铁路快速客运网络旅客列车开行方案优化研究
|
摘要
预计到2020年,我国铁路将逐步形成由客运专线、城际铁路和既有提速线路相配套的、总里程约5万km的铁路快速客运网络。制定面向整个铁路快速客运网络的旅客列车开行方案,需要确定列车的始发站、终到站、列车类别、列车定员、运行径路、停站序列、开行数量等要素,是一类基于复杂网络的大规模组合优化问题。
本文将车站其划分为集结站或非集结站,将网络中的客流按给定规则向集结站集结；设计了带有随机客流OD和柔性约束的旅客列车开行方案机会约束目标规划模型和算法；研究了网络中通过能力限制区段等特殊情况下的运输组织方法；采用初步开发的旅客列车开行方案决策支持系统对一个自构造网络进行了算例分析与方案比较。
论文的主要研究工作包括以下几个方面：
(1)铁路快速客运网络的抽象描述
在深入分析铁路快速客运网络中车站、线路、客流、列车、径路等因素的基础上,考虑车站在网络中的地位、作用等因素,将车站划分为集结站与非集结站,并将网络中的客流按给定规则向集结站集结,从而为旅客列车开行方案的优化创造了有利条件。
(2)铁路旅客列车开行方案优化模型
兼顾铁路、旅客以及其他各方利益,以极大化铁路企业经济效益、极小化旅客出行成本等为优化目标,以通过能力约束、列车运用约束、服务水平约束等为约束条件,建立了旅客列车开行方案优化的确定性多目标硬约束模型；将目标函数和软约束转换为目标约束,根据旅客列车开行方案多目标多属性群决策问题中目标优先级与权重的确定方法,通过引入优先因子、正负偏差量及权重,建立了旅客列车开行方案优化的确定性目标规划模型；进一步以路网中站间OD流量作为随机参数,在一定的置信水平下,建立了旅客列车开行方案优化的机会约束目标规划模型。
(3)铁路旅客列车开行方案优化算法
考虑站间客流OD的随机性,对机会约束目标规划模型设计了基于随机模拟的遗传算法,主要包括：基因的自然数编／解码、基于客流OD随机分布的初始种群生成、基于序的评价函数计算、遗传算子设计,并采用了自适应的交叉、变异算子保证种群多样性,避免算法早熟现象的产生。
(4)特殊情况下的运输组织方法
分析车站能力、区间能力等约束条件未能严格满足情况下的运输组织方法,重点研究通过能力限制区段的运输组织方法。阐述了通过能力限制区段的基本理论,针对提速线路、客运专线或城际客运专线三种线路的特点,设计了成组追踪法、分时段运行法以及重联运行法等多种运输组织方法,解决了求解旅客列车开行方案目标规划模型时出现正偏差给运输组织带来的困难,从而使求出的旅客列车开行方案在运输组织上具有可行性。
(5)算例分析与方案比较
采用初步开发的铁路快速客运网络旅客列车开行方案决策支持系统,基于一个自构造网络进行了算例分析与方案比较。结果表明,所建立的优化模型对铁路旅客列车开行方案决策问题的描述更加全面,而设计的优化算法能够在较短的时间内生成合理的旅客列车开行方案,验证了本文有关模型和算法的有效性和实用性。
旅客列车开行方案优化研究是铁路旅客运输系统优化的应用基础研究。论文紧扣铁路快速客运网络中不同车站与客流的重要程度的差异性,描述了客流在网络中的输送机理,设计了旅客列车开行方案的机会约束目标规划模型与算法,研究了特殊情况下的运输组织方法。论文提出的理论与方法形成了一个相对完整的理论体系,不仅对实现铁路旅客列车开行方案的决策优化具有实际意义,同时对丰富我国铁路旅客运输组织理论也具有重要参考价值。
By the year 2020, it is expected that railways in China would have been formed into express passenger transportation network, including passenger-dedicated lines, intercity rail lines and existing speed-rising railway lines up to 50,000km in total mileage. Formulating the passenger train operation scheme oriented to the whole express passgener transportation network needs to determine a series of components, such as the departing station, arrival station, train types, fixed members, running route, station orders, etc., which belongs to a large scale combination and optimization problem based on the complex network.
On the basis of station positions and functions, and passenger volume, this study divides the stations into muster and non-muster ones, and aggregates the passenger flow to muster stations according to the given rules; Then the chance constraints objective programming models and algorithms are designed with stochastic passenger flow OD and flexible constraints passenger operation scheme. Moverover, the transportation organization methods are studied under special conditions, and the initially-developed passenger train operation scheme decision support system is adopted to exemplify and compare one self-structured network. The main work of the study includes the following aspects:
(1)Abstract description of railway express passenger transportation network
By analyzing the various factors in the transportation network, and considering the stations'status and functions, muster stations and non-muster stations are divided. The passenger flow in the network is clustered according to the given rules, which establishes the hierarchy express passenger transportation network.
(2) Railway passenger train operation scheme optimization model
First, by giving consideration to railway, passengers and other benefits, deterministic multiple objective contrainted model of passenger train operation scheme optimization is established with constraining carrying capacity, train operation and service level; based on the results, the objective function and soft constraints are transformed into objective constraints, and deterministic objective programming model is set up by introducing priori factor, positive and negative deviation, and weights; Then by considering OD flow within translation stations in the network as random parameter, chance constraints objective programming model is represented at certain confidence interval.
(3) Railway passenger train operation scheme optimization algorithm
By considering the randomness of passenger flow OD, stochastic simulatoin-based genetic algorithm is proposed on chance constrain objective programming model, including natual coding/uncoding of gene, initial population generation of random distribution based on passenger flow OD, evaluation function calculation in the form of order and genetic operators. Self-adpative crossing and mutation operators are utilized to make sure the population diversity and to avoid premature convergence of genetic algorithm.
(4) Transport organization methods under special circumstances
Through analyzing the transportation organization methods under unsatisfied condtions with station and section capacity constraints, the methods on restricted section of carrying capacity are studied with emphasis. By explaining the basic theory on restricted section of carrying capacity, and aiming at the features of speed-rising lines, passenger-dedicated lines and intercity passenger special lines, various methods, such as group tracking method, shifting operating method, reconnection operating method, etc. are designed correspondingly to figure out the trouble for transportation organization when the positive deviation occurs while solving the programming model, so as to make the passenger train operating scheme feasible.
(5)Example analysis and scheme comparison
The decision support system of express passenger transportation network scheme is developed initially, and the example analysis and scheme comparison are conducted with the self-structured network. The results indicat that the optimized model can describe the descion-making problems of passenger train operation scheme more completely, while the designed algorithm can generate the suitable passenger train layout and flow distribution schemes in short time, which verifies the effectiveness and practice of the proposed models and algorithms.
The optimization study on passenger train operation scheme of railway express passenger transportation network is one of the basic theories research. Concentrated on the difference among various stations in express passenger transportation network and importance extent of passenger flow, this study utilizes various research approaches from qualitative to quantitative, from the local to the global and multi level solutions in order to optimize the whole network and the train flow distribution schemes. The models and algorithms presented in this study reveal the rules of passenger train layout and flow distribution optimization and form into a relatively complete system. The results can not only help to realize the computer-aided decision making of railway passenger train operation scheme, but also enrich railway passenger transportation organization theory in China.
本文将车站其划分为集结站或非集结站,将网络中的客流按给定规则向集结站集结；设计了带有随机客流OD和柔性约束的旅客列车开行方案机会约束目标规划模型和算法；研究了网络中通过能力限制区段等特殊情况下的运输组织方法；采用初步开发的旅客列车开行方案决策支持系统对一个自构造网络进行了算例分析与方案比较。
论文的主要研究工作包括以下几个方面：
(1)铁路快速客运网络的抽象描述
在深入分析铁路快速客运网络中车站、线路、客流、列车、径路等因素的基础上,考虑车站在网络中的地位、作用等因素,将车站划分为集结站与非集结站,并将网络中的客流按给定规则向集结站集结,从而为旅客列车开行方案的优化创造了有利条件。
(2)铁路旅客列车开行方案优化模型
兼顾铁路、旅客以及其他各方利益,以极大化铁路企业经济效益、极小化旅客出行成本等为优化目标,以通过能力约束、列车运用约束、服务水平约束等为约束条件,建立了旅客列车开行方案优化的确定性多目标硬约束模型；将目标函数和软约束转换为目标约束,根据旅客列车开行方案多目标多属性群决策问题中目标优先级与权重的确定方法,通过引入优先因子、正负偏差量及权重,建立了旅客列车开行方案优化的确定性目标规划模型；进一步以路网中站间OD流量作为随机参数,在一定的置信水平下,建立了旅客列车开行方案优化的机会约束目标规划模型。
(3)铁路旅客列车开行方案优化算法
考虑站间客流OD的随机性,对机会约束目标规划模型设计了基于随机模拟的遗传算法,主要包括：基因的自然数编／解码、基于客流OD随机分布的初始种群生成、基于序的评价函数计算、遗传算子设计,并采用了自适应的交叉、变异算子保证种群多样性,避免算法早熟现象的产生。
(4)特殊情况下的运输组织方法
分析车站能力、区间能力等约束条件未能严格满足情况下的运输组织方法,重点研究通过能力限制区段的运输组织方法。阐述了通过能力限制区段的基本理论,针对提速线路、客运专线或城际客运专线三种线路的特点,设计了成组追踪法、分时段运行法以及重联运行法等多种运输组织方法,解决了求解旅客列车开行方案目标规划模型时出现正偏差给运输组织带来的困难,从而使求出的旅客列车开行方案在运输组织上具有可行性。
(5)算例分析与方案比较
采用初步开发的铁路快速客运网络旅客列车开行方案决策支持系统,基于一个自构造网络进行了算例分析与方案比较。结果表明,所建立的优化模型对铁路旅客列车开行方案决策问题的描述更加全面,而设计的优化算法能够在较短的时间内生成合理的旅客列车开行方案,验证了本文有关模型和算法的有效性和实用性。
旅客列车开行方案优化研究是铁路旅客运输系统优化的应用基础研究。论文紧扣铁路快速客运网络中不同车站与客流的重要程度的差异性,描述了客流在网络中的输送机理,设计了旅客列车开行方案的机会约束目标规划模型与算法,研究了特殊情况下的运输组织方法。论文提出的理论与方法形成了一个相对完整的理论体系,不仅对实现铁路旅客列车开行方案的决策优化具有实际意义,同时对丰富我国铁路旅客运输组织理论也具有重要参考价值。
By the year 2020, it is expected that railways in China would have been formed into express passenger transportation network, including passenger-dedicated lines, intercity rail lines and existing speed-rising railway lines up to 50,000km in total mileage. Formulating the passenger train operation scheme oriented to the whole express passgener transportation network needs to determine a series of components, such as the departing station, arrival station, train types, fixed members, running route, station orders, etc., which belongs to a large scale combination and optimization problem based on the complex network.
On the basis of station positions and functions, and passenger volume, this study divides the stations into muster and non-muster ones, and aggregates the passenger flow to muster stations according to the given rules; Then the chance constraints objective programming models and algorithms are designed with stochastic passenger flow OD and flexible constraints passenger operation scheme. Moverover, the transportation organization methods are studied under special conditions, and the initially-developed passenger train operation scheme decision support system is adopted to exemplify and compare one self-structured network. The main work of the study includes the following aspects:
(1)Abstract description of railway express passenger transportation network
By analyzing the various factors in the transportation network, and considering the stations'status and functions, muster stations and non-muster stations are divided. The passenger flow in the network is clustered according to the given rules, which establishes the hierarchy express passenger transportation network.
(2) Railway passenger train operation scheme optimization model
First, by giving consideration to railway, passengers and other benefits, deterministic multiple objective contrainted model of passenger train operation scheme optimization is established with constraining carrying capacity, train operation and service level; based on the results, the objective function and soft constraints are transformed into objective constraints, and deterministic objective programming model is set up by introducing priori factor, positive and negative deviation, and weights; Then by considering OD flow within translation stations in the network as random parameter, chance constraints objective programming model is represented at certain confidence interval.
(3) Railway passenger train operation scheme optimization algorithm
By considering the randomness of passenger flow OD, stochastic simulatoin-based genetic algorithm is proposed on chance constrain objective programming model, including natual coding/uncoding of gene, initial population generation of random distribution based on passenger flow OD, evaluation function calculation in the form of order and genetic operators. Self-adpative crossing and mutation operators are utilized to make sure the population diversity and to avoid premature convergence of genetic algorithm.
(4) Transport organization methods under special circumstances
Through analyzing the transportation organization methods under unsatisfied condtions with station and section capacity constraints, the methods on restricted section of carrying capacity are studied with emphasis. By explaining the basic theory on restricted section of carrying capacity, and aiming at the features of speed-rising lines, passenger-dedicated lines and intercity passenger special lines, various methods, such as group tracking method, shifting operating method, reconnection operating method, etc. are designed correspondingly to figure out the trouble for transportation organization when the positive deviation occurs while solving the programming model, so as to make the passenger train operating scheme feasible.
(5)Example analysis and scheme comparison
The decision support system of express passenger transportation network scheme is developed initially, and the example analysis and scheme comparison are conducted with the self-structured network. The results indicat that the optimized model can describe the descion-making problems of passenger train operation scheme more completely, while the designed algorithm can generate the suitable passenger train layout and flow distribution schemes in short time, which verifies the effectiveness and practice of the proposed models and algorithms.
The optimization study on passenger train operation scheme of railway express passenger transportation network is one of the basic theories research. Concentrated on the difference among various stations in express passenger transportation network and importance extent of passenger flow, this study utilizes various research approaches from qualitative to quantitative, from the local to the global and multi level solutions in order to optimize the whole network and the train flow distribution schemes. The models and algorithms presented in this study reveal the rules of passenger train layout and flow distribution optimization and form into a relatively complete system. The results can not only help to realize the computer-aided decision making of railway passenger train operation scheme, but also enrich railway passenger transportation organization theory in China.
引文
[1]刘志军.用科学发展观统领铁路工作,深入推进铁路跨越式发展,为我国经济社会又快又好发展作出更大贡献[J].铁道经济研究,2006,(1)：2-18.
[2]铁道部经济规划研究院.中长期铁路网规划调整方案研究报告[R].北京：铁道部经济规划研究院,2007.
[3]郑健.新时期铁路客运站建设的指导总则与实践[J].铁道学报,2007,29(6)：95-100.
[4]汪铭,和平.中国铁路发展迎来黄金机遇期[N].人民铁道,2008-11-30.
[5]黄民.铁路“十一五”发展战略研究[M].北京：中国铁道出版社,2008.
[6]Ministry of Railways of the People's Republic of China. (2008). China's Cabinet approves huge money infusion to rail construction, http://english.gov.cn/2008-10/2 7/content_1132303.htm(October 27,2008)
[7]叶怀珍.旅客运输组织[M].成都：西南交通大学出版社,2000.
[8]杜文,肖龙文.旅客运输组织[M].第2版.成都：西南交通大学出版社,2008.
[9]王甦男.旅客运输[M].北京：中国铁道出版社,2003.
[10]Papadimitriou C H, Steiglitz K. Combinatorial Optimization:Algorithms and Complexity[M]. Prentice Hall Inc.1982.
[11]Hochbaum D S. Approximation algorithm s for NP-hard problems[M]. Boston:PW S Publising Company,1995.
[12]闫海峰,董守清,李群仁.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)：69-71,75.
[13]中华人民共和国铁道部.铁路客运专线运营调度系统总体技术方案[Z].中国铁道出版社,2008.
[14]汪波.基于周期化运行的轨道交通列车开行方案和运行图研究[D].北京交通大学,2007.
[15]中华人民共和国铁道部.铁路旅客运输管理规程[S].北京冲国铁道出版社,1994,10：35～42.
[16]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(自然科学版),2000,35(2),230-234.
[17]韩冰.秦沈客运专线客车开行方案及相关问题的研究[J].中国铁路,2003,(2)：37-40.
[18]张鹏.广深Ⅲ、Ⅳ线城际列车开行方案探讨[J].铁道运输与经济,2005,27(4)：53-55.
[19]程晓毛.合九铁路旅客列车开行方案的优化[J].铁道运输与经济,2007,29(1)：55-56.
[20]吴庆民.闽浙赣省会城市圈客车开行方案选择[J].铁道运输与经济,1989,(6)：20-21.
[21]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.
[22]王心岗,张毅.西安铁路分局完善旅客列车开行方案的建议[J].铁道运输与经济,2004,26(5)：39-40.
[23]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.
[24]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,1995,19(A01)：9-14.
[25]沈庆衍,郎茂祥.关于京沪高速铁路旅客列车开行方案的研究[J].铁道运输与经济,1994,16(3)：4-7.
[26]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,(11)：16-20.
[27]赵鹏,杨浩.京沪高速铁路列车开行模式的研究[J].北京交通大学学报,2006,30(3)：5-9.
[28]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,2000,34(S1),11-14.
[29]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.
[30]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.
[31]孙焰,施其洲,赵源等.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)：1005-1008,1014.
[32]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,1998,33(4)：400-404.
[33]Chang, Y H, Yeh C H, and Shen C C.A multi-objective model for passenger train services planning:application to Taiwan's high-speed rail line[J]. Transportation Research Part B,2000, (34):91-106.
[34]史峰：邓连波：黎新华等.客运专线相关旅客列车开行方案研究[J].铁道学报,2004,26(2)：16-20.
[35]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.
[36]彭其渊.客运专线运输组织[M].北京：科学出版社,2007.
[37]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.
[38]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.
[39]邓连波.客运专线相关旅客列车开行方案优化研究[D].中南大学,2007.
[40]史峰,邓连波,霍亮.旅客列车开行方案的模型和算法[J].中国铁道科学,2007,28(3),110-116.
[41]何宇强,张好智,毛保华.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.
[42]史峰,周文梁,陈彦等.基于弹性需求的旅客列车开行方案优化研究[J].铁道学报,2008,30(3),1-6.
[43]Serafini P, Ukovich W. A Mathematical Model for Periodic Scheduling Problems [J]. SIAM J. Discrete Math,1989,2(4):550-581.
[44]Serafini P, Ukovich W. A Mathematical Model for the Fixe-time Traffic control problem [J]. European Journal of Operation Research,1989,42 (2):152-165.
[45]Gert sbakh, Serafini P. Periodic t ransportation schedules with flexible departure times: An interactive approach based on the periodic event scheduling problem and thedeficit function approach [J]. European Journal of Operation Research,1991,50 (3):298-309.
[46]须田竟.东海道新干線[M].东京：大正出版株式会社,1989.
[47]Bussieck M R, Kreuzer P, Zimmermann U T. Optimal lines for railway systems [J]. European Journal of Operational Research,1996,96:54-63.
[48]MA Odijk. Railway Timetable Generation [D]. Delf t:Delft University of Technology, 1997.
[49]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.
[50]Christian Liebchen, Rolf H. Mohring. A Case Study in Periodic Timetabling [J]. Elect ronic Notes in Theoretical Computer Science,2002,66 (6):1-14.
[51]Christian Liebchen. Periodic Timetable Optimization in Public Transport [M]. Berlin: dissertation, de,2006.
[52]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.
[53]William H KLam, J ing Zhou, Zhao Hancheng. A Capacity Restraint Transit Assignment with Elastic Line Frequency[J]. Transportation Research B,2002,36 (10): 919-938.
[54]Xianyi Wu and Xian Zhou. Stochastic scheduling to minimize expected maximum lateness[J]. European Journal of Operational Research, Volume 190, Issue 1,1 October 2008, Pages 103-115.
[55]LEI Quang-sheng, CHEN Jian. An algorithm for transit assignment with elastic demand under capacity constrain[C]//Proceedings of the 5th world congress on intelligent control and automation. Hang Zhou, P. R. China:2004,5245-5247.
[56]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.
[57]陶思宇,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.
[58]肖建明.旅客列车开行效益及投入产出分析[J].铁道运输与经济,2003,25(9)：32-24.
[59]陈军团,吕红霞,李珂等.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)：7-9.
[60]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.
[61]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,1999,21(6)：43-45.
[62]杜学东,高自友.铁路旅客列车开行效益分析与决策支持系统[J].铁道学报,2003,25(3)：13-18.
[63]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(10)：58-60.
[64]史峰,邓连波,霍亮.客运专线旅客列车开行方案优化系统设计[J].系统工程,2006,24(11)：24-30.
[65]黄鉴.客运专线旅客列车开行方案研究[D].西南交通大学,2005.
[66]陶思宇.铁路旅客列车开行方案经济效益评价研究及其计算机实现[D].华东交通大学,2006.
[67]王海志.客运专线旅客列车开行方案研究[D].铁道部科学研究院,2006.
[68]冯枫.客运专线高速客车开行方案的计算与评价[D].北京交通大学,2007.
[69]闫海峰.客运专线旅客列车开行方案优化研究[R].铁道科学研究院,博士后出站报告,2007.
[70]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,2001,23(10)：30-33.
[71]滕志民,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)：1-16.
[72]孙焰,季令,张国宝.双线区段通过能力及相关因素分析[J]铁道学报,2001,23(02)：1-7.
[73]左大杰,王慈光,马驷等.西安—兰州客运专线运输组织模式研究[J].铁道运输与经济,2008,30(1)：22-25.
[74]倪少权,左大杰,王慈光.高速铁路越行站分布对通过能力的影响[J].中国铁道科学,2005,26(3)：7-10.
[75]户佐安.200km/h客货混跑铁路运输组织模式及相关问题研究[D].西南交通大学,2005.
[76]宋艳.干线提速区段通过能力计算方法研究[D].北京交通大学,2007.
[77]铁道部运输局.既有线提速200km/h行车组织[M].中国铁道出版社,2006.
[78]杨肇夏,杨宇栋,孙全欣等.京沪高速铁路区间通过能力计算参数及列车扣除系数的探讨[J].北方交通大学学报,1995,19(S1)：1-8.
[79]郑健.我国铁路客站规划与建设[J].铁道经济研究,2007,(4)：20-30.
[80]殷剑宏,吴开亚.图论及其算法[M].合肥：中国科学技术大学出版社,2003.
[81]牛惠民.铁路枢纽编组站作业分工整体优化的研究[D].北京：北方交通大学,1999.
[82]牛惠民.车流波动条件下铁路枢纽编组站作业分工的优化[J].铁道学报,2003,25(1)：3-8.
[83]张常顺,任建华.铁路客流影响因素及其对策分析[J].内蒙古科技与经济,2007,(11S)：325-326.
[84]刘琦.影响铁路客流的因素及相关度分析[J].上海铁道大学学报,1999,20(2)：41-44.
[85]何平.数理统计与多元统计[M].成都：西南交通大学出版社,2007.
[86]张羽成,吕红霞,王宝杰.基于图论的列车运行径路分析与构造[J].西南交通大学学报,35(3)：273-276.
[87]倪少权,杨明伦,彭其渊.计算机编制列车运行图专家系统之研究[J].西南交通大学学报,1995,30(5)：550-556.
[88]何治宇,黄超.基于聚类的序列分段算法[J].计算机与现代化,2008,150(2)：45-48.
[89]铁道部.铁路动车组运用维修规程[Z].北京：中国铁道出版社,2007.
[90]铁道部.铁路客车运用维修规程[Z].北京：中国铁道出版社,2006.
[91]彭其渊,闫海峰,魏德勇.集装箱班列运输组织[M].成都：四川出版集团·四川科学技术出版社,2005.
[92]Xu Z S. Intuitionistic fuzzy aggregation oprators. IEEE Transactions on Fuzzy Systems,2007,15:1179-1187.
[93]徐泽水,直觉模糊信息集成理论及应用[M].北京：科学出版社,2008.
[94]周宇峰,魏法杰.基于模糊判断矩阵信息确定专家权重的方法[J].中国管理科学2006,14(3)：71.
[95]靖稳锋,魏红,段惠娣.遗传算法及其发展现状[J].西安工业学院学报.2000,20(3)：230～235.
[96]Xu Z S An overview of methods for determining OWA weights. International Journal of Intelligent Systems,2005,20:843-865.
[97]胡思继.铁路行车组织[M].北京：中国铁道出版社,1998.
[98]彭其渊,王慈光.铁路行车组织[M].北京：中国铁道出版社,2007.
[99]杨浩,何世伟.铁路运输组织学[M].北京：中国铁道出版社,2001.
[100]铁道部.铁路技术管理规程(第十版)[Z].北京：中国铁道出版社,2006.
[101]闫海峰,彭其渊,刘焰林.单线铁路旅客列车开行能力的研究[J].西南交通大学学报.2002,37(5)：515-519.
[102]何华武.快速发展的中国高速铁路[J].学术动态,2006,(4)：1-16.
[103]何华武.建立中国高速铁路技术体系的研究[J].铁道运输与经济,2006,28(12)：1-10.
[104]刘志军.我国铁路现代化的回顾与展望[J].理论学习与探索,2008,(1)：3-9.
[105]何华武.创新的中国高速铁路技术(上)[J].中国工程科学,2007,9(9)：1-15.
[106]何华武.创新的中国高速铁路技术(下)[J].中国工程科学,2007,9(10)：1-14.
[107]何华武.中国铁路发展与科技创新[J].铁道工程学报,2007,(7)：1-11.
[108]胡亚东.全面贯彻落实科学发展观又好又快推进运输工作为和谐铁路建设作出新贡献——在全路运输工作会议上的报告(摘要)[J].中国铁路,2008,(2)：6-17.
[109]张曙光.动车组与客运专线系统集成[J].铁道经济研究,2007,(3)：1-7.
[110]刘志军.铁路旅客车站设计指南[M].北京：中国铁道出版社.2006.
[111]郑健.当代中国铁路旅客车站设计综述[J].建筑学报,2009,(4)：1-6.
[112]Goldberg D E. Genetic algorithms in search, optimization and machine learning[M].Addison Wesley.1989,7.1-7.42.
[113]Ji X Y. Models and algorithm for stochastic shortest path problem[J]. Applied Mathematics and Computation.2005,170(1),503-514.
[114]Koza J R. Genetic Programming[M].Cambridge, MIT Press,1992.
[115]Liu B D, and Iwamura, K. Modelling stochastic decision systems using dependent-chance programming[J]. European Journal of Operational Research.1997, 101(1),193-203.
[116]Liu B D. Dependent-chance goal programming and its genetic algorithm based approach. Mathematical and Computer Modelling.1996,24(7),43-52.
[117]Liu B D. Uncertain programming:a unifying optimization theory in various uncertain environments[J]. Applied Mathematics and Computation.2001,120(1-3), 227-234.
[118]Liu B D. Uncertain programming:modeling, evolutionary computation and application[A]. In proceedings of 4th of joint conference on information sciences, North Carolina, USA, October 23-28,1998.
[119]Maciej Klimek, Masaya Matsuura and Yasunori Okabe. Stochastic flows and finite block frames[J]. Journal of Mathematical Analysis and Applications, Volume 342, Issue 2,15 June 2008, Pages 816-829.
[120]Mitchell M. An introduction to genetic algorithms[M].The MIT Press,1996.
[121]Shangyao Yan, Ching-Hui Tang and Tseng-Chih Fu. An airline scheduling model and solution algorithms under stochastic demands[J]. European Journal of Operational Research, Volume 190, Issue 1,1 October 2008, Pages 22-39
[122]ZUO Dajie, WANG Ciguang, LI Yinghong. Application Condition and Operation Procedure of Motor Train Unit Multi-Connection within Passenger Dedicated Lines[C]. International Conference on Transportation Engineering 2009, ICTE 2009,556-561.
[123]ZUO Dajie. Stochastic static wagon-flow allocation model in a marshalling station[C]. International Conference on Transportation Engineering 2007, ICTE 2007, 3636-3641.
[124]马驷,倪少权,詹文华.双线自动闭塞区段旅客列车扣除系数的研究[J].西南交通大学学报,2003,38(1)：70-74.
[125]彭其渊,闫海峰.复线自闭区段旅客列车提速与车站间距的关系[J].西南交通大学学报,2003,38(6)：615-618.
[126]铁道部.铁路200-250km/h既有线技术管理办法[Z].北京：中国铁道出版社,2008.
[127]铁道部.铁路客运专线客运服务系统总体技术方案[Z].北京：中国铁道出版社,2008.
[128]严余松.双线自动闭塞区段旅客列车扣除系数计算方法的探讨[J].西南交通大学学报(自然科学版),1997,32(1)：11-15.
[129]左大杰,王慈光.客运专线动车组列车重联运行相关问题探讨[J].铁道运输与经济,2009,31(7)：32-34.
[130]聂磊,赵鹏,贾利民等.客运专线运输组织技术[M].北京：北京交通大学出版社,2008.
[131]Atanassov K.Intuituinistic fuzzy sets.In:Sgurev V ed. Ⅶ ITKR's Session, Sofia, June 1983.
[132]Atanassov K.Intuituinistic fuzzy sets. Fuzzy Sets and Systems,1986,20:87-96.
[133]Xu Z S,Yager RR. Some geometric aggregation operators based on intuiuionistic fuzzy sets. International Journal of General Systems,2006,35:417-433.
[134]Chen S M,Tan N M.Handling multicriteria fuzzy decision-making problems based on vague set theory. Fuzzy sets and Systems,1994,67:163-172.
[135]Hong D H,Choi C H. Munlticriteria fuzzy decision-making problems based on vague set theory. Fuzzy sets and Systems,2000,114:103-113.
[136]钱立新.世界高速铁路技术[M].北京：中国铁道出版社,2003.
[137]刘宝碇.随机规划与模糊规划[M].北京：清华大学出版社,1998.
[138]Liu, B.D. (1996). "Dependent-chance goal programming and its genetic algorithm based approach." Mathematical and Computer Modelling,24(7),43-52.
[139]Liu, B.D., and Iwamura, K. (1997). "Modelling stochastic decision systems using dependent-chance programming." European Journal of Operational Research,101(1), 193-203.
[140]Liu, B.D. (2001). "Uncertain programming:a unifying optimization theory in various uncertain environments." Applied Mathematics and Computation,120(1-3), 227-234.
[141]Goldberg, D.E. (1989). "Genetic algorithms in search optimization and machine learning." Addison Wesley,7.1-7.42.
[142]左大杰,王慈光,倪少权.旅客留剩率与列车上座率的关系研究[J].铁道运输与经济,2010,32(7)：25-28
[143]ZUO Dajie, WANG Ciguang. Group Tracking Method:A New Method of Transport Organization in Capacity-Restricted Section for Railway Speed-Raising Lines[C]// International Conference on Logistics Engineering and Management (ICLEM 2010), Chengdu, China, October,2010. ASCE, United States:(已录用)
[144]郑时德,吴汉琳.铁路行车组织[M].北京：中国铁道出版社,1988.
[2]铁道部经济规划研究院.中长期铁路网规划调整方案研究报告[R].北京：铁道部经济规划研究院,2007.
[3]郑健.新时期铁路客运站建设的指导总则与实践[J].铁道学报,2007,29(6)：95-100.
[4]汪铭,和平.中国铁路发展迎来黄金机遇期[N].人民铁道,2008-11-30.
[5]黄民.铁路“十一五”发展战略研究[M].北京：中国铁道出版社,2008.
[6]Ministry of Railways of the People's Republic of China. (2008). China's Cabinet approves huge money infusion to rail construction, http://english.gov.cn/2008-10/2 7/content_1132303.htm(October 27,2008)
[7]叶怀珍.旅客运输组织[M].成都：西南交通大学出版社,2000.
[8]杜文,肖龙文.旅客运输组织[M].第2版.成都：西南交通大学出版社,2008.
[9]王甦男.旅客运输[M].北京：中国铁道出版社,2003.
[10]Papadimitriou C H, Steiglitz K. Combinatorial Optimization:Algorithms and Complexity[M]. Prentice Hall Inc.1982.
[11]Hochbaum D S. Approximation algorithm s for NP-hard problems[M]. Boston:PW S Publising Company,1995.
[12]闫海峰,董守清,李群仁.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)：69-71,75.
[13]中华人民共和国铁道部.铁路客运专线运营调度系统总体技术方案[Z].中国铁道出版社,2008.
[14]汪波.基于周期化运行的轨道交通列车开行方案和运行图研究[D].北京交通大学,2007.
[15]中华人民共和国铁道部.铁路旅客运输管理规程[S].北京冲国铁道出版社,1994,10：35～42.
[16]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(自然科学版),2000,35(2),230-234.
[17]韩冰.秦沈客运专线客车开行方案及相关问题的研究[J].中国铁路,2003,(2)：37-40.
[18]张鹏.广深Ⅲ、Ⅳ线城际列车开行方案探讨[J].铁道运输与经济,2005,27(4)：53-55.
[19]程晓毛.合九铁路旅客列车开行方案的优化[J].铁道运输与经济,2007,29(1)：55-56.
[20]吴庆民.闽浙赣省会城市圈客车开行方案选择[J].铁道运输与经济,1989,(6)：20-21.
[21]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.
[22]王心岗,张毅.西安铁路分局完善旅客列车开行方案的建议[J].铁道运输与经济,2004,26(5)：39-40.
[23]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.
[24]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,1995,19(A01)：9-14.
[25]沈庆衍,郎茂祥.关于京沪高速铁路旅客列车开行方案的研究[J].铁道运输与经济,1994,16(3)：4-7.
[26]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,(11)：16-20.
[27]赵鹏,杨浩.京沪高速铁路列车开行模式的研究[J].北京交通大学学报,2006,30(3)：5-9.
[28]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,2000,34(S1),11-14.
[29]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.
[30]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.
[31]孙焰,施其洲,赵源等.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)：1005-1008,1014.
[32]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,1998,33(4)：400-404.
[33]Chang, Y H, Yeh C H, and Shen C C.A multi-objective model for passenger train services planning:application to Taiwan's high-speed rail line[J]. Transportation Research Part B,2000, (34):91-106.
[34]史峰：邓连波：黎新华等.客运专线相关旅客列车开行方案研究[J].铁道学报,2004,26(2)：16-20.
[35]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.
[36]彭其渊.客运专线运输组织[M].北京：科学出版社,2007.
[37]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.
[38]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.
[39]邓连波.客运专线相关旅客列车开行方案优化研究[D].中南大学,2007.
[40]史峰,邓连波,霍亮.旅客列车开行方案的模型和算法[J].中国铁道科学,2007,28(3),110-116.
[41]何宇强,张好智,毛保华.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.
[42]史峰,周文梁,陈彦等.基于弹性需求的旅客列车开行方案优化研究[J].铁道学报,2008,30(3),1-6.
[43]Serafini P, Ukovich W. A Mathematical Model for Periodic Scheduling Problems [J]. SIAM J. Discrete Math,1989,2(4):550-581.
[44]Serafini P, Ukovich W. A Mathematical Model for the Fixe-time Traffic control problem [J]. European Journal of Operation Research,1989,42 (2):152-165.
[45]Gert sbakh, Serafini P. Periodic t ransportation schedules with flexible departure times: An interactive approach based on the periodic event scheduling problem and thedeficit function approach [J]. European Journal of Operation Research,1991,50 (3):298-309.
[46]须田竟.东海道新干線[M].东京：大正出版株式会社,1989.
[47]Bussieck M R, Kreuzer P, Zimmermann U T. Optimal lines for railway systems [J]. European Journal of Operational Research,1996,96:54-63.
[48]MA Odijk. Railway Timetable Generation [D]. Delf t:Delft University of Technology, 1997.
[49]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.
[50]Christian Liebchen, Rolf H. Mohring. A Case Study in Periodic Timetabling [J]. Elect ronic Notes in Theoretical Computer Science,2002,66 (6):1-14.
[51]Christian Liebchen. Periodic Timetable Optimization in Public Transport [M]. Berlin: dissertation, de,2006.
[52]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.
[53]William H KLam, J ing Zhou, Zhao Hancheng. A Capacity Restraint Transit Assignment with Elastic Line Frequency[J]. Transportation Research B,2002,36 (10): 919-938.
[54]Xianyi Wu and Xian Zhou. Stochastic scheduling to minimize expected maximum lateness[J]. European Journal of Operational Research, Volume 190, Issue 1,1 October 2008, Pages 103-115.
[55]LEI Quang-sheng, CHEN Jian. An algorithm for transit assignment with elastic demand under capacity constrain[C]//Proceedings of the 5th world congress on intelligent control and automation. Hang Zhou, P. R. China:2004,5245-5247.
[56]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.
[57]陶思宇,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.
[58]肖建明.旅客列车开行效益及投入产出分析[J].铁道运输与经济,2003,25(9)：32-24.
[59]陈军团,吕红霞,李珂等.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)：7-9.
[60]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.
[61]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,1999,21(6)：43-45.
[62]杜学东,高自友.铁路旅客列车开行效益分析与决策支持系统[J].铁道学报,2003,25(3)：13-18.
[63]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(10)：58-60.
[64]史峰,邓连波,霍亮.客运专线旅客列车开行方案优化系统设计[J].系统工程,2006,24(11)：24-30.
[65]黄鉴.客运专线旅客列车开行方案研究[D].西南交通大学,2005.
[66]陶思宇.铁路旅客列车开行方案经济效益评价研究及其计算机实现[D].华东交通大学,2006.
[67]王海志.客运专线旅客列车开行方案研究[D].铁道部科学研究院,2006.
[68]冯枫.客运专线高速客车开行方案的计算与评价[D].北京交通大学,2007.
[69]闫海峰.客运专线旅客列车开行方案优化研究[R].铁道科学研究院,博士后出站报告,2007.
[70]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,2001,23(10)：30-33.
[71]滕志民,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)：1-16.
[72]孙焰,季令,张国宝.双线区段通过能力及相关因素分析[J]铁道学报,2001,23(02)：1-7.
[73]左大杰,王慈光,马驷等.西安—兰州客运专线运输组织模式研究[J].铁道运输与经济,2008,30(1)：22-25.
[74]倪少权,左大杰,王慈光.高速铁路越行站分布对通过能力的影响[J].中国铁道科学,2005,26(3)：7-10.
[75]户佐安.200km/h客货混跑铁路运输组织模式及相关问题研究[D].西南交通大学,2005.
[76]宋艳.干线提速区段通过能力计算方法研究[D].北京交通大学,2007.
[77]铁道部运输局.既有线提速200km/h行车组织[M].中国铁道出版社,2006.
[78]杨肇夏,杨宇栋,孙全欣等.京沪高速铁路区间通过能力计算参数及列车扣除系数的探讨[J].北方交通大学学报,1995,19(S1)：1-8.
[79]郑健.我国铁路客站规划与建设[J].铁道经济研究,2007,(4)：20-30.
[80]殷剑宏,吴开亚.图论及其算法[M].合肥：中国科学技术大学出版社,2003.
[81]牛惠民.铁路枢纽编组站作业分工整体优化的研究[D].北京：北方交通大学,1999.
[82]牛惠民.车流波动条件下铁路枢纽编组站作业分工的优化[J].铁道学报,2003,25(1)：3-8.
[83]张常顺,任建华.铁路客流影响因素及其对策分析[J].内蒙古科技与经济,2007,(11S)：325-326.
[84]刘琦.影响铁路客流的因素及相关度分析[J].上海铁道大学学报,1999,20(2)：41-44.
[85]何平.数理统计与多元统计[M].成都：西南交通大学出版社,2007.
[86]张羽成,吕红霞,王宝杰.基于图论的列车运行径路分析与构造[J].西南交通大学学报,35(3)：273-276.
[87]倪少权,杨明伦,彭其渊.计算机编制列车运行图专家系统之研究[J].西南交通大学学报,1995,30(5)：550-556.
[88]何治宇,黄超.基于聚类的序列分段算法[J].计算机与现代化,2008,150(2)：45-48.
[89]铁道部.铁路动车组运用维修规程[Z].北京：中国铁道出版社,2007.
[90]铁道部.铁路客车运用维修规程[Z].北京：中国铁道出版社,2006.
[91]彭其渊,闫海峰,魏德勇.集装箱班列运输组织[M].成都：四川出版集团·四川科学技术出版社,2005.
[92]Xu Z S. Intuitionistic fuzzy aggregation oprators. IEEE Transactions on Fuzzy Systems,2007,15:1179-1187.
[93]徐泽水,直觉模糊信息集成理论及应用[M].北京：科学出版社,2008.
[94]周宇峰,魏法杰.基于模糊判断矩阵信息确定专家权重的方法[J].中国管理科学2006,14(3)：71.
[95]靖稳锋,魏红,段惠娣.遗传算法及其发展现状[J].西安工业学院学报.2000,20(3)：230～235.
[96]Xu Z S An overview of methods for determining OWA weights. International Journal of Intelligent Systems,2005,20:843-865.
[97]胡思继.铁路行车组织[M].北京：中国铁道出版社,1998.
[98]彭其渊,王慈光.铁路行车组织[M].北京：中国铁道出版社,2007.
[99]杨浩,何世伟.铁路运输组织学[M].北京：中国铁道出版社,2001.
[100]铁道部.铁路技术管理规程(第十版)[Z].北京：中国铁道出版社,2006.
[101]闫海峰,彭其渊,刘焰林.单线铁路旅客列车开行能力的研究[J].西南交通大学学报.2002,37(5)：515-519.
[102]何华武.快速发展的中国高速铁路[J].学术动态,2006,(4)：1-16.
[103]何华武.建立中国高速铁路技术体系的研究[J].铁道运输与经济,2006,28(12)：1-10.
[104]刘志军.我国铁路现代化的回顾与展望[J].理论学习与探索,2008,(1)：3-9.
[105]何华武.创新的中国高速铁路技术(上)[J].中国工程科学,2007,9(9)：1-15.
[106]何华武.创新的中国高速铁路技术(下)[J].中国工程科学,2007,9(10)：1-14.
[107]何华武.中国铁路发展与科技创新[J].铁道工程学报,2007,(7)：1-11.
[108]胡亚东.全面贯彻落实科学发展观又好又快推进运输工作为和谐铁路建设作出新贡献——在全路运输工作会议上的报告(摘要)[J].中国铁路,2008,(2)：6-17.
[109]张曙光.动车组与客运专线系统集成[J].铁道经济研究,2007,(3)：1-7.
[110]刘志军.铁路旅客车站设计指南[M].北京：中国铁道出版社.2006.
[111]郑健.当代中国铁路旅客车站设计综述[J].建筑学报,2009,(4)：1-6.
[112]Goldberg D E. Genetic algorithms in search, optimization and machine learning[M].Addison Wesley.1989,7.1-7.42.
[113]Ji X Y. Models and algorithm for stochastic shortest path problem[J]. Applied Mathematics and Computation.2005,170(1),503-514.
[114]Koza J R. Genetic Programming[M].Cambridge, MIT Press,1992.
[115]Liu B D, and Iwamura, K. Modelling stochastic decision systems using dependent-chance programming[J]. European Journal of Operational Research.1997, 101(1),193-203.
[116]Liu B D. Dependent-chance goal programming and its genetic algorithm based approach. Mathematical and Computer Modelling.1996,24(7),43-52.
[117]Liu B D. Uncertain programming:a unifying optimization theory in various uncertain environments[J]. Applied Mathematics and Computation.2001,120(1-3), 227-234.
[118]Liu B D. Uncertain programming:modeling, evolutionary computation and application[A]. In proceedings of 4th of joint conference on information sciences, North Carolina, USA, October 23-28,1998.
[119]Maciej Klimek, Masaya Matsuura and Yasunori Okabe. Stochastic flows and finite block frames[J]. Journal of Mathematical Analysis and Applications, Volume 342, Issue 2,15 June 2008, Pages 816-829.
[120]Mitchell M. An introduction to genetic algorithms[M].The MIT Press,1996.
[121]Shangyao Yan, Ching-Hui Tang and Tseng-Chih Fu. An airline scheduling model and solution algorithms under stochastic demands[J]. European Journal of Operational Research, Volume 190, Issue 1,1 October 2008, Pages 22-39
[122]ZUO Dajie, WANG Ciguang, LI Yinghong. Application Condition and Operation Procedure of Motor Train Unit Multi-Connection within Passenger Dedicated Lines[C]. International Conference on Transportation Engineering 2009, ICTE 2009,556-561.
[123]ZUO Dajie. Stochastic static wagon-flow allocation model in a marshalling station[C]. International Conference on Transportation Engineering 2007, ICTE 2007, 3636-3641.
[124]马驷,倪少权,詹文华.双线自动闭塞区段旅客列车扣除系数的研究[J].西南交通大学学报,2003,38(1)：70-74.
[125]彭其渊,闫海峰.复线自闭区段旅客列车提速与车站间距的关系[J].西南交通大学学报,2003,38(6)：615-618.
[126]铁道部.铁路200-250km/h既有线技术管理办法[Z].北京：中国铁道出版社,2008.
[127]铁道部.铁路客运专线客运服务系统总体技术方案[Z].北京：中国铁道出版社,2008.
[128]严余松.双线自动闭塞区段旅客列车扣除系数计算方法的探讨[J].西南交通大学学报(自然科学版),1997,32(1)：11-15.
[129]左大杰,王慈光.客运专线动车组列车重联运行相关问题探讨[J].铁道运输与经济,2009,31(7)：32-34.
[130]聂磊,赵鹏,贾利民等.客运专线运输组织技术[M].北京：北京交通大学出版社,2008.
[131]Atanassov K.Intuituinistic fuzzy sets.In:Sgurev V ed. Ⅶ ITKR's Session, Sofia, June 1983.
[132]Atanassov K.Intuituinistic fuzzy sets. Fuzzy Sets and Systems,1986,20:87-96.
[133]Xu Z S,Yager RR. Some geometric aggregation operators based on intuiuionistic fuzzy sets. International Journal of General Systems,2006,35:417-433.
[134]Chen S M,Tan N M.Handling multicriteria fuzzy decision-making problems based on vague set theory. Fuzzy sets and Systems,1994,67:163-172.
[135]Hong D H,Choi C H. Munlticriteria fuzzy decision-making problems based on vague set theory. Fuzzy sets and Systems,2000,114:103-113.
[136]钱立新.世界高速铁路技术[M].北京：中国铁道出版社,2003.
[137]刘宝碇.随机规划与模糊规划[M].北京：清华大学出版社,1998.
[138]Liu, B.D. (1996). "Dependent-chance goal programming and its genetic algorithm based approach." Mathematical and Computer Modelling,24(7),43-52.
[139]Liu, B.D., and Iwamura, K. (1997). "Modelling stochastic decision systems using dependent-chance programming." European Journal of Operational Research,101(1), 193-203.
[140]Liu, B.D. (2001). "Uncertain programming:a unifying optimization theory in various uncertain environments." Applied Mathematics and Computation,120(1-3), 227-234.
[141]Goldberg, D.E. (1989). "Genetic algorithms in search optimization and machine learning." Addison Wesley,7.1-7.42.
[142]左大杰,王慈光,倪少权.旅客留剩率与列车上座率的关系研究[J].铁道运输与经济,2010,32(7)：25-28
[143]ZUO Dajie, WANG Ciguang. Group Tracking Method:A New Method of Transport Organization in Capacity-Restricted Section for Railway Speed-Raising Lines[C]// International Conference on Logistics Engineering and Management (ICLEM 2010), Chengdu, China, October,2010. ASCE, United States:(已录用)
[144]郑时德,吴汉琳.铁路行车组织[M].北京：中国铁道出版社,1988.