基于周期化运行的轨道交通列车开行方案和运行图研究
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摘要
随着以列车运行速度为代表的铁路技术装备水平的不断提高,以及人们对运输需求的日益增长,在我国轨道交通实行以列车周期运行为特征的运输组织模式成为可能。
本文深入分析了周期化列车运行的特点,根据我国国情、轨道交通的特点以及发展方向,提出在我国轨道交通系统实行列车周期化运行的运输组织模式;将列车周期化运行与我国快速轨道交通的路网结构、车流性质、实际要求等具体情况相结合,围绕制定列车周期开行方案和编制列车周期运行图两个主题,通过详细的影响因素分析,分别建立了模型,设计了相应求解算法,对符合我国国情的列车周期化运行的相关组织理论进行了深入研究。
本文主要包括以下几方面的内容:
(1)提出了单元周期运行图的表示周期运行图的方法,分析了轨道交通采用周期化运行模式的优点以及采用条件。提出了基于列车周期运行的条件下,线路通过能力新的评价标准——组合通过能力。以京沪客运专线为背景,研究了不同列车开行模式下的组合通过能力。结合我国国情,分析了在我国快速轨道交通网采用基于周期化运行组织模式的可行性和必要性。
(2)介绍了周期事件排序问题(PESP),构建了基于约束图的PESP模型框架,研究并归纳了PESP模型的周期约束及其可行解的一些特点和性质,对一些主要性质给出了证明方法。深入研究了周期势差模型。将PESP模型与其他相关模型进行了比较,并且研究了PESP适合列车运行图铺划的优势。研究了求解PESP的复杂性并给出了改进了的反推求解算法。
(3)研究了城际轨道交通列车周期开行方案的制定。从运输企业、乘客利益以及总体最优的观点出发,充分考虑到客流的不确定性,分别建立了不同目标的单目标机会约束模型和多目标机会约束模型,给出了极大模理想点求解多目标规划、等价类求解机会约束规划的方法,研究了针对此模型的遗传算法。以京津城际轨道交通线为背景,求解了不同条件下的最优列车周期开行方案,分析了计算方法和不同条件下模型所得结果。
(4)研究了客运专线网周期列车开行方案的制定。提出将合并式列车开行方案和拆分式列车开行方案相结合,减少列车的开行种类,简化开行方案的制定。从减少运输企业成本支出、减少乘客换乘观点出发,考虑客流的不确定性,建立了相应单目标模型和多目标模型。对不同等级列车客流分配、改进的最短路算法、机会约束确定性等价类转换、将非线性规划模型转化为线性规划模型进行简化以及模型求解的遗传算法进行了研究。以一定规模的客运专线网络为背景,结合我国的实际情况,分别求解了该路网中、高速列车混行,纯高速列车运行以及列车交错停车运行等不同条件下的列车周期开行方案。
(5)研究了周期运行图的编制理论,并编制了实际周期运行图。分别讨论了编制周期运行图需考虑的具体周期约束及其周期势差表示,深入研究了动车组循环套跑模式下折返周期约束的表示及其计算方法、旅客换乘周期约束的表示及其计算方法、动车组使用数量的计算。以PESP理论、周期势差模型为基础,建立了周期运行图网络模型,研究了网络模型生成树的选择、决策变量的取值特点,研究了模型求解前简化的方法,设计了遗传算法对模型进行求解;编制了树状和网状轨道交通实际单元周期运行图。
With the improvement of rail technology and equipment, which is demonstrated by train speed, and the increasing transportation demand, it becomes possible to operate transportation management mode with periodic running as its characteristics for the rail traffic in China.
This thesis analyzes the features of train periodic running, according to the national condition, the features of rail traffic and developing direction of China; introduces the idea that the rail traffic system in China applies a transportation management mode of periodic running; combining periodic running with the specific situation of rail network structure, property of car flow and realistic demand of high speed rail traffic in China, focusing on building periodic running operation plan and periodic working diagram, by way of analyzing influencing factors, establishes the models and designs the corresponding solving algorithms and makes further discussion on the relevant management theories of periodic running mode in accordance with the China's national condition.
This thesis includes the following content:
(1) This part introduces the method to demonstrate periodic working diagram with unit periodic working diagram, analyzes the merits and conditions to use periodic working mode for rail traffic. A new evaluation standard, under the condition of periodic running, of line capacity-combined line capacity, is brought forward. With the Beijing-Shanghai dedicated passenger line as the background, the line capacities of different rail operation modes are discussed. According to the national condition, it analyzes the feasibility and necessity of applying the management mode based on periodic running mode to high speed rail traffic network in China.
(2) This part introduces Periodic Event Scheduling Problem (PESP) theory, builds a PESP model structure based on restraint graph, studies and summarizes the features and properties of the periodic constraint of PESP model and the feasible solution thereof and provides some proving method for some major features. The periodic tension model is then studied. It also compares PESP model with other relative models and discusses the appropriateness of PESP for building a rail working diagram and complexity of solving PESP, and then provides an improved converse solving algorithm, raising the effectiveness of model solving.
(3) Study on periodic operation plan of inter-city rail traffic. Based on such factors as transportation enterprises, passenger's interest and systematic optimality, considering the uncertainty of passenger flow, this part respectively builds the single objective chance constraint model and the multi-objective chance constraint model of different objectives, provides the methods of max module ideal point solving multi-objective programs and deterministic equivalents solving chance constraint programs and studies the genetic algorithm in accordance with these models. With Beijing-Tianjin inter-city rail traffic as the background, this paper solves the optimal periodic working plan and analyzes the calculation method and the results under different models.
(4) Study on periodic operation plan of the dedicated passenger lines network. This part introduces the idea of combining coupling operation plan with sharing operation plan, reducing rail operation types and simplifying the establishment of operation plan. Considering reducing cost of transportation enterprises and passengers transferring and the uncertainty of passenger flow, the corresponding single-objective model and multi-objective model are built. It also studies the deterministic equivalents of car's passenger flow distribution between different grades, the improved the SP algorithm and the transformation of chance constraints deterministic equivalents, from nonlinearity program model to linearity program model for simplification, and genetic algorithm for model solving. With the dedicated passenger lines network of certain size as the background and considering the reality in China, the paper makes the solutions for periodic operation plans under such different conditions as within this rail network, mid-high speed train mixed running mode, pure high speed cars' operation and train alternate stop mode.
(5) Study the theory of building a periodic working diagram and build a real periodic working diagram. This part discusses the specific periodic restraints and the periodic tensions expressions thereof, studies the turnaround period constraint expressions and the calculation thereof, passenger transferring periodic constraint expressions and the calculation thereof and the number of motor train unit to be used under the cycle usage model of motor train unit. Based on PESP theory and periodic tension model, the paper builds a periodic working diagram net model, studies the selection of network model spanning tree and value features of decisive variations and the method of simplification, designs a genetic algorithm to solve the model, and builds real rail traffic periodic working diagrams.
本文深入分析了周期化列车运行的特点,根据我国国情、轨道交通的特点以及发展方向,提出在我国轨道交通系统实行列车周期化运行的运输组织模式;将列车周期化运行与我国快速轨道交通的路网结构、车流性质、实际要求等具体情况相结合,围绕制定列车周期开行方案和编制列车周期运行图两个主题,通过详细的影响因素分析,分别建立了模型,设计了相应求解算法,对符合我国国情的列车周期化运行的相关组织理论进行了深入研究。
本文主要包括以下几方面的内容:
(1)提出了单元周期运行图的表示周期运行图的方法,分析了轨道交通采用周期化运行模式的优点以及采用条件。提出了基于列车周期运行的条件下,线路通过能力新的评价标准——组合通过能力。以京沪客运专线为背景,研究了不同列车开行模式下的组合通过能力。结合我国国情,分析了在我国快速轨道交通网采用基于周期化运行组织模式的可行性和必要性。
(2)介绍了周期事件排序问题(PESP),构建了基于约束图的PESP模型框架,研究并归纳了PESP模型的周期约束及其可行解的一些特点和性质,对一些主要性质给出了证明方法。深入研究了周期势差模型。将PESP模型与其他相关模型进行了比较,并且研究了PESP适合列车运行图铺划的优势。研究了求解PESP的复杂性并给出了改进了的反推求解算法。
(3)研究了城际轨道交通列车周期开行方案的制定。从运输企业、乘客利益以及总体最优的观点出发,充分考虑到客流的不确定性,分别建立了不同目标的单目标机会约束模型和多目标机会约束模型,给出了极大模理想点求解多目标规划、等价类求解机会约束规划的方法,研究了针对此模型的遗传算法。以京津城际轨道交通线为背景,求解了不同条件下的最优列车周期开行方案,分析了计算方法和不同条件下模型所得结果。
(4)研究了客运专线网周期列车开行方案的制定。提出将合并式列车开行方案和拆分式列车开行方案相结合,减少列车的开行种类,简化开行方案的制定。从减少运输企业成本支出、减少乘客换乘观点出发,考虑客流的不确定性,建立了相应单目标模型和多目标模型。对不同等级列车客流分配、改进的最短路算法、机会约束确定性等价类转换、将非线性规划模型转化为线性规划模型进行简化以及模型求解的遗传算法进行了研究。以一定规模的客运专线网络为背景,结合我国的实际情况,分别求解了该路网中、高速列车混行,纯高速列车运行以及列车交错停车运行等不同条件下的列车周期开行方案。
(5)研究了周期运行图的编制理论,并编制了实际周期运行图。分别讨论了编制周期运行图需考虑的具体周期约束及其周期势差表示,深入研究了动车组循环套跑模式下折返周期约束的表示及其计算方法、旅客换乘周期约束的表示及其计算方法、动车组使用数量的计算。以PESP理论、周期势差模型为基础,建立了周期运行图网络模型,研究了网络模型生成树的选择、决策变量的取值特点,研究了模型求解前简化的方法,设计了遗传算法对模型进行求解;编制了树状和网状轨道交通实际单元周期运行图。
With the improvement of rail technology and equipment, which is demonstrated by train speed, and the increasing transportation demand, it becomes possible to operate transportation management mode with periodic running as its characteristics for the rail traffic in China.
This thesis analyzes the features of train periodic running, according to the national condition, the features of rail traffic and developing direction of China; introduces the idea that the rail traffic system in China applies a transportation management mode of periodic running; combining periodic running with the specific situation of rail network structure, property of car flow and realistic demand of high speed rail traffic in China, focusing on building periodic running operation plan and periodic working diagram, by way of analyzing influencing factors, establishes the models and designs the corresponding solving algorithms and makes further discussion on the relevant management theories of periodic running mode in accordance with the China's national condition.
This thesis includes the following content:
(1) This part introduces the method to demonstrate periodic working diagram with unit periodic working diagram, analyzes the merits and conditions to use periodic working mode for rail traffic. A new evaluation standard, under the condition of periodic running, of line capacity-combined line capacity, is brought forward. With the Beijing-Shanghai dedicated passenger line as the background, the line capacities of different rail operation modes are discussed. According to the national condition, it analyzes the feasibility and necessity of applying the management mode based on periodic running mode to high speed rail traffic network in China.
(2) This part introduces Periodic Event Scheduling Problem (PESP) theory, builds a PESP model structure based on restraint graph, studies and summarizes the features and properties of the periodic constraint of PESP model and the feasible solution thereof and provides some proving method for some major features. The periodic tension model is then studied. It also compares PESP model with other relative models and discusses the appropriateness of PESP for building a rail working diagram and complexity of solving PESP, and then provides an improved converse solving algorithm, raising the effectiveness of model solving.
(3) Study on periodic operation plan of inter-city rail traffic. Based on such factors as transportation enterprises, passenger's interest and systematic optimality, considering the uncertainty of passenger flow, this part respectively builds the single objective chance constraint model and the multi-objective chance constraint model of different objectives, provides the methods of max module ideal point solving multi-objective programs and deterministic equivalents solving chance constraint programs and studies the genetic algorithm in accordance with these models. With Beijing-Tianjin inter-city rail traffic as the background, this paper solves the optimal periodic working plan and analyzes the calculation method and the results under different models.
(4) Study on periodic operation plan of the dedicated passenger lines network. This part introduces the idea of combining coupling operation plan with sharing operation plan, reducing rail operation types and simplifying the establishment of operation plan. Considering reducing cost of transportation enterprises and passengers transferring and the uncertainty of passenger flow, the corresponding single-objective model and multi-objective model are built. It also studies the deterministic equivalents of car's passenger flow distribution between different grades, the improved the SP algorithm and the transformation of chance constraints deterministic equivalents, from nonlinearity program model to linearity program model for simplification, and genetic algorithm for model solving. With the dedicated passenger lines network of certain size as the background and considering the reality in China, the paper makes the solutions for periodic operation plans under such different conditions as within this rail network, mid-high speed train mixed running mode, pure high speed cars' operation and train alternate stop mode.
(5) Study the theory of building a periodic working diagram and build a real periodic working diagram. This part discusses the specific periodic restraints and the periodic tensions expressions thereof, studies the turnaround period constraint expressions and the calculation thereof, passenger transferring periodic constraint expressions and the calculation thereof and the number of motor train unit to be used under the cycle usage model of motor train unit. Based on PESP theory and periodic tension model, the paper builds a periodic working diagram net model, studies the selection of network model spanning tree and value features of decisive variations and the method of simplification, designs a genetic algorithm to solve the model, and builds real rail traffic periodic working diagrams.
引文
[1]秋山 芳弘.世界の高速铁道[J].JREA.2005,48(11):39-46.
[2]世界铁路技术发展趋势[R].铁道科学研究院.2006.
[3]Gunther Ellwa.欧洲高速铁路网的规划与实施[J].世界铁路,1994.1:12-14.
[4]高速铁路运输组织技术[R].北方交通大学.2004.
[5]世界高速铁路的发展与我国高速铁路列车等级划分的研究[R].北方交通大学.2004.
[6]国家《中长期铁路网规划》简介.中国水运.2007.03:58-59.
[7]A.A.Assad.Modeling of Rail Network:Toward a Routing/Makeup Model.Transportation Research.1980,14B:101-114.
[8]A.A.Assad.A Class of Train-Scheduling Problems[J].Transportation Science.1980,16(3):281-310.
[9]A.A.Assad.Models of Rail Transportation.Transportation Research.1980,14A:205-220.
[10]M.R.Bussieck,T.Winter,Uwe T Zimmermann.Discrete Optimization in Public Rail Transport[J].Mathematical Programming.1997,79:415-444.
[11]钱仲侯.高速铁道概论(第2版)[M].北京:中国铁道出版社.1999.
[12]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.
[13]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):32-34.
[14]王荣华,谢如鹤,李庆云.广深铁路实施客运公交化的启示[J].铁道经济研究.2006.4:36-39.
[15]徐行方,朱学杰.沪宁杭城际列车开行密度的统计分析[J].同济大学学报(自然科学版).2005,33(2).
[16]陈慧,杨浩.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.
[17]周双贵,尚寿亭.一般周期事件排序的网络模型及算法[J].铁道学报.2001,23(2):13-16.
[18]汪波,杨浩.基于规格运行图的铁路客运专线通过能力的研究[C].2005 全国博士生学术论坛(交通运输学科)论文集.北京:中国铁道出版社,2005:292-299.
[19]汪波,杨浩,张志华.基于周期运行图的京津列车开行方案研究[J].铁道学报.2007,20(2):8-13.
[20]汪波,杨浩,牛丰等.周期运行图编制的模型与算法研究[J].铁道学报.2007,23(5):8-13.
[21]須田 寬.東海道新幹線[M].東京:大正出版株式会社,1989.
[22]#12
[23]#12
[24]柯 契夫列夫,周振庆等译.铁路旅客运输[M].北京:中国铁道出版社,1986:292-296.
[25]Jean-Francois Cordeau,Paolo Toth,Danniele Vigo.A Survey of Optimization Models for Train Routing and Scheduling[J].Transportation Science.1998,32(4):380-404.
[26]N.S.A.Ghoneim,S.C.Wirasinaghe.Optimum Zone Structure during Peak Periods for Existing Urban Rail Lines.Transportation Research Part B.1986,20B:7-18.
[27] A.ceder. A Procedure to Adjust Transit Trip Departure Times through Minimizing the Maximum Headway. Computers Operation Research.l991,18(5):417-431.
[28] K.Natchtigall. Time Depending Shortest-Path Problems with Applications to Railway Networks. European Journal of Operational Research.l995,83:154-166.
[29] M.R.Bussieck, Peter Kreuzer, Uwe T Zimmermann.Optimal Lines for Railway System[J]. European Journal of Operational Research.l996,96:54-63.
[30] M.T. Claessens, N.M. van Dijk, Zwaneveld. Cost Optimal Allocation of Rail Passenger Lines[J].European Journal of Operational Research.1998,110 (3) :474-489.
[31] M.R.Bussieck.Optimal Lines in Public Rail Transport[Dissertation],1998.
[32] Katja Boos. Line planning in railway system[Z]. 2002.10.
[33]Chang Y H,Yeh C H,Shen C C.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.
[34] M.R.Bussieck, T.Lindner,M.E.lubbecke. A Fast Algorithm for Near Cost Optimal Line Plans[R]. math.tuberlin.de.2002.
[35] Jan-Willem Goossens, Stan van Hoesel, Leo Kroon. On solving multi-type line planning problem[J]. European Journal of Operational Research.2006,168(2):403-424.
[36] Jan-Willem Goossens, Stan van Hoesel, Leo Kroon. A Branch-and-Cut Approach for Solving Line Planning Problem[R].Netherland.2001.
[37] Jan-Willem Goossens. Models and Algorithms for Railway Line Planning Problem[Dissertation],2004.
[38] Ralf Borndorfer,Martin Grotschel,M.E.Pfetsch. Models for line planning in Public Transport[R].BerIin Germany.2004.
[39] Voorhoeve. Rail Scheduling With Discrete Sets[R]. Eindhoven University of technology, Netherland.1993.
[40] Schrijver A.,Steenbeek A. Timetable construction[R]. Netherland.1993.
[41] Steenbeek A. Timetable construction for Railed[R]. Netherland.1994.
[42] M.A.Odijk,van der Aalst W.M.P. A Petri Net Based tool to Evaluate the Performance of Railway Junction Track Layouts(C).Proceedings of The European Simulation Multiconference, Barcelona.1994.207-211.
[43] Rozema. RailEase:Ondersteuning bij het specificeren van Railinfrastructuur in Knooppunten[R]. Deilt University of Technology, Delft,Netherland.l994.
[44] J.H.A. van den Berg, M.A.Odijk. DONS: Computer aided design of regular service timetables[M].Railway Operations, Computers in railways IV.1994,2:109-115.
[45] J.S.Hooghiemstra. Design of Regular Interval Timetables for Strategic and Tactical Railway Planning [M].Railway Operations, Computers in railways V. 1996,1:393-402.
[46] Jurjen S. Hooghiemstra, Maurice J.G. Teunisse. The Use Of Simulation In The Planning Of The Dutch Railway Services[C]. Proceedings of the 1998 Winter Simulation Conference D.J. Medeiros, E.F. Watson, J.S. Carson and M.S. Manivannan, eds.1998.1139-1145. routing
[47] K.Natchtigall. Periodic Network Optimization with Different Arc Frequencies[J].Discrete Applied Mathematics.l996(69):l-17.
[48] K.Natchtigall, S.Voget. A genetic algorithm approach to periodic railway synchronization[J].Computers & Operations Research.1996,23(5):453-463.
[49]K.Natchtigall,S.Voget.Minimizing Waiting Times in Integrated Fixed Interval Timetables By Upgrading Railway Tracks.European Journal of Operational Research.1997,103:610-627.
[50]M.A.Odijk.A Constraint Generation Algorithm for the Construction of Periodic Railway Timetables.Transportation Research Part B.1996,30(6):455-464.
[51]Carloe Giesemann.Periodic Timetable Generation[C].Seminar on Algorithms and Models for Railway Optimization.2002.University of Constance.
[52]M A Odijk.Railway Timetable Generation[M].Delft:Delft University of Technology,1997.
[53]P.J.Zwaneveld,L.G.Kroon,H.E.Romeijn Salomon,S.Dauzere-Peres,S.P.M.Van Holland H.W.Ambergen.Routing Trains Through Railway Stations:Model Formulation and Algorithms[J].Transportation Science.1996,30:181-194.
[54]Peter J.Zwaneveld,Leo G.Kroon,Stan P.M.van Hoesel.Routing trains through a railway station based on a Node Packing model[J].European Journal of Operational Research.2001,128(1):14-33.
[55]Christian Liebchen,Rolf H.Mohring.A Case Study in Periodic Timetabling[J].Electronic Notes in Theoretical Computer Science.2002,66(6):1-14.
[56]Christian Liebchen.Symmetry for Periodic Railway Timetables[J].Electronic Notes in Theoretical Computer Science.2004,92:43-51.
[57]Narayan Rangaraj.An Analysis of Cyclic Timetables for Suburban Rail Services[J].ABHIVYAKTI.2005,16(1):26-30.
[58]Solution of Real-World Train Timetabling Problems
[59]Leo G.Kroon,Leon W.P.Peeters.A Variable Trip Time Model for Cyclic Railway Timetabling[J].Transportation Science.2002,37(2):198-212.
[60]Leon.Peeters.Cyclic Railway Timetable Optimization[Dissertation],2003.
[61]Christian Liebchen,Mark Proksch,Frank H.Wagner.Performance of Algorithms for Periodic Timetable Optimization[R].Technische Universitat Berlin.2004.
[62]Liebchen,Christian and Rolf H.M"ohring.The modeling power of the periodic event scheduling problem:Railway timetables - and beyond.Preprint 020/2004,TU Berlin,Mathematical Institute.To appear in Springer LNCS Volume Algorithmic Methods for Railway Optimization.An extended abstract has been accepted for publication in Proceedings of the Ninth International Workshop on Computer-Aided Scheduling of Public Transport(CASPT).2004:3-77.
[63]Thomas Lindner.Train Schedule Optimization in Public Rail Transport[Dissertation],2000.
[64]#12
[65]魏庆朝 孔永健.磁悬浮铁路系统与技术[M].北京:中国科学技术出版社.2003.
[66]#12
[67]岡田 広.中国の鉄道と高速鉄道計画[J].JREA.1999,42(5):5-9.
[68]#12
[69]#12
[70]#12
[71]#12
[72]東海道山陽新幹線時刻表(2007.7-2007.9).JR東海.
[73]東北、山形、秋田新幹線時刻表(2007.7).JR西日本.
[74]上越、長野新幹線時刻表(2007.7).JR西日本.
[75]兰淑梅.京沪高速铁路客车开行方案有关问题的研究[J].铁道运输经济.2002,24(5):32-34.
[76]国家发展和改革委员会交通运输司.《环渤海京津冀地区、长江三角洲地区、珠江三角洲地区城际轨道交通网规划》内容简介[J].交通运输系统工程与信息.2005,8(4):8-9.
[77]Serafini P,Ukovich W.A Mathematical Model for Periodic Scheduling Problems[J].SIAMJ.Discrete Math,1989,2(4):550-581.
[78]Serafini P,Ukovich W.A Mathematical Model for the Fixed-Time Traffic Control Problem[J].European Journal of Operation Research,1989,42(2):152-165.
[79]C.Hanen.Study of a NP-hard Cyclic Scheduling Problem:the Recurrent Job-Shop.European Journal of Operation Research.1994,72:82-101.
[80]Gertsbakh,Serafini P.Periodic Transportation Schedules with Flexible Departure Times.European Journal of Operation Research.1991,40:298-309.
[81]Rockafellar R.T.Network flowers and Monotonic Optimization.New York:John Wiley.1984.173-201.
[82]王朝瑞.图论[M].北京:北京理工大学出版社,2001.
[83]殷剑宏,吴开业.图论及其算法[M].合肥:中国科学技术大学出版社.2005.
[84]徐俊明.图论及其应用(第二版)[M].合肥:中国科学技术大学出版社.2005.
[85]Wong,Rachel C.W.and Janny M.Y.Leung.Timetable synchronization for mass transit railway[C].Homepage of the 9th International Conference on Computer-Aided Scheduling of Public Transport(CASPT),Mark Hickman,PituMirchandani,and Stefan Voβ,2004.
[86]Daduna,Joachim R.,Isabel Branco,and Jos'e M.Pinto Paixao(Eds.).Computer-Aided Transit Scheduling-Proceedings of the Sixth International Workshop on Computer-Aided Scheduling of Public Transport,Volume 430 of Lecture Notes in Economics and Mathematical Systems.Springer.1995.
[87]Daduna,Joachim R.and Stefan Voβ.Practical Experiences in Schedule Synchronization.见 Daduna et al.(1995),pp.39-55.1995.
[88]Liebchen,Christian,Mark Proksch,and Frank H.Wagner.Performance of Algorithms for Periodic Timetable Optimization.In Mark Hickman(Ed.),Computer-Aided Transit Scheduling-Proceedings of the Ninth International Workshop on Computer-Aided Scheduling of Public Transport(CASPT),Lecture Notes in Economics and Mathematical Systems.Springer.2005
[88]徐行方,忻铁朕2,项宝余.城际列车的概念及其开行条件[J].同济大学学报.2003,31(4):432-436.
[89]徐行方,朱学杰.沪宁杭城际列车开行密度的统计分析[J].同济大学学报(自然科学版).2005,33(2):174-178.
[90]冯启富.关于京津城际轨道交通公交化的研究[J].铁道经济研究.2006.03:28-30.
[91]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,2004,26(2):16-20.
[92]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.
[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):1006-1008.
[94]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.1994,3:4-7.
[95]彭其渊,罗建.客运专线开行夕发朝至旅客列车的研究[J].西南交通大学学报,2006,41(5):626-631.
[96]黄鉴.客运专线旅客列车开行方案研究[D].西南交通大学.2006.
[97]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):31-35.
[98]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(2):124-129.
[99]韩冰.秦沈客运专线客车开行方案及相关问题的研究[J].铁路运输.2003.2:37-40.
[100]叶怀珍,杨永兰,王彦.铁路旅客列车开行方案问题的探讨.西南交通大学学报.2000,35(2):230-232.
[101]张拥军.高速列车开行方案研究[J].西南交通大学学报.1998,33(4):400-104.
[102]南敬林.京沪通道旅客行为时间价值研究[J].铁道经济研究.2002.03:36-39.
[103]高自友,四兵锋.市场竞争条件下铁路旅客票价制定的模型与算法[J].交通运输系统工程与信息,2001,11(1):50-55.
[104]岳超源.决策理论与方法[M].北京:科学出版社.2003.
[105]刘宝碇,赵瑞清.随即规划与模糊规划[M].北京:清华大学出版社.1998.
[106]刘宝碇,赵瑞清,王纲.不确定规划及其应用[M].北京:清华大学出版社&Springer Press.2003.
[107]邢文讯,谢金星.现代优化计算算法[M].北京:清华大学出版社.1999.
[108]玄光南,陈润伟著.于歆杰,周根贵译.遗传算法与工程优化[M].北京:清华大学出版社.2004.
[109]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):1508-1611.
[110]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.
[111]甄静.京沪线铁路客流规律分析[J].中国铁道科学.2002,23(2):122-126.
[112]谢如鹤,邱祝强等.Logit模型在广深铁路客流分担率估算中的应用[J]..中国铁道科学.2006,27(3):111-116
[113]仇智勇.铁路客运专线的客运量预测[J].铁道运输与经济.2004.4(47-48).
[114]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):571-575.
[115]史峰,黎新华,莫辉辉等.铁路OD分配优化方法[J].2004.25(4):116-119.
[116]马波涛,张于心,赵翠霞.运用Logit模型对高速客流分担率的估计[J].北方交通大学学报.2003,27(2):66-69.
[117]王喆,彭其渊,谢小淞.基于遗传算法的铁路旅客列车开行路径优化的研究[J].铁路计算机运用.2006,15(12):4-6.
[118]陈曦,费奇,李炜.基于启发式策略的最短路径算法[J].华中科技大学学报(自然科学版).2006,34(12):4-6.
[119]George B Dantzig.Linear Programming and Extensions[M].Princeton,New Jersey,USA:Princeton University Press.1963:361-367.
[120]Frederick S Hillier,Gerald J.Lieberman.Introduction to Operations Research[M].San Francisco,California,USA:Holden-Day,InC.2001:384388.
[121]史峰,黎新华,秦进,邓连波.单线列车运行图铺划的时问循环迭代优化方法[J].铁道学报.2005,27(1):1-5.
[122]彭其渊,杨明伦,等.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.
[123]孙焰,李致中.单线区段货物列车运行图的一种优化方法[J].铁道学报.1991,13(1):60-71.
[124]郭富娥.利用电子计算机编制列车运行图的研究[J].世界铁路,1993,1:6-11.
[125]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.
[126]马建军,胡思继等.京沪高速铁路列车运行图编制基本理论的研究[J].北方交通大学学报.2002,26(2):47-50.
[127]倪少权,吕红霞,杨明伦.计算机编制列车运行图系统的研究[J].铁道运输与经济,2001.7:31-35.
[128]杨明伦,彭其渊,倪少权.列车运行图编制系统的数据库适应性[J].铁道运输与经济.1996,(4):35-36.
[129]倪少权,刘继勇.计算机编制列车运行图系统调整系统设计及实现[J].西南交通大学学报.2001,37(3):240-245.
[130]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.2003,38(3):332-335.
[131]周磊山,胡思继,等.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.
[132]马建军.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].北方交通大学.
[133]徐炜.计算机编制列车运行图的方法研究[D].大陆交通大学.2005.
[134]王仲峰.计算机编制列车运行图方法的研究与运用[D].铁道科学研究院.2005.
[135]王仲峰,张巍,高林等.遗传算法在编制列车运行图中的运用[J].铁道运输与经济.2005,27(4):82-84.
[136]贾永刚,杜旭升.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):77-78.
[137]彭其渊,朱松年,王培.网络列车运行图的数学模型及算法研究[J].铁道学报.2001,23(1):1-8.
[138]彭其渊,杨明伦.计算机编制双线实用货物列车运行图的整数规划模型及求解算法[M].北京:中国铁道出版社.1994.
[139]彭其渊,杨明伦.京沪线列车运行图计算机编制系统的设计及实现[J].西南交通大学学报,增刊.1996.
[140]马建军,胡思继,许红等.京沪高速铁路列车运行图编制基本理论的研究[J].北方交通大学学报.2002,26(2).
[141]马建军,胡思继,周曦.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 通大学交通.2002,26(5):28-31.
[142]Horton,Joseph Douglas.A Polynomial-Time Algorithm to Find the Shortest Cycle Basis Of a Graph[J].SIAM Journal on Computing.1988,16(2):358-366.
[143]Golynski,Alexander and Joseph Douglas Horton.A Polynomial Time Algorithm to Find the Minimum Cycle Basis Of a Regular Matroid[C].In Martti Penttonen and Erik Meineche Schmidt (Eds.),SWAT,Volume 2368 of Lecture Notes in Computer Science:200-209.2002
[144]Aarts,Emile H.L.and Jan Karel Lenstra(Eds.)Local Search in Combinatorial Optimization.John Wiley & Sons Ltd.1997.
[145]戴锋.Visual C++程序设计基础[M].北京:清华大学出版社.2001.
[146]袁丁,傅一平.Visual C++精彩实例详解.北京:机械工业出版社.2003.
[2]世界铁路技术发展趋势[R].铁道科学研究院.2006.
[3]Gunther Ellwa.欧洲高速铁路网的规划与实施[J].世界铁路,1994.1:12-14.
[4]高速铁路运输组织技术[R].北方交通大学.2004.
[5]世界高速铁路的发展与我国高速铁路列车等级划分的研究[R].北方交通大学.2004.
[6]国家《中长期铁路网规划》简介.中国水运.2007.03:58-59.
[7]A.A.Assad.Modeling of Rail Network:Toward a Routing/Makeup Model.Transportation Research.1980,14B:101-114.
[8]A.A.Assad.A Class of Train-Scheduling Problems[J].Transportation Science.1980,16(3):281-310.
[9]A.A.Assad.Models of Rail Transportation.Transportation Research.1980,14A:205-220.
[10]M.R.Bussieck,T.Winter,Uwe T Zimmermann.Discrete Optimization in Public Rail Transport[J].Mathematical Programming.1997,79:415-444.
[11]钱仲侯.高速铁道概论(第2版)[M].北京:中国铁道出版社.1999.
[12]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.
[13]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):32-34.
[14]王荣华,谢如鹤,李庆云.广深铁路实施客运公交化的启示[J].铁道经济研究.2006.4:36-39.
[15]徐行方,朱学杰.沪宁杭城际列车开行密度的统计分析[J].同济大学学报(自然科学版).2005,33(2).
[16]陈慧,杨浩.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.
[17]周双贵,尚寿亭.一般周期事件排序的网络模型及算法[J].铁道学报.2001,23(2):13-16.
[18]汪波,杨浩.基于规格运行图的铁路客运专线通过能力的研究[C].2005 全国博士生学术论坛(交通运输学科)论文集.北京:中国铁道出版社,2005:292-299.
[19]汪波,杨浩,张志华.基于周期运行图的京津列车开行方案研究[J].铁道学报.2007,20(2):8-13.
[20]汪波,杨浩,牛丰等.周期运行图编制的模型与算法研究[J].铁道学报.2007,23(5):8-13.
[21]須田 寬.東海道新幹線[M].東京:大正出版株式会社,1989.
[22]#12
[23]#12
[24]柯 契夫列夫,周振庆等译.铁路旅客运输[M].北京:中国铁道出版社,1986:292-296.
[25]Jean-Francois Cordeau,Paolo Toth,Danniele Vigo.A Survey of Optimization Models for Train Routing and Scheduling[J].Transportation Science.1998,32(4):380-404.
[26]N.S.A.Ghoneim,S.C.Wirasinaghe.Optimum Zone Structure during Peak Periods for Existing Urban Rail Lines.Transportation Research Part B.1986,20B:7-18.
[27] A.ceder. A Procedure to Adjust Transit Trip Departure Times through Minimizing the Maximum Headway. Computers Operation Research.l991,18(5):417-431.
[28] K.Natchtigall. Time Depending Shortest-Path Problems with Applications to Railway Networks. European Journal of Operational Research.l995,83:154-166.
[29] M.R.Bussieck, Peter Kreuzer, Uwe T Zimmermann.Optimal Lines for Railway System[J]. European Journal of Operational Research.l996,96:54-63.
[30] M.T. Claessens, N.M. van Dijk, Zwaneveld. Cost Optimal Allocation of Rail Passenger Lines[J].European Journal of Operational Research.1998,110 (3) :474-489.
[31] M.R.Bussieck.Optimal Lines in Public Rail Transport[Dissertation],1998.
[32] Katja Boos. Line planning in railway system[Z]. 2002.10.
[33]Chang Y H,Yeh C H,Shen C C.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.
[34] M.R.Bussieck, T.Lindner,M.E.lubbecke. A Fast Algorithm for Near Cost Optimal Line Plans[R]. math.tuberlin.de.2002.
[35] Jan-Willem Goossens, Stan van Hoesel, Leo Kroon. On solving multi-type line planning problem[J]. European Journal of Operational Research.2006,168(2):403-424.
[36] Jan-Willem Goossens, Stan van Hoesel, Leo Kroon. A Branch-and-Cut Approach for Solving Line Planning Problem[R].Netherland.2001.
[37] Jan-Willem Goossens. Models and Algorithms for Railway Line Planning Problem[Dissertation],2004.
[38] Ralf Borndorfer,Martin Grotschel,M.E.Pfetsch. Models for line planning in Public Transport[R].BerIin Germany.2004.
[39] Voorhoeve. Rail Scheduling With Discrete Sets[R]. Eindhoven University of technology, Netherland.1993.
[40] Schrijver A.,Steenbeek A. Timetable construction[R]. Netherland.1993.
[41] Steenbeek A. Timetable construction for Railed[R]. Netherland.1994.
[42] M.A.Odijk,van der Aalst W.M.P. A Petri Net Based tool to Evaluate the Performance of Railway Junction Track Layouts(C).Proceedings of The European Simulation Multiconference, Barcelona.1994.207-211.
[43] Rozema. RailEase:Ondersteuning bij het specificeren van Railinfrastructuur in Knooppunten[R]. Deilt University of Technology, Delft,Netherland.l994.
[44] J.H.A. van den Berg, M.A.Odijk. DONS: Computer aided design of regular service timetables[M].Railway Operations, Computers in railways IV.1994,2:109-115.
[45] J.S.Hooghiemstra. Design of Regular Interval Timetables for Strategic and Tactical Railway Planning [M].Railway Operations, Computers in railways V. 1996,1:393-402.
[46] Jurjen S. Hooghiemstra, Maurice J.G. Teunisse. The Use Of Simulation In The Planning Of The Dutch Railway Services[C]. Proceedings of the 1998 Winter Simulation Conference D.J. Medeiros, E.F. Watson, J.S. Carson and M.S. Manivannan, eds.1998.1139-1145. routing
[47] K.Natchtigall. Periodic Network Optimization with Different Arc Frequencies[J].Discrete Applied Mathematics.l996(69):l-17.
[48] K.Natchtigall, S.Voget. A genetic algorithm approach to periodic railway synchronization[J].Computers & Operations Research.1996,23(5):453-463.
[49]K.Natchtigall,S.Voget.Minimizing Waiting Times in Integrated Fixed Interval Timetables By Upgrading Railway Tracks.European Journal of Operational Research.1997,103:610-627.
[50]M.A.Odijk.A Constraint Generation Algorithm for the Construction of Periodic Railway Timetables.Transportation Research Part B.1996,30(6):455-464.
[51]Carloe Giesemann.Periodic Timetable Generation[C].Seminar on Algorithms and Models for Railway Optimization.2002.University of Constance.
[52]M A Odijk.Railway Timetable Generation[M].Delft:Delft University of Technology,1997.
[53]P.J.Zwaneveld,L.G.Kroon,H.E.Romeijn Salomon,S.Dauzere-Peres,S.P.M.Van Holland H.W.Ambergen.Routing Trains Through Railway Stations:Model Formulation and Algorithms[J].Transportation Science.1996,30:181-194.
[54]Peter J.Zwaneveld,Leo G.Kroon,Stan P.M.van Hoesel.Routing trains through a railway station based on a Node Packing model[J].European Journal of Operational Research.2001,128(1):14-33.
[55]Christian Liebchen,Rolf H.Mohring.A Case Study in Periodic Timetabling[J].Electronic Notes in Theoretical Computer Science.2002,66(6):1-14.
[56]Christian Liebchen.Symmetry for Periodic Railway Timetables[J].Electronic Notes in Theoretical Computer Science.2004,92:43-51.
[57]Narayan Rangaraj.An Analysis of Cyclic Timetables for Suburban Rail Services[J].ABHIVYAKTI.2005,16(1):26-30.
[58]Solution of Real-World Train Timetabling Problems
[59]Leo G.Kroon,Leon W.P.Peeters.A Variable Trip Time Model for Cyclic Railway Timetabling[J].Transportation Science.2002,37(2):198-212.
[60]Leon.Peeters.Cyclic Railway Timetable Optimization[Dissertation],2003.
[61]Christian Liebchen,Mark Proksch,Frank H.Wagner.Performance of Algorithms for Periodic Timetable Optimization[R].Technische Universitat Berlin.2004.
[62]Liebchen,Christian and Rolf H.M"ohring.The modeling power of the periodic event scheduling problem:Railway timetables - and beyond.Preprint 020/2004,TU Berlin,Mathematical Institute.To appear in Springer LNCS Volume Algorithmic Methods for Railway Optimization.An extended abstract has been accepted for publication in Proceedings of the Ninth International Workshop on Computer-Aided Scheduling of Public Transport(CASPT).2004:3-77.
[63]Thomas Lindner.Train Schedule Optimization in Public Rail Transport[Dissertation],2000.
[64]#12
[65]魏庆朝 孔永健.磁悬浮铁路系统与技术[M].北京:中国科学技术出版社.2003.
[66]#12
[67]岡田 広.中国の鉄道と高速鉄道計画[J].JREA.1999,42(5):5-9.
[68]#12
[69]#12
[70]#12
[71]#12
[72]東海道山陽新幹線時刻表(2007.7-2007.9).JR東海.
[73]東北、山形、秋田新幹線時刻表(2007.7).JR西日本.
[74]上越、長野新幹線時刻表(2007.7).JR西日本.
[75]兰淑梅.京沪高速铁路客车开行方案有关问题的研究[J].铁道运输经济.2002,24(5):32-34.
[76]国家发展和改革委员会交通运输司.《环渤海京津冀地区、长江三角洲地区、珠江三角洲地区城际轨道交通网规划》内容简介[J].交通运输系统工程与信息.2005,8(4):8-9.
[77]Serafini P,Ukovich W.A Mathematical Model for Periodic Scheduling Problems[J].SIAMJ.Discrete Math,1989,2(4):550-581.
[78]Serafini P,Ukovich W.A Mathematical Model for the Fixed-Time Traffic Control Problem[J].European Journal of Operation Research,1989,42(2):152-165.
[79]C.Hanen.Study of a NP-hard Cyclic Scheduling Problem:the Recurrent Job-Shop.European Journal of Operation Research.1994,72:82-101.
[80]Gertsbakh,Serafini P.Periodic Transportation Schedules with Flexible Departure Times.European Journal of Operation Research.1991,40:298-309.
[81]Rockafellar R.T.Network flowers and Monotonic Optimization.New York:John Wiley.1984.173-201.
[82]王朝瑞.图论[M].北京:北京理工大学出版社,2001.
[83]殷剑宏,吴开业.图论及其算法[M].合肥:中国科学技术大学出版社.2005.
[84]徐俊明.图论及其应用(第二版)[M].合肥:中国科学技术大学出版社.2005.
[85]Wong,Rachel C.W.and Janny M.Y.Leung.Timetable synchronization for mass transit railway[C].Homepage of the 9th International Conference on Computer-Aided Scheduling of Public Transport(CASPT),Mark Hickman,PituMirchandani,and Stefan Voβ,2004.
[86]Daduna,Joachim R.,Isabel Branco,and Jos'e M.Pinto Paixao(Eds.).Computer-Aided Transit Scheduling-Proceedings of the Sixth International Workshop on Computer-Aided Scheduling of Public Transport,Volume 430 of Lecture Notes in Economics and Mathematical Systems.Springer.1995.
[87]Daduna,Joachim R.and Stefan Voβ.Practical Experiences in Schedule Synchronization.见 Daduna et al.(1995),pp.39-55.1995.
[88]Liebchen,Christian,Mark Proksch,and Frank H.Wagner.Performance of Algorithms for Periodic Timetable Optimization.In Mark Hickman(Ed.),Computer-Aided Transit Scheduling-Proceedings of the Ninth International Workshop on Computer-Aided Scheduling of Public Transport(CASPT),Lecture Notes in Economics and Mathematical Systems.Springer.2005
[88]徐行方,忻铁朕2,项宝余.城际列车的概念及其开行条件[J].同济大学学报.2003,31(4):432-436.
[89]徐行方,朱学杰.沪宁杭城际列车开行密度的统计分析[J].同济大学学报(自然科学版).2005,33(2):174-178.
[90]冯启富.关于京津城际轨道交通公交化的研究[J].铁道经济研究.2006.03:28-30.
[91]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,2004,26(2):16-20.
[92]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.
[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):1006-1008.
[94]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.1994,3:4-7.
[95]彭其渊,罗建.客运专线开行夕发朝至旅客列车的研究[J].西南交通大学学报,2006,41(5):626-631.
[96]黄鉴.客运专线旅客列车开行方案研究[D].西南交通大学.2006.
[97]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):31-35.
[98]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(2):124-129.
[99]韩冰.秦沈客运专线客车开行方案及相关问题的研究[J].铁路运输.2003.2:37-40.
[100]叶怀珍,杨永兰,王彦.铁路旅客列车开行方案问题的探讨.西南交通大学学报.2000,35(2):230-232.
[101]张拥军.高速列车开行方案研究[J].西南交通大学学报.1998,33(4):400-104.
[102]南敬林.京沪通道旅客行为时间价值研究[J].铁道经济研究.2002.03:36-39.
[103]高自友,四兵锋.市场竞争条件下铁路旅客票价制定的模型与算法[J].交通运输系统工程与信息,2001,11(1):50-55.
[104]岳超源.决策理论与方法[M].北京:科学出版社.2003.
[105]刘宝碇,赵瑞清.随即规划与模糊规划[M].北京:清华大学出版社.1998.
[106]刘宝碇,赵瑞清,王纲.不确定规划及其应用[M].北京:清华大学出版社&Springer Press.2003.
[107]邢文讯,谢金星.现代优化计算算法[M].北京:清华大学出版社.1999.
[108]玄光南,陈润伟著.于歆杰,周根贵译.遗传算法与工程优化[M].北京:清华大学出版社.2004.
[109]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):1508-1611.
[110]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.
[111]甄静.京沪线铁路客流规律分析[J].中国铁道科学.2002,23(2):122-126.
[112]谢如鹤,邱祝强等.Logit模型在广深铁路客流分担率估算中的应用[J]..中国铁道科学.2006,27(3):111-116
[113]仇智勇.铁路客运专线的客运量预测[J].铁道运输与经济.2004.4(47-48).
[114]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):571-575.
[115]史峰,黎新华,莫辉辉等.铁路OD分配优化方法[J].2004.25(4):116-119.
[116]马波涛,张于心,赵翠霞.运用Logit模型对高速客流分担率的估计[J].北方交通大学学报.2003,27(2):66-69.
[117]王喆,彭其渊,谢小淞.基于遗传算法的铁路旅客列车开行路径优化的研究[J].铁路计算机运用.2006,15(12):4-6.
[118]陈曦,费奇,李炜.基于启发式策略的最短路径算法[J].华中科技大学学报(自然科学版).2006,34(12):4-6.
[119]George B Dantzig.Linear Programming and Extensions[M].Princeton,New Jersey,USA:Princeton University Press.1963:361-367.
[120]Frederick S Hillier,Gerald J.Lieberman.Introduction to Operations Research[M].San Francisco,California,USA:Holden-Day,InC.2001:384388.
[121]史峰,黎新华,秦进,邓连波.单线列车运行图铺划的时问循环迭代优化方法[J].铁道学报.2005,27(1):1-5.
[122]彭其渊,杨明伦,等.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.
[123]孙焰,李致中.单线区段货物列车运行图的一种优化方法[J].铁道学报.1991,13(1):60-71.
[124]郭富娥.利用电子计算机编制列车运行图的研究[J].世界铁路,1993,1:6-11.
[125]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.
[126]马建军,胡思继等.京沪高速铁路列车运行图编制基本理论的研究[J].北方交通大学学报.2002,26(2):47-50.
[127]倪少权,吕红霞,杨明伦.计算机编制列车运行图系统的研究[J].铁道运输与经济,2001.7:31-35.
[128]杨明伦,彭其渊,倪少权.列车运行图编制系统的数据库适应性[J].铁道运输与经济.1996,(4):35-36.
[129]倪少权,刘继勇.计算机编制列车运行图系统调整系统设计及实现[J].西南交通大学学报.2001,37(3):240-245.
[130]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.2003,38(3):332-335.
[131]周磊山,胡思继,等.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.
[132]马建军.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].北方交通大学.
[133]徐炜.计算机编制列车运行图的方法研究[D].大陆交通大学.2005.
[134]王仲峰.计算机编制列车运行图方法的研究与运用[D].铁道科学研究院.2005.
[135]王仲峰,张巍,高林等.遗传算法在编制列车运行图中的运用[J].铁道运输与经济.2005,27(4):82-84.
[136]贾永刚,杜旭升.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):77-78.
[137]彭其渊,朱松年,王培.网络列车运行图的数学模型及算法研究[J].铁道学报.2001,23(1):1-8.
[138]彭其渊,杨明伦.计算机编制双线实用货物列车运行图的整数规划模型及求解算法[M].北京:中国铁道出版社.1994.
[139]彭其渊,杨明伦.京沪线列车运行图计算机编制系统的设计及实现[J].西南交通大学学报,增刊.1996.
[140]马建军,胡思继,许红等.京沪高速铁路列车运行图编制基本理论的研究[J].北方交通大学学报.2002,26(2).
[141]马建军,胡思继,周曦.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 通大学交通.2002,26(5):28-31.
[142]Horton,Joseph Douglas.A Polynomial-Time Algorithm to Find the Shortest Cycle Basis Of a Graph[J].SIAM Journal on Computing.1988,16(2):358-366.
[143]Golynski,Alexander and Joseph Douglas Horton.A Polynomial Time Algorithm to Find the Minimum Cycle Basis Of a Regular Matroid[C].In Martti Penttonen and Erik Meineche Schmidt (Eds.),SWAT,Volume 2368 of Lecture Notes in Computer Science:200-209.2002
[144]Aarts,Emile H.L.and Jan Karel Lenstra(Eds.)Local Search in Combinatorial Optimization.John Wiley & Sons Ltd.1997.
[145]戴锋.Visual C++程序设计基础[M].北京:清华大学出版社.2001.
[146]袁丁,傅一平.Visual C++精彩实例详解.北京:机械工业出版社.2003.