,2006,28(5)：77-79.
[48]陈刚,史峰.铁路旅客列车运行图编制要点分析[J].铁道运输与经济,2004,(5)：37-38.
[49]时颢.我国高速铁路列车运行图采用模式的分析[J].铁道学报,2000,22(1)：92-97.
[50]李菊,张晓霖.用计算机绘制列车运行图[J].北方交通大学学报,1994(4)：537-541.
[51]杨肇夏,胡安洲.列车运行图动态性能及其指标体系的研究[J].铁道学报,1993,15(4)：46-56.
[52]胡思继,孙全欣,胡锦云.区段内列车晚点传播理论的研究[J].中国铁道科学,1994(2)：41-54.
[53]杨肇夏,胡安洲,李菊等.列车晚点传播模拟系统[J].铁道学报,1995(2)：17-24.
[54]孙焰,李致中.列车运行图的均衡性标准[J].长沙铁道学院学报,1993,11(2)：63-68.
[55]孙焰,李致中.列车运行图最优初始布点方法[J].长沙铁道学院学报,1997,15(4)：80-87.
[56]符卓.优化车底使用数的客车运行方案图编制方法[J].铁道学报,1996,18(6)：69-75.
[57]符卓.方便旅客施行的列车到发点优化确定方法[J].长沙铁道学院学报,1998,16(3)：30-33.
[58]张星臣,胡安洲.基于运行线上撒点储备能力分配模式下运行方案铺画模型[J].北方交通大学学报,1997,21(3)：273-279.
[59]张星臣,杨浩.运行张群间冗余储备能力分配模式的计算机模拟研究[J].系统工程理论与实践,1997,17(10)：84-90.
[60]彭其渊,杨明伦.计算机编制复线实用货物列车运行图的整数规划模型及
求解方法[J].中国铁道科学,1994,15(4)：60-66.
[61]彭其渊,杨明伦.单线实用货物列车运行图计算机编制系统[J].西南交通大学学报,1995,30(5)：537-542.
[62]孙焰.单线列车运行图优化理论及计算机编制方法：[博士学位论文].长沙：长沙铁道学院,1997.
[63]史峰.定序单线列车运行图的原始—对偶算法[J].铁道学报,1996,018(001)：8-20.
[64]史峰,黎新华,等.单线列车运行图铺划的时间循环迭代优化方法[J].铁道学报,2005,27(1)：1-5.
[65]史峰,黎新华,等.单线列车运行调整最早冲突优化方法[J].中国铁道科学,2005,26(1)：106-113.
[66]黎新华.单线区段列车运行图铺划与运行调整优化方法研究[D].长沙：中南大学,2005.
[67]彭其渊,王宝杰,周党瑞.基于实用的一种网络列车运行图计算方法[J].西南交通大学学报,1999,34(5)：588-593.
[68]彭其渊,杨明伦.单线区段实用货物列车运行图的优化模型及算法[J].铁道学报,1995,17(3)：15-20.
[69]马建军,胡思继.基于网状线路的京沪高速铁路列车运行图编制理论的研究[J].中国铁道科学,2002,23(5)：135-137.
[70]聂磊,郭富娥.计算机编制高速铁路列车运行图的研究[J].中国铁道科学,1997,18(1)：101-110.
[71]许红,马建军,等.客运专线列车运行图编制模型及计算方法研究[J].铁道学报,2007,29(2)：1-7.
[72]马建军,胡思继.网状线路列车运行图实验平台基础理论的研究[J].北方交通大学学报,2002,026(005)：9-12,18.
[73]彭其渊,王培等.网络列车运行图的数学模型及算法研究[J].铁道学报,2001,023(001)：1-8.
[74]倪少权,吕红霞,杨明伦.全路列车运行图编制系统设计的研究[J].西南交通大学学报,2003,038(003)：332-335.
[75]马建军,胡思继.基于网状线路的京沪高速铁路列车运行图编制理论的研究[D].北京：北京交通大学,2001.
[76]周磊山,胡思继,马建军,乐逸祥.计算机编制网状线路列车运行图方法研究[J].铁道学报,1998,20(5)：15-21.
[77]马建军,周磊山,胡思继.计算机编制网状线路列车运行图系统研究[J].铁
道学报,2000,22(1)：7,11.
[78]王甦男.旅客运输[M].北京：中国铁道出版社,2003.
[79]徐琳.应用层次分析法确定旅客列车开行方案的研究[J].铁道经济研究,2001(3)：46-48.
[80]藤志民,李景民,周生力.网运分离客车开行方案的确定方法[J].哈尔滨铁道科技,2002(1)：8-9.
[81]兰淑梅.京沪高速铁路客车开行方案有关问题的研究[J].铁道运输与经济,2002,24(5)：31-34.
[82]叶怀珍,任民.用DEA方法评价旅客列车运营的相对有效性[J].西南交通大学学报,1998,33(3)：235-239.
[83]许朝阳.优化厦门站客运列车开行方案的探讨[J].铁道运输与经济,2003,25(9)：37-38.
[84]贾俊芳,孙晚华,刘华.城际列车开行方案的客运量预测及评价[J].北京交通大学学报,2004,28(6)：5-98.
[85]韩延慧,聂磊,刘钢.高速铁路合并式列车开行方案分析与设计[J].铁道运输与经济,2001,3(10)：30-33.
[86]陈瑞怀.沪宁线城际旅客列车开行方案探讨[J].铁道运输与经济.2005,27(3)：56-57.
[87]胡辉.旅客列车开行方案系统的开发研究[J].铁道运输与经济,2004,26(9)：58-60.
[88]周立新.铁路旅客列车开行方案决策模型[J].上海交通大学学报,2002(s1)：11-14.
[89]查伟雄,符卓.直通旅客列车开行方案优化方法研究[J].铁道学报,2000,22(5)：1-5.
[90]张拥军,任民,杜文.高速列车开行方案研究[J].西南交通大学学报,1998(4)：400-404.
[91]查伟雄,熊桂林,万国栋.旅客列车开行方案决策支持系统研究[J].系统工程,2004,22(6)：78-82.
[92]李庆云,陈治亚.旅客列车开行方案研究[J].长沙铁道学院学报,2001,19(4)：31-34.
[93]孙焰,施其洲,赵源,孔庆瑜.城市轨道交通列车开行方案的确定[J].同济大学学报(自然科学版),2004,32(8)：1005-1008..
[94]中南大学交通运输工程学院.武广郑西客运专线旅客列车开行方案研究报告[R].2003,8.
[95]刘志昌.上海铁路局旅客列车开行方案优化探讨[J].上海铁道科技,2001,(1)：8-10.
[96]胡思继,孙全欣,冯春霞.京沪线客流和旅客快车开行方案的分析[J].北方交通大学学报,1998,19(4)：9-14.
[97]贾俊芳.铁路城际列车经营效果评价方法研究[J].铁道经济研究,2003,(4)：42-45.
[98]甄静,赵映莲.论高速铁路旅客列车开行方案设计[J].中国铁路,1998,(10)：16-20.
[99]胡思继.铁路行车组织[M].北京：中国铁道出版社,1998.
[100]邓连波,史峰.旅客列车开行方案的评价指标体系研究[J].中国铁道科学,2006(3).
[101]中南大学交通运输工程学院.客运专线旅客列车开行方案优化研究报告[R].2005,11.
[102]中南大学交通运输工程学院.客运专线客车开行方案优化软件设计说明书[R].2005,11.
[103]中华人民共和国铁道部.铁路运输企业成本费用管理核算规程[S].北京：中国铁道出版社,1998：1-19,115-128.
[104]单文浩,叶怀珍.按经济效益原则确定旅客列车满员率的研究[J].西南交通大学学报,2000,35(3)：235-238.
[105]崔炳谋,范今.旅客列车开行经济有利性分析系统的研究与开发[J].铁道运输与经济,1999(6)：43-48.
[106]Fu, Z. Wright, M. Train plan model for British rail freight services through the channel tunnel [J]. Journal ofthe Operational Research Society 45,384-391, 1994.
[107]Israeli, Y. Ceder, A. Multi-objective approach for designing transit routes with frequencies [A]. In:Bianco, L., Toth, P. (Eds.),Advanced Methods in Transportation Analysis, Springer, Berlin, pp.157-182,1996.
[108]Bussieck M. R., winter T. Zimmermann UT. Discrete optimization in public rail transport [J]. Mathematical Programming 79,415-444,1997.
[109]刘万明.关于高速客运专线旅客换乘问题的思考[J].铁道运输与经济,1999(4)：21-23
[110]史峰,邓连波.铁路旅客列车换乘网络设计[J].铁道科学与工程,2004(1).
[111]张彦.铁路客票中转换乘多径路选择问题研究[J].铁道运输与经济,1997,(8)： 11-13
[112]王华,季令.我国铁路客运合理径路选择研究[J].上海铁道大学学报,1999,20(4)：51-54.
[113]邓连波,史峰,等.基于铁路列车开行方案的客流分配方法[A].2005年交通运输工程学科博士论坛[q：北京,47-51.
[114]史峰,马均培等.客运中转径路的换乘模型和算法[J].铁道学报,1999,21(5)： 1-4
[115]李致中,史峰等.铁路运输管理的数学模型计算法[M].武汉：华中理工大学出版社,1995年.
[116]向联慧.客运中转换乘的优化模型与算法[D].长沙铁道学院硕士学位论文,2000年.
[117]黄海军.城市交通网络平衡分析—理论与实践[M].北京：人民交通出版社.1994年.
[118]汤奇志,时颢.沪宁高速铁路运输组织的探讨[J].铁道运输与经济,1997,19(2)：33-36.
[119]张咏.对福建铁路中长途旅客运输的思考[J].铁道运输与经济,2002,24(12)：31-32.
[120]康海燕.北京轨道交通客流预测模型的研究[J].铁道运输与经济,2002,24(12)：21-23.
[121]吕慎,过秀成.轨道线网客流预测方法研究[J].系统工程理论与实践,2001,(8)：106-110.
[122]徐行方,徐瑞华.高速客运专线列车运行组织相关问题的研究[J].同济大学学报,2003,31(5):572-575.
[123]兰淑梅,赵映莲,汤奇志.论京沪高速铁路客流及其组织方案[J].中国铁道科学,2002,23(3)：124-129.
[124]欧国立,张笑雪.地铁运营成本分析与研究[J].北方交通大学学报,1998,18(3)：271-275.
[125]周炜.铁路单列旅客列车成本效益核算方法[J].上海交通大学学报,2000,34(s1)：42-45.
[126]柳进,张巍,刘新.计算机编制全路直通客车方案优化系统的研究[J].中国铁道科学,2004,25(2)：121-125.
[127]翟德友,王文利.改进蓝烟铁路客车开行方案的可行性研究[J].铁路运输与经济,2002,24(8)：21-22.
[128]彭其渊,闫海峰,魏德勇.武广客运专线运输组织模式研究[J].西南交通大学学报,2004,39(6)：703-707.
[129]Sang Nguyen, Stefano Pallottino, Federico Malucelli.A modeling Framework for passenger assignment on a transport network with timetables [J]. Transportation Science,2001,35(3):238-249.
[130]LEI Quang-sheng, CHEN Jian.An algorithm for transit assignment with elastic demand under capacity constrain[A].Proceedings of the 5th world congress on intelligent control and automation[C], Hang Zhou, P. R. China, 2004,5245-5247.
[131]Ziyou GAO, Jianjun Wu, Huijun Sun. Solution algorithm for the bi-level discrete network design problem [J]. Transportation Research Part B, 2005(39):479-495.
[132]M. E. T. Horn. Multi-modal and demand-responsive passenger transport systems:a modelling framework with embedded control systems [J]. Transportation Research Part A 36:167-188,2002.
[133]O. Mekkaoui, A. de Palma, R. Lindsey. Optimal Bus Timetables and Trip Timing Preferences[R]. Working paper, Universite de Cergy-Pontoise.
[134]Washington State Department of Transportation. Public Transportation and Intercity Rail Passenger Plan for Washington State (1997-2006)[R]. December, 1996.
[135]Kazuo Iwama and Eiji Miyano. Routing Problems on the Mesh of Buses [J]. JOURNAL OF ALGORITHMS 20,613-6311996
[136]Janic Milan. The Trans European Railway Network-Three levels of services for the passengers [J]. Transport Policy, Vol.3, No.3, pp99-104,1996
[137]Fu Z and Eglese R. Train planning and timetabling-a kind of open vehicle routing problem with soft time windows[R]. Presented in IFORS 2002, Edinburgh, UK.2002.
[138]Ali Haghani, Mohamadreza Banihashemi, Kun-Hung Chiang. A comparative analysis of bus transit vehicle scheduling models [J]. Transportation Research Part B 37 (2003):301-322
[139]SzpigelB. Optimal train scheduling on a single track railway [A]. In:Ross, M(Ed). OR'72,North Holland Publishing Co. pp.343-352
[140]Ismail Sahin. Railway traffic control and train scheduling based on inter-train conflict management [J]. Transportation Research Part B 33,1999:511-534
[141]Peng qiyuan,The optimizing model and its solution for making train working graph with computer on seperative division of double-track lines[J],Jounal of
South West Jiaotong University, No.2,1994
[142]Dorfman, M.J.; Medanic, J. Scheduling trains on a railway network using a discrete event model of railway traffic[J] Transportation Research Part B: Methodological Volume:38, Issue:1, January,2004, pp.81-98
[143]Caprara, Alberto; Fischetti, Matteo; Toth, Paolo; Vigo, Daniele; Guida, Pier Luigi Algorithms for railway crew management[J] Mathematical Programming Volume:79, Issue:1-3, October 1,1997, pp.125-141
[144]Goumopoulos, Christos; Housos, Efthymios Efficient trip generation with a rule modeling system for crew scheduling problems[J] Journal of Systems and Software Volume:69, Issue:1-2, January 1,2004, pp.43-56
[145]Ghoseiri, Keivan; Szidarovszky, Ferenc; Asgharpour, Mohammad Jawad A multi-objective train scheduling model and solution[J] Transportation Research Part B:Methodological Volume:38, Issue:10, December,2004, pp.927-952
[146]Chiang, Te-Wei; Hau, Hai-Yen; Chiang, Hwan-Ming; Ko, Su-Yun; Hsieh, Chao-Ho, Knowledge-based system for railway scheduling[J], Data& Knowledge Engineering 271998, pp.289-312
[147]A. Erdmann, A. Nolte, A. Noltemeier, R. Schrader. Mathematical models in airline schedule planning:A survey [J]. Annals of Operations Research 107, 117-142,2001
[148]Avishai (AVI) Ceder. Planning and evaluation of passenger ferry service in Hong Kong [J]. Transportation (2006) 33:133-152
[149]Richard Freling, Ramon M. Lentink, Albert P.M. Wagelmans. A Decision Support System for Crew Planning in Passenger Transportation Using a Flexible Branch-and-Price Algorithm [J]. Annals of Operations Research 127, 203-222,2004
[150]J.S. MASHFORD, B.S. MARKSJO. A genetic-based methodology for hybrid electric vehicles sizing [J]. Annals of Operations Research 108,293-313,2001.
[151]Chaug-Ing Hsu, Wen-Ming Chung. A model for market share distribution between high-speed and conventional rail services in a transportation corridor. Annals of Regional Science (1997) 31:121-153
[152]Xuesong Zhou, Ming Zhong. Bicriteria train scheduling for high-speed passenger railroad planning applications[J]. European Journal of Operational Research,167:752-771,2005.
[153]Te-Wei Chiang, Ha&Yen Haua, Hwan-Ming Chiang,et al. Knowledge-based
system for railway scheduling[J]. Data& Knowledge Engineering,1998(27): 289-312.
[154]Xuesong Zhou, Ming Zhong. Single-track train timetabling with guaranteed optimality:Branch-and-bound algorithms with enhanced lower bounds [J]. Transportation Research Part 41B,320-341,2007.
[155]Peng Q Y,Research on the intelligent system for train regulation[A]. Traffic And Transportation Studies. Processing of ICTIS 2000[C]. Beijing:China Association for Science and Technology,2000:602-607.
[156]Joaqui'n Rodriguez. A constraint programming model for real-time train scheduling at junctions [J]. Transportation Research 41B,231-245,2007.
[157]Vivian Salim, Xiaoqiang Cai. A genetic algorithm for railway scheduling with environmental considerations[J]. Environmental Modelling& Sojtware, Vol.12, No.4, pp.301-309,1997.
[158]Alberto Caprara, Michele Monaci, Paolo Toth, et al. A Lagrangian heuristic algorithm for a real-world train timetabling problem [J].Discrete Applied Mathematics,2006(154):738-753.
[159]Andrea D'Ariano, Dario Pacciarelli b, Marco Pranzo. Assessment of flexible timetables in real-time traffic management of a railway bottleneck[J]. Transportation Research Part 16C,232-245,2008.
[160]Mark Wardman, Jeremy Shires, William Lythgoe, et al. Consumer benefits and demand impacts of regular train timetables[J]. International Journal of Transport Management,2004(2):39-49.
[161]P. Vansteenwegen, D.Van Oudheusden. Developing railway timetables which guarantee a better service[J]. European Journal of Operational Research, 2006(173):337-350.
[162]Karl Nachtigall, Stefan Voget. Minimizing waiting times in integrated fixed interval timetables by upgrading railway tracks[J]. European Journal of Operational Research 103,1997(103):610-627.
[163]Leo Kroon,Ga'bor Maroti, Mathijn Retel Helmrich, et al. Stochastic improvement of cyclic railway timetables[J]. Transportation Research Part B,1-18,2008.
[164]Alessandro Chierici, Roberto Cordone. The demand-dependent optimization of regular train timetables[J]. Electronic Notes in Discrete Mathematics, 2004(17):99-104.
[165]邓连波.客运专线相关旅客列车开行方案优化研究[D].长沙：中南大学,2007.
[166]马建军,王宝杰等.京沪高速铁路高中速列车到发时间域的计算方法[J].北方交通大学学报,2002,026(005)：28-31.
[167]马建军,胡思继等.基于京沪高速铁路运行图的高速路网理论研究[J].铁道学报,200,024(003)：1-4.
[168]马建军,许红,胡思继.京沪高速铁路列车运行图指标评价体系的研究[J].北方交通大学学报,2003,027(005)：46-50,81.
[169]郎茂祥,沈庆衍.高中速共线运行下运行图的模拟铺划[J].铁道学报,1996,018(A00)：118-121.
[170]李岱安.中国铁路运输成本计算系统的研究[J].铁道学报,1999,21(6)：96-100.
[171]曾鸣凯,黄鉴,彭其渊.客运专线旅客列车开行方案的客流分配方法[J].西南交通大学学报,2006,41(5):571-574.
[172]徐炜.计算机编制列车运行图的方法研究：[硕士学位论文].大连：大连交通大学,2005.
[173]王仲峰.计算机编制列车运行图方法的研究与运用：[硕士学位论文].北京：铁道科学研究院,2005.
[174]刘梅林,郭富娥.苏联铁路利用电子计算机编制列车运行图综述[J].世界铁路,1991,000(004)：6-10.
[175]周小棋,郭富娥.计算机辅助编制旅客列车运行详图的研究[J].铁道学报,1992,014(003)：65-71.
[176]郭富娥.计算机编制双线列车运行图的研究[J].铁道运输与经济,1998,020(005)：26-27.
[177]郭富娥.高速铁路高、中速旅客列车混行的运行方案探讨[J].中国铁路,1998(9)：15-19.
[178]郭富娥,柳进等.高速线与既有线列车运行图衔接问题的研究[J].中国铁路,2000(7)：25-27.
[179]彭其渊,倪少权.复线列车运行图计算机编制系统的设计原理及功能[J].学术动态报导,1997,000(002)：3-6.
[180]彭其渊,王军.网络列车运行图分布式数据库访问设计[J].西南交通大学学报,2000,35(003)：264-267.
[181]倪少权,杨明伦.计算机编制全路直通旅客列车运行图的研究[J].铁道运输与经济.2002.024(006).41-43.
[182]史峰,胡安洲.机车周转图的线性配置算法[J].铁道学报,1996,018(004)：18-24.
[183]李夏苗,查伟雄.以客运为主繁忙干线区段列车运行调整计划的优化[J].铁道学报,1999,021(006)：10-14.
[184]叶峻青,李夏苗.繁忙单线铁路区段列车运行调整计划的优化[J].交通运输工程学报,2002,002(002)：120-122.
[185]查伟雄,陈治亚.复线列车运行调整理论与方法的研究[J].铁道学报,2000,22(001)：12-16.
[186]符卓.旅客列车运行方案图优化编制方法的研究[J].铁道学报,1996,18(4)：10-17.
[187]陈团生,毛保华,何宇强.旅客列车发车时间域优化研究[J].铁道学报,2006,28(4)：12-16.
[188]刘怀亮.模拟退火算法及其改进[J].广州大学学报(自然科学版),2005,4(6)：503-506.
[189]邢文训,谢金星.现代优化算法[M].北京：清华大学出版社.2001.
[2]未来20年我国支线航空运输,http://www.southcn.com/news/china/zgkx/.
[3]杨月芳.旅游列车开行方案及相关问题研究[J].铁道经济研究,2001(6)：39-41.
[4]罗玉屏,叶怀珍,陈继红.确定直通旅客列车开行的效益原则[J].西南交通大学学报,1998,33(4)：405-410.
[5]叶怀珍,杨永兰,王彦.铁路旅客列车开行方案问题的探讨[J].西南交通大学学报,2000,35(2)：230-234.
[6]贾俊芳.旅游列车开行方案经济效益评价方法研究[J].北方交通大学学报,2002,26(2)：87-90.
[7]汪波,杨浩,张志华.基于周期运行图的京津城际铁路列车开行方案研究[J].铁道学报,2007,29(2)：8-13.
[8]夏阳,周让.引入客运专线后旅客列车停车方案研究[J].四川建筑,2005(4)：39-40.
[9]陈慧.客运专线周期运行图列车开行方案的研究[J].铁道运输与经济,2006,28(12)：80-83.
[10]徐行方,季令.既有线快速列车开行方案的研究[J].铁道运输与经济,1996,18(7)：7-9.
[11]史峰,邓连波,黎新华,方琪根.客运专线相关旅客列车开行方案研究[J].铁道学报,2004(2).
[12]史峰,邓连波,霍亮.旅客列车开行方案的双层规划模型和算法[J].中国铁道科学,2007,28(3)：110-116.
[13]闫海峰.客运专线列车开行方案优化思路综述[J].铁道运输与经济,2008,30(5)：66-69.
[14]雷蕾.城际客运专线列车开行方案分析[J].现代商贸工业,2009,(5)：259-259.
[15]赵钢,彭其渊.城际铁路列车开行方案优化分析[J].交通科技与经济,2008,(6)：104-105.
[16]何宇强,张好智,毛保华等.客运专线旅客列车开行方案的多目标双层规划模型[J],铁道学报,2006,28(5)：6-10.
[17]肖龙文,史峰.铁路公交化旅客列车开行方案优化[J],湖南大学学报(自然科学版),2009,36(1)：85-88.
[18]徐瑞华,邹晓磊.客运专线列车开行方案的优化方法研究[J],同济大学学报(自然科学版),2005,33(12)：1699-1703.
[19]查伟雄,符卓.直通旅客列车开行方案优化方法的研究[J],铁道学报,2000,22(5)：1-5.
[20]吴柏青.城际客运专线运输组织相关问题研究：[硕士学位论文].成都：西南交通大学,2008.
[21]徐行方,向劲松.区域性城际列车开行方案的研究[J],同济大学学报(自然科学版),2008,36(5)：650-654.
[22]张玉召,张红伟.旅客列车开行方案的DEA分析与评价[J],兰州交通大学学报,2008,27(6)：83-86.
[23]陈军团,吕红霞.旅客列车运输成本测算及盈亏分析[J],铁道运输与经济,2006,28(9)：5-9.
[24]宋伟,吕红霞.铁路旅客列车开行绩效评价研究[J],铁道运输与经济,2009,31(1)：16-19.
[25]李剑,刘会林.铁路旅客列车开行方案经济效益评价系统的开发[J],铁道运输与经济,2008,30(5)：26-28.
[26]陶诗宇,查伟雄.旅客列车开行方案经济效益的评价方法[J].中国铁路,2005,(8)：42-45.
[27]邓连波,史峰.旅客列车开行方案评价指标体系[J].中国铁道科学,2006,27(3).106-110.
[28]Assad A. A. Models for rail transportation [J]. Transportation Research 14A, 205-220,1980.
[29]Harker, PT. The use of ATCS in scheduling and operating railroads:Models, algorithms and applications [J]. Transportation Research Record 1263,101-110,1990.
[30]Higgins, A., Kozan, E., Ferreira, L. Optimal scheduling of trains on a single line track[J]. Transportation Research B,147-161,1996.
[31]Michael R. Bussieck,Peter Kreuzer,Uwe T. Zimmermann. Optimal lines for railway systems [J]. European Journal of Operational Research,1996(96), 54-63.
[32]Current, J., Min, H. Multiobjective design of transportation networks: taxonomy and annotation [J]. European Journal of Operational Research 26, 187-201,1986.
[33]Salzborn, EJ. M. Timetables for a suburban rail transit system [J].
Transportation Science3,279-316,1969.
[34]Assad, A. A. A class of train-scheduling problems [J]. Transportation Science 16, 281-310,1982.
[35]Ghoneim N. S. A., Wirasinghe S. C. Optimum zone structure during peak periods for existing urban rail lines [J]. Transportation Research 20B,7-18, 1986.
[36]Sone S. Novel train stopping patterns for high-frequency, high-speed train scheduling [A]. In:Murthy, T. K. S., Allan, J., Hill, R. J., Sciutto, G., Sone,5. (Eds.), Computers in Railways 111, Technology, vol.2. Computational Mechanics Publications, Southampton, UK, pp.107-118,1992.
[37]Sone,S. High-speed, high-density train allocation [A]. In:Murthy, T. K. S., Mellitt, B., Brebbia, C.A., Sciutto, G., Sone, S. (Eds.), Computers in Railways IV, Railway Operations, vol.2. Computational Mechanics Publications, Southampton, UK, pp.11-18,1994.
[38]Claessens, M. T. A mathematical programming model to determine a set of operation lines at minimal costs [A]. In:Murthy T. K. S., Mellitt B., Brebbia C. A., Sciutto G., Sone S. (Eds.), Computers in Railways IV, Railway Operations, vol.2. Computational Mechanics Publications, Southampton, UK, pp.117-123,1994.
[39]Salzborn, EJ. M. The minimum fleet size for a suburban railway system [J]. Transportation Science4,383-402,1970.
[40]Eisele, D. O. Application of zone theory to a suburban rail transit network [J]. Traffic Quarterly 22,49-67,1968.
[41]Anthony, R. N. Planning and control systems:a framework for analysis[J]. Harvard University, Boston,1965.
[42]Hooghiemstra, J. S. Design of regular interval time tables for strategic and tactical railway planning [A]. In:Allan J., Brebbia C. A., Hill R. J., Sciutto G.., Sone S. (Eds.),Computers in railways V, vol.1. Computational Mechanics Publications, Southampton, UK, pp.393-402,1996.
[43]M. T. Claessens, N. M. van Dijk, P. J. Zwaneveld. Cost optimal allocation of rail passenger lines [J]. European Journal of Operational Research,1998(110): 474-489.
[44]Yu-Hern Chang, Chung-Hsing Yeh, Ching-Cheng Shen. A multiobjective model for passenger train services planning:application to Taiwan's high-speed
rail line [J]. Transportation Research Part B,2000(34),91-106.
[45]MASHFORD J.S., MARKSJO B.S. Airline base schedule optimisation by flight network annealing [J]. Annals of Operations Research 108,293-313, 2001.
[46]Carlos Martins, Margarida Pato. Search strategies for the feeder bus network design problem [J]. European Journal of Operational Research, 1998(106):325-340.
[47]贾永刚,杜旭生.我国客运专线列车运行图编制的有关问题[J].铁道运输与经济,2006,28(5)：77-79.
[48]陈刚,史峰.铁路旅客列车运行图编制要点分析[J].铁道运输与经济,2004,(5)：37-38.
[49]时颢.我国高速铁路列车运行图采用模式的分析[J].铁道学报,2000,22(1)：92-97.
[50]李菊,张晓霖.用计算机绘制列车运行图[J].北方交通大学学报,1994(4)：537-541.
[51]杨肇夏,胡安洲.列车运行图动态性能及其指标体系的研究[J].铁道学报,1993,15(4)：46-56.
[52]胡思继,孙全欣,胡锦云.区段内列车晚点传播理论的研究[J].中国铁道科学,1994(2)：41-54.
[53]杨肇夏,胡安洲,李菊等.列车晚点传播模拟系统[J].铁道学报,1995(2)：17-24.
[54]孙焰,李致中.列车运行图的均衡性标准[J].长沙铁道学院学报,1993,11(2)：63-68.
[55]孙焰,李致中.列车运行图最优初始布点方法[J].长沙铁道学院学报,1997,15(4)：80-87.
[56]符卓.优化车底使用数的客车运行方案图编制方法[J].铁道学报,1996,18(6)：69-75.
[57]符卓.方便旅客施行的列车到发点优化确定方法[J].长沙铁道学院学报,1998,16(3)：30-33.
[58]张星臣,胡安洲.基于运行线上撒点储备能力分配模式下运行方案铺画模型[J].北方交通大学学报,1997,21(3)：273-279.
[59]张星臣,杨浩.运行张群间冗余储备能力分配模式的计算机模拟研究[J].系统工程理论与实践,1997,17(10)：84-90.
[60]彭其渊,杨明伦.计算机编制复线实用货物列车运行图的整数规划模型及
求解方法[J].中国铁道科学,1994,15(4)：60-66.
[61]彭其渊,杨明伦.单线实用货物列车运行图计算机编制系统[J].西南交通大学学报,1995,30(5)：537-542.
[62]孙焰.单线列车运行图优化理论及计算机编制方法：[博士学位论文].长沙：长沙铁道学院,1997.
[63]史峰.定序单线列车运行图的原始—对偶算法[J].铁道学报,1996,018(001)：8-20.
[64]史峰,黎新华,等.单线列车运行图铺划的时间循环迭代优化方法[J].铁道学报,2005,27(1)：1-5.
[65]史峰,黎新华,等.单线列车运行调整最早冲突优化方法[J].中国铁道科学,2005,26(1)：106-113.
[66]黎新华.单线区段列车运行图铺划与运行调整优化方法研究[D].长沙：中南大学,2005.
[67]彭其渊,王宝杰,周党瑞.基于实用的一种网络列车运行图计算方法[J].西南交通大学学报,1999,34(5)：588-593.
[68]彭其渊,杨明伦.单线区段实用货物列车运行图的优化模型及算法[J].铁道学报,1995,17(3)：15-20.
[69]马建军,胡思继.基于网状线路的京沪高速铁路列车运行图编制理论的研究[J].中国铁道科学,2002,23(5)：135-137.
[70]聂磊,郭富娥.计算机编制高速铁路列车运行图的研究[J].中国铁道科学,1997,18(1)：101-110.
[71]许红,马建军,等.客运专线列车运行图编制模型及计算方法研究[J].铁道学报,2007,29(2)：1-7.
[72]马建军,胡思继.网状线路列车运行图实验平台基础理论的研究[J].北方交通大学学报,2002,026(005)：9-12,18.
[73]彭其渊,王培等.网络列车运行图的数学模型及算法研究[J].铁道学报,2001,023(001)：1-8.
[74]倪少权,吕红霞,杨明伦.全路列车运行图编制系统设计的研究[J].西南交通大学学报,2003,038(003)：332-335.
[75]马建军,胡思继.基于网状线路的京沪高速铁路列车运行图编制理论的研究[D].北京：北京交通大学,2001.
[76]周磊山,胡思继,马建军,乐逸祥.计算机编制网状线路列车运行图方法研究[J].铁道学报,1998,20(5)：15-21.
[77]马建军,周磊山,胡思继.计算机编制网状线路列车运行图系统研究[J].铁
道学报,2000,22(1)：7,11.
[78]王甦男.旅客运输[M].北京：中国铁道出版社,2003.
[79]徐琳.应用层次分析法确定旅客列车开行方案的研究[J].铁道经济研究,2001(3)：46-48.
[80]藤志民,李景民,周生力.网运分离客车开行方案的确定方法[J].哈尔滨铁道科技,2002(1)：8-9.
[81]兰淑梅.京沪高速铁路客车开行方案有关问题的研究[J].铁道运输与经济,2002,24(5)：31-34.
[82]叶怀珍,任民.用DEA方法评价旅客列车运营的相对有效性[J].西南交通大学学报,1998,33(3)：235-239.
[83]许朝阳.优化厦门站客运列车开行方案的探讨[J].铁道运输与经济,2003,25(9)：37-38.
[84]贾俊芳,孙晚华,刘华.城际列车开行方案的客运量预测及评价[J].北京交通大学学报,2004,28(6)：5-98.
[85]韩延慧,聂磊,刘钢.高速铁路合并式列车开行方案分析与设计[J].铁道运输与经济,2001,3(10)：30-33.
[86]陈瑞怀.沪宁线城际旅客列车开行方案探讨[J].铁道运输与经济.2005,27(3)：56-57.
[87]胡辉.旅客列车开行方案系统的开发研究[J].铁道运输与经济,2004,26(9)：58-60.
[88]周立新.铁路旅客列车开行方案决策模型[J].上海交通大学学报,2002(s1)：11-14.
[89]查伟雄,符卓.直通旅客列车开行方案优化方法研究[J].铁道学报,2000,22(5)：1-5.
[90]张拥军,任民,杜文.高速列车开行方案研究[J].西南交通大学学报,1998(4)：400-404.
[91]查伟雄,熊桂林,万国栋.旅客列车开行方案决策支持系统研究[J].系统工程,2004,22(6)：78-82.
[92]李庆云,陈治亚.旅客列车开行方案研究[J].长沙铁道学院学报,2001,19(4)：31-34.
[93]孙焰,施其洲,赵源,孔庆瑜.城市轨道交通列车开行方案的确定[J].同济大学学报(自然科学版),2004,32(8)：1005-1008..
[94]中南大学交通运输工程学院.武广郑西客运专线旅客列车开行方案研究报告[R].2003,8.
[95]刘志昌.上海铁路局旅客列车开行方案优化探讨[J].上海铁道科技,2001,(1)：8-10.
[96]胡思继,孙全欣,冯春霞.京沪线客流和旅客快车开行方案的分析[J].北方交通大学学报,1998,19(4)：9-14.
[97]贾俊芳.铁路城际列车经营效果评价方法研究[J].铁道经济研究,2003,(4)：42-45.
[98]甄静,赵映莲.论高速铁路旅客列车开行方案设计[J].中国铁路,1998,(10)：16-20.
[99]胡思继.铁路行车组织[M].北京：中国铁道出版社,1998.
[100]邓连波,史峰.旅客列车开行方案的评价指标体系研究[J].中国铁道科学,2006(3).
[101]中南大学交通运输工程学院.客运专线旅客列车开行方案优化研究报告[R].2005,11.
[102]中南大学交通运输工程学院.客运专线客车开行方案优化软件设计说明书[R].2005,11.
[103]中华人民共和国铁道部.铁路运输企业成本费用管理核算规程[S].北京：中国铁道出版社,1998：1-19,115-128.
[104]单文浩,叶怀珍.按经济效益原则确定旅客列车满员率的研究[J].西南交通大学学报,2000,35(3)：235-238.
[105]崔炳谋,范今.旅客列车开行经济有利性分析系统的研究与开发[J].铁道运输与经济,1999(6)：43-48.
[106]Fu, Z. Wright, M. Train plan model for British rail freight services through the channel tunnel [J]. Journal ofthe Operational Research Society 45,384-391, 1994.
[107]Israeli, Y. Ceder, A. Multi-objective approach for designing transit routes with frequencies [A]. In:Bianco, L., Toth, P. (Eds.),Advanced Methods in Transportation Analysis, Springer, Berlin, pp.157-182,1996.
[108]Bussieck M. R., winter T. Zimmermann UT. Discrete optimization in public rail transport [J]. Mathematical Programming 79,415-444,1997.
[109]刘万明.关于高速客运专线旅客换乘问题的思考[J].铁道运输与经济,1999(4)：21-23
[110]史峰,邓连波.铁路旅客列车换乘网络设计[J].铁道科学与工程,2004(1).
[111]张彦.铁路客票中转换乘多径路选择问题研究[J].铁道运输与经济,1997,(8)： 11-13
[112]王华,季令.我国铁路客运合理径路选择研究[J].上海铁道大学学报,1999,20(4)：51-54.
[113]邓连波,史峰,等.基于铁路列车开行方案的客流分配方法[A].2005年交通运输工程学科博士论坛[q：北京,47-51.
[114]史峰,马均培等.客运中转径路的换乘模型和算法[J].铁道学报,1999,21(5)： 1-4
[115]李致中,史峰等.铁路运输管理的数学模型计算法[M].武汉：华中理工大学出版社,1995年.
[116]向联慧.客运中转换乘的优化模型与算法[D].长沙铁道学院硕士学位论文,2000年.
[117]黄海军.城市交通网络平衡分析—理论与实践[M].北京：人民交通出版社.1994年.
[118]汤奇志,时颢.沪宁高速铁路运输组织的探讨[J].铁道运输与经济,1997,19(2)：33-36.
[119]张咏.对福建铁路中长途旅客运输的思考[J].铁道运输与经济,2002,24(12)：31-32.
[120]康海燕.北京轨道交通客流预测模型的研究[J].铁道运输与经济,2002,24(12)：21-23.
[121]吕慎,过秀成.轨道线网客流预测方法研究[J].系统工程理论与实践,2001,(8)：106-110.
[122]徐行方,徐瑞华.高速客运专线列车运行组织相关问题的研究[J].同济大学学报,2003,31(5):572-575.
[123]兰淑梅,赵映莲,汤奇志.论京沪高速铁路客流及其组织方案[J].中国铁道科学,2002,23(3)：124-129.
[124]欧国立,张笑雪.地铁运营成本分析与研究[J].北方交通大学学报,1998,18(3)：271-275.
[125]周炜.铁路单列旅客列车成本效益核算方法[J].上海交通大学学报,2000,34(s1)：42-45.
[126]柳进,张巍,刘新.计算机编制全路直通客车方案优化系统的研究[J].中国铁道科学,2004,25(2)：121-125.
[127]翟德友,王文利.改进蓝烟铁路客车开行方案的可行性研究[J].铁路运输与经济,2002,24(8)：21-22.
[128]彭其渊,闫海峰,魏德勇.武广客运专线运输组织模式研究[J].西南交通大学学报,2004,39(6)：703-707.
[129]Sang Nguyen, Stefano Pallottino, Federico Malucelli.A modeling Framework for passenger assignment on a transport network with timetables [J]. Transportation Science,2001,35(3):238-249.
[130]LEI Quang-sheng, CHEN Jian.An algorithm for transit assignment with elastic demand under capacity constrain[A].Proceedings of the 5th world congress on intelligent control and automation[C], Hang Zhou, P. R. China, 2004,5245-5247.
[131]Ziyou GAO, Jianjun Wu, Huijun Sun. Solution algorithm for the bi-level discrete network design problem [J]. Transportation Research Part B, 2005(39):479-495.
[132]M. E. T. Horn. Multi-modal and demand-responsive passenger transport systems:a modelling framework with embedded control systems [J]. Transportation Research Part A 36:167-188,2002.
[133]O. Mekkaoui, A. de Palma, R. Lindsey. Optimal Bus Timetables and Trip Timing Preferences[R]. Working paper, Universite de Cergy-Pontoise.
[134]Washington State Department of Transportation. Public Transportation and Intercity Rail Passenger Plan for Washington State (1997-2006)[R]. December, 1996.
[135]Kazuo Iwama and Eiji Miyano. Routing Problems on the Mesh of Buses [J]. JOURNAL OF ALGORITHMS 20,613-6311996
[136]Janic Milan. The Trans European Railway Network-Three levels of services for the passengers [J]. Transport Policy, Vol.3, No.3, pp99-104,1996
[137]Fu Z and Eglese R. Train planning and timetabling-a kind of open vehicle routing problem with soft time windows[R]. Presented in IFORS 2002, Edinburgh, UK.2002.
[138]Ali Haghani, Mohamadreza Banihashemi, Kun-Hung Chiang. A comparative analysis of bus transit vehicle scheduling models [J]. Transportation Research Part B 37 (2003):301-322
[139]SzpigelB. Optimal train scheduling on a single track railway [A]. In:Ross, M(Ed). OR'72,North Holland Publishing Co. pp.343-352
[140]Ismail Sahin. Railway traffic control and train scheduling based on inter-train conflict management [J]. Transportation Research Part B 33,1999:511-534
[141]Peng qiyuan,The optimizing model and its solution for making train working graph with computer on seperative division of double-track lines[J],Jounal of
South West Jiaotong University, No.2,1994
[142]Dorfman, M.J.; Medanic, J. Scheduling trains on a railway network using a discrete event model of railway traffic[J] Transportation Research Part B: Methodological Volume:38, Issue:1, January,2004, pp.81-98
[143]Caprara, Alberto; Fischetti, Matteo; Toth, Paolo; Vigo, Daniele; Guida, Pier Luigi Algorithms for railway crew management[J] Mathematical Programming Volume:79, Issue:1-3, October 1,1997, pp.125-141
[144]Goumopoulos, Christos; Housos, Efthymios Efficient trip generation with a rule modeling system for crew scheduling problems[J] Journal of Systems and Software Volume:69, Issue:1-2, January 1,2004, pp.43-56
[145]Ghoseiri, Keivan; Szidarovszky, Ferenc; Asgharpour, Mohammad Jawad A multi-objective train scheduling model and solution[J] Transportation Research Part B:Methodological Volume:38, Issue:10, December,2004, pp.927-952
[146]Chiang, Te-Wei; Hau, Hai-Yen; Chiang, Hwan-Ming; Ko, Su-Yun; Hsieh, Chao-Ho, Knowledge-based system for railway scheduling[J], Data& Knowledge Engineering 271998, pp.289-312
[147]A. Erdmann, A. Nolte, A. Noltemeier, R. Schrader. Mathematical models in airline schedule planning:A survey [J]. Annals of Operations Research 107, 117-142,2001
[148]Avishai (AVI) Ceder. Planning and evaluation of passenger ferry service in Hong Kong [J]. Transportation (2006) 33:133-152
[149]Richard Freling, Ramon M. Lentink, Albert P.M. Wagelmans. A Decision Support System for Crew Planning in Passenger Transportation Using a Flexible Branch-and-Price Algorithm [J]. Annals of Operations Research 127, 203-222,2004
[150]J.S. MASHFORD, B.S. MARKSJO. A genetic-based methodology for hybrid electric vehicles sizing [J]. Annals of Operations Research 108,293-313,2001.
[151]Chaug-Ing Hsu, Wen-Ming Chung. A model for market share distribution between high-speed and conventional rail services in a transportation corridor. Annals of Regional Science (1997) 31:121-153
[152]Xuesong Zhou, Ming Zhong. Bicriteria train scheduling for high-speed passenger railroad planning applications[J]. European Journal of Operational Research,167:752-771,2005.
[153]Te-Wei Chiang, Ha&Yen Haua, Hwan-Ming Chiang,et al. Knowledge-based
system for railway scheduling[J]. Data& Knowledge Engineering,1998(27): 289-312.
[154]Xuesong Zhou, Ming Zhong. Single-track train timetabling with guaranteed optimality:Branch-and-bound algorithms with enhanced lower bounds [J]. Transportation Research Part 41B,320-341,2007.
[155]Peng Q Y,Research on the intelligent system for train regulation[A]. Traffic And Transportation Studies. Processing of ICTIS 2000[C]. Beijing:China Association for Science and Technology,2000:602-607.
[156]Joaqui'n Rodriguez. A constraint programming model for real-time train scheduling at junctions [J]. Transportation Research 41B,231-245,2007.
[157]Vivian Salim, Xiaoqiang Cai. A genetic algorithm for railway scheduling with environmental considerations[J]. Environmental Modelling& Sojtware, Vol.12, No.4, pp.301-309,1997.
[158]Alberto Caprara, Michele Monaci, Paolo Toth, et al. A Lagrangian heuristic algorithm for a real-world train timetabling problem [J].Discrete Applied Mathematics,2006(154):738-753.
[159]Andrea D'Ariano, Dario Pacciarelli b, Marco Pranzo. Assessment of flexible timetables in real-time traffic management of a railway bottleneck[J]. Transportation Research Part 16C,232-245,2008.
[160]Mark Wardman, Jeremy Shires, William Lythgoe, et al. Consumer benefits and demand impacts of regular train timetables[J]. International Journal of Transport Management,2004(2):39-49.
[161]P. Vansteenwegen, D.Van Oudheusden. Developing railway timetables which guarantee a better service[J]. European Journal of Operational Research, 2006(173):337-350.
[162]Karl Nachtigall, Stefan Voget. Minimizing waiting times in integrated fixed interval timetables by upgrading railway tracks[J]. European Journal of Operational Research 103,1997(103):610-627.
[163]Leo Kroon,Ga'bor Maroti, Mathijn Retel Helmrich, et al. Stochastic improvement of cyclic railway timetables[J]. Transportation Research Part B,1-18,2008.
[164]Alessandro Chierici, Roberto Cordone. The demand-dependent optimization of regular train timetables[J]. Electronic Notes in Discrete Mathematics, 2004(17):99-104.
[165]邓连波.客运专线相关旅客列车开行方案优化研究[D].长沙：中南大学,2007.
[166]马建军,王宝杰等.京沪高速铁路高中速列车到发时间域的计算方法[J].北方交通大学学报,2002,026(005)：28-31.
[167]马建军,胡思继等.基于京沪高速铁路运行图的高速路网理论研究[J].铁道学报,200,024(003)：1-4.
[168]马建军,许红,胡思继.京沪高速铁路列车运行图指标评价体系的研究[J].北方交通大学学报,2003,027(005)：46-50,81.
[169]郎茂祥,沈庆衍.高中速共线运行下运行图的模拟铺划[J].铁道学报,1996,018(A00)：118-121.
[170]李岱安.中国铁路运输成本计算系统的研究[J].铁道学报,1999,21(6)：96-100.
[171]曾鸣凯,黄鉴,彭其渊.客运专线旅客列车开行方案的客流分配方法[J].西南交通大学学报,2006,41(5):571-574.
[172]徐炜.计算机编制列车运行图的方法研究：[硕士学位论文].大连：大连交通大学,2005.
[173]王仲峰.计算机编制列车运行图方法的研究与运用：[硕士学位论文].北京：铁道科学研究院,2005.
[174]刘梅林,郭富娥.苏联铁路利用电子计算机编制列车运行图综述[J].世界铁路,1991,000(004)：6-10.
[175]周小棋,郭富娥.计算机辅助编制旅客列车运行详图的研究[J].铁道学报,1992,014(003)：65-71.
[176]郭富娥.计算机编制双线列车运行图的研究[J].铁道运输与经济,1998,020(005)：26-27.
[177]郭富娥.高速铁路高、中速旅客列车混行的运行方案探讨[J].中国铁路,1998(9)：15-19.
[178]郭富娥,柳进等.高速线与既有线列车运行图衔接问题的研究[J].中国铁路,2000(7)：25-27.
[179]彭其渊,倪少权.复线列车运行图计算机编制系统的设计原理及功能[J].学术动态报导,1997,000(002)：3-6.
[180]彭其渊,王军.网络列车运行图分布式数据库访问设计[J].西南交通大学学报,2000,35(003)：264-267.
[181]倪少权,杨明伦.计算机编制全路直通旅客列车运行图的研究[J].铁道运输与经济.2002.024(006).41-43.
[182]史峰,胡安洲.机车周转图的线性配置算法[J].铁道学报,1996,018(004)：18-24.
[183]李夏苗,查伟雄.以客运为主繁忙干线区段列车运行调整计划的优化[J].铁道学报,1999,021(006)：10-14.
[184]叶峻青,李夏苗.繁忙单线铁路区段列车运行调整计划的优化[J].交通运输工程学报,2002,002(002)：120-122.
[185]查伟雄,陈治亚.复线列车运行调整理论与方法的研究[J].铁道学报,2000,22(001)：12-16.
[186]符卓.旅客列车运行方案图优化编制方法的研究[J].铁道学报,1996,18(4)：10-17.
[187]陈团生,毛保华,何宇强.旅客列车发车时间域优化研究[J].铁道学报,2006,28(4)：12-16.
[188]刘怀亮.模拟退火算法及其改进[J].广州大学学报(自然科学版),2005,4(6)：503-506.
[189]邢文训,谢金星.现代优化算法[M].北京：清华大学出版社.2001.