基于车流匹配的技术站列车运行线接续模型及算法研究
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摘要
列车运行图是列车在铁路区间运行及在车站到发或通过时刻的技术文件,它规定各次列车占用区间的程序,列车在每个车站到发或通过时刻,列车在区间的运行时分以及列车在车站的停车时分等,是铁路组织列车运行的基础。当货物列车运行线铺完之后,需要解决技术站直通列车运行线接续优化问题以及确定邻接区段上的各类到达解体与自编始发列车运行线。以往在确定技术站的各类到解与编发列车运行线时,仅从列车种类的均衡性出发,并没有考虑车流与运行线相结合这一因素,这样编制的列车运行图往往会导致有调中转车在站的总停留时间较长。
为了使列车运行图与列车编组计划协调配合,技术站的车流与列车运行线最大限度地结合起来,在解决技术站邻接区段的列车运行线分配优化问题时,还要保证车流在技术站的良好接续。本文在借鉴国内外研究成果的基础上,研究了基于车流匹配的技术站列车运行线接续问题,建立了相关问题的数学模型,并结合运筹学、组合数学以及智能优化算法,设计各问题的有效求解算法,论文的主要研究工作包括以下几个方面：
1.介绍了编制货物列车运行图的步骤,通过对直通列车、到达解体与自编始发列车在技术站的作业过程的分析,得出技术站直通列车接续时间标准和中转车流接续时间标准,为解决技术站列车运行线接续优化问题奠定了基础。
2.根据技术站相邻区段的列车运行线对应的时刻和直通列车的接续时间标准,以直通列车在站的总停留时间最少为目标建立数学模型,并将其转化为网络流模型,用最小费用流算法,为直通列车选择到达和出发运行线,实现直通列车在技术站的最优接续。
3.综合考虑流线结合及各类始发列车在技术站的均衡性,根据技术站的到达车流和列车编组计划,以有调中转车在技术站总停留时间最少、技术站各方向同类始发列车序号间隔的方差之和最小以及始发列车的密集度之和最小为目标,建立多目标优化模型,解决技术站始发列车运行线的接续问题,并设计多目标蚁群算法进行求解。该算法的搜索过程就是每次迭代构造出当前蚁群的非劣解,并通过更新非劣解所属路径上的信息素量,使蚁群搜索到的非劣解逐步逼近Pareto最优解。
4.在编制货物列车运行图时,应尽量使技术站各方向的到发列车均衡地分布,避免相同种类的列车在车站密集地到发。根据技术站衔接各区段上到发列车运行线对应的时刻、计划的到达车流和列车编组计划,以中转车在技术站的停留时间最少和技术站邻接区段到发列车分类的均衡性为目标,建立技术站到解和编发列车运行线接续的协调优化模型。针对这一多目标优化模型的特点,先设计启发式算法求解有调中转车在技术站的最少停留时间,然后利用调整策略改进各类到解和编发列车的均衡性,最后从有利交换方案集中,选择非劣方案作为问题的最优解。
Train diagram regulates the order in which a train occupies a section, the time at which a train arrives and departs at the station, together with the operation time at section, dwell time at station, therefore, Train diagram is the technical document for train operations, and the basis of train railway organizations. When train paths adjacent to the technical station are determined, the train number allocation is one of the most important aspects of computerized train diagram. Previously, from the point of view of the equilibrium of trains, the research didn't take account of transfer cars connection resulting in the longer dwell time of transfer cars at the technical station. In order to coordinate train diagram with train formation plan, combine car flow with train path at the greatest degree, train number allocation must optimize car flow connection. Based on research wagon-flow allocation at the technical station at home and abroad, the dissertation studies train path connection, builds the mathematical models of related problems, seeking the effective algorithms combined with operational research,combinatorial mathematics and intelligence algorithm.The main research of the dissertation is as follows:
1. By introducing procedure of train working diagram, and analyzing operation process of through trains, arriving train and departing train at technical station, the connection time standard of through train and transit car has been obtained, which lays the foundation for optimization of through trains connection and train number allocation.
2. According to through train's connection time standard and the period of train path at technical station, mathematical model aiming at the minimum dwell time of through trains is set up. The problem is converted into a network flow model added into a source and a sink, solved by minimum cost flow algorithm. Finally, the optimal scheme of selecting arrival and departure path of through trains is obtained.
3. Taking account of the combination of car-flows, railway line and departure train category equilibrium. Based on the time of departure train path and train formation plan, the mathematical model of departure train number allocation at technical station, with the aims of the minimum dwell time of transit cars, train category equilibrium and the minimum train intensity, is set up. Multi-objective ant colony algorithm is designed, which ants construct corrent noninferior solutions each iteration and renew the quantity of pheromone of the path belonging to noninferior solutions, noninferior solutions which are near to pareto optimal solution will be found.
4. In the process of freight train diagram compilation, it is designed to make a balanced layout of arrival and departure trains of various directions, with the purpose to avoid the intensive arrival and departure for trains of the same kinds at the technical station. For the technical station where the train number of inbound and departure path have not been determined, the problem of train number allocation of inbound and departure path should be solved after train path has been drawn up. Based on the time of inbound and departure train path, inbound car flow and train formation plan, the mathematical model of train number allocation at technical station, with the aims of the minimum dwell time of transit cars and train category equilibrium, is set up. According to the characteristics of multi-objective optimization model, firstly the minimum dwell time of transit cars is obtained by the proposed heuristic algorithm, secondly train category equilibrium is improved by adjustment strategy, finally the noninferior solutions of advantageous exchange set are the optimal solution.
为了使列车运行图与列车编组计划协调配合,技术站的车流与列车运行线最大限度地结合起来,在解决技术站邻接区段的列车运行线分配优化问题时,还要保证车流在技术站的良好接续。本文在借鉴国内外研究成果的基础上,研究了基于车流匹配的技术站列车运行线接续问题,建立了相关问题的数学模型,并结合运筹学、组合数学以及智能优化算法,设计各问题的有效求解算法,论文的主要研究工作包括以下几个方面：
1.介绍了编制货物列车运行图的步骤,通过对直通列车、到达解体与自编始发列车在技术站的作业过程的分析,得出技术站直通列车接续时间标准和中转车流接续时间标准,为解决技术站列车运行线接续优化问题奠定了基础。
2.根据技术站相邻区段的列车运行线对应的时刻和直通列车的接续时间标准,以直通列车在站的总停留时间最少为目标建立数学模型,并将其转化为网络流模型,用最小费用流算法,为直通列车选择到达和出发运行线,实现直通列车在技术站的最优接续。
3.综合考虑流线结合及各类始发列车在技术站的均衡性,根据技术站的到达车流和列车编组计划,以有调中转车在技术站总停留时间最少、技术站各方向同类始发列车序号间隔的方差之和最小以及始发列车的密集度之和最小为目标,建立多目标优化模型,解决技术站始发列车运行线的接续问题,并设计多目标蚁群算法进行求解。该算法的搜索过程就是每次迭代构造出当前蚁群的非劣解,并通过更新非劣解所属路径上的信息素量,使蚁群搜索到的非劣解逐步逼近Pareto最优解。
4.在编制货物列车运行图时,应尽量使技术站各方向的到发列车均衡地分布,避免相同种类的列车在车站密集地到发。根据技术站衔接各区段上到发列车运行线对应的时刻、计划的到达车流和列车编组计划,以中转车在技术站的停留时间最少和技术站邻接区段到发列车分类的均衡性为目标,建立技术站到解和编发列车运行线接续的协调优化模型。针对这一多目标优化模型的特点,先设计启发式算法求解有调中转车在技术站的最少停留时间,然后利用调整策略改进各类到解和编发列车的均衡性,最后从有利交换方案集中,选择非劣方案作为问题的最优解。
Train diagram regulates the order in which a train occupies a section, the time at which a train arrives and departs at the station, together with the operation time at section, dwell time at station, therefore, Train diagram is the technical document for train operations, and the basis of train railway organizations. When train paths adjacent to the technical station are determined, the train number allocation is one of the most important aspects of computerized train diagram. Previously, from the point of view of the equilibrium of trains, the research didn't take account of transfer cars connection resulting in the longer dwell time of transfer cars at the technical station. In order to coordinate train diagram with train formation plan, combine car flow with train path at the greatest degree, train number allocation must optimize car flow connection. Based on research wagon-flow allocation at the technical station at home and abroad, the dissertation studies train path connection, builds the mathematical models of related problems, seeking the effective algorithms combined with operational research,combinatorial mathematics and intelligence algorithm.The main research of the dissertation is as follows:
1. By introducing procedure of train working diagram, and analyzing operation process of through trains, arriving train and departing train at technical station, the connection time standard of through train and transit car has been obtained, which lays the foundation for optimization of through trains connection and train number allocation.
2. According to through train's connection time standard and the period of train path at technical station, mathematical model aiming at the minimum dwell time of through trains is set up. The problem is converted into a network flow model added into a source and a sink, solved by minimum cost flow algorithm. Finally, the optimal scheme of selecting arrival and departure path of through trains is obtained.
3. Taking account of the combination of car-flows, railway line and departure train category equilibrium. Based on the time of departure train path and train formation plan, the mathematical model of departure train number allocation at technical station, with the aims of the minimum dwell time of transit cars, train category equilibrium and the minimum train intensity, is set up. Multi-objective ant colony algorithm is designed, which ants construct corrent noninferior solutions each iteration and renew the quantity of pheromone of the path belonging to noninferior solutions, noninferior solutions which are near to pareto optimal solution will be found.
4. In the process of freight train diagram compilation, it is designed to make a balanced layout of arrival and departure trains of various directions, with the purpose to avoid the intensive arrival and departure for trains of the same kinds at the technical station. For the technical station where the train number of inbound and departure path have not been determined, the problem of train number allocation of inbound and departure path should be solved after train path has been drawn up. Based on the time of inbound and departure train path, inbound car flow and train formation plan, the mathematical model of train number allocation at technical station, with the aims of the minimum dwell time of transit cars and train category equilibrium, is set up. According to the characteristics of multi-objective optimization model, firstly the minimum dwell time of transit cars is obtained by the proposed heuristic algorithm, secondly train category equilibrium is improved by adjustment strategy, finally the noninferior solutions of advantageous exchange set are the optimal solution.
引文
[1]杨浩.铁路运输组织学.北京：中国铁道出版社,2004
[2]胡思继.铁路行车组织.北京：中国铁道出版社,2004
[3]马桂贞.铁路站场及枢纽.成都：西南交通大学出版社,2003
[4]彭其渊,闫海峰,石子明.计算机编制列车运行图的理论与方法.成都：西南交通大学出版社,2004
[5]王慈光.运输模型及优化.第二版.成都：西南交通大学出版社,2010：98-107
[6]郭富娥.论利用电子计算机编制列车运行图.计算机应用,1992,1：35-38
[7]胡思继.列车运行组织及通过能力理论.北京：中国铁道出版社,1993
[8]胡思继.列车运行图编制理论.北京：中国铁道出版社,2007
[9]彭其渊,吕红霞.计算机编制列车运行图实验教程.成都：西南交通大学出版社,2007
[10]郭富娥.日本近期开发的列车运行图编制系统.中国铁路,1995,8：38-40
[11]A. Caprara, M. Fischetti, P. Modeling and solving the train timetabling problem, Oper. Res.2002,50:851-861
[12]Shaw-Ching Chang, Yu-Chi Chung. From timetabling to train regulation—a new train operation model Information and Software Technology,Volume 47,Issue 9,15 June,2005:575-585
[13]Ji-Won Chung, Seog-Moon Oh, In-Chan Choi. A hybrid genetic algorithm for train sequencing in the Korean railway. Omega,2007,37 (3):555-565
[14]Yusin Lee, Chuen-Yih Chen. A heuristic for the train pathing and timetabling problem.Transportation Research Part B:Methodological,2009,43:837-851
[15]Xuesong Zhou, Ming Zhong. Single-track train timetabling with guaranteed optimality:Branch-and-bound algorithms with enhanced lower bounds. Transportation Research Part B:Methodological,2007,41(3):320-341
[16]Andrea D'Ariano, Dario Pacciarelli, Marco Pranzo. A branch and bound algorithm for scheduling trains in a railway network. European Journal of Operational Research,2007,183(2):644-657
[17]Enrique Castillo, Inmaculada Gallego, Jose Maria Urena, et al. Timetabling optimization of a mixed double- and single-tracked railway network. Applied Mathematical Modelling,2011,35(2):859-878
[18]Yu Hern Chang, Ching Cheng Shen. A multiobjective model for passenger train services planning application to Taiwan's high-speed rail line. Transportation Research Part B:Methodological,2000,34(3):91-106
[19]Valentina Cacchiani, Alberto Caprara, Paolo Toth. Scheduling extra freight trains on railway network. Transportation Research Part B:Methodological,2010, 44:215-231
[20]Caprara A., Michele M., Toth p.,et al. A Lagrangian heuristic algorithm for a real-world train timetabling problem. Discrete Applied Mathematics,2006,154(5): 738-753
[21]柳进.计算机绘制列车运行图的设计方法.铁道运输与经济,1997,5：30-38
[22]郭富娥.计算机编制双线列车运行图的研究.铁道运输与经济,1998,5：26-27
[23]郭富娥.高速线与既有线列车运行图衔接问题的研究.高速铁路,2000,7：25-27
[24]凌熙,杨浩,王亮斌.基于MAS的列车运行图智能编制系统建模方法研究,铁道运输与经济,2009,31(7)：81-84
[25]杨肇夏,孔庆钤.微计算机编制双线自动闭塞方向货物列车运行图的研究,铁道学报,1985,(4)：63-72
[26]周磊山.计算机快速处理铁路列车运行图的新方法,铁道运输与经济,1992,(7)：27-30
[27]李菊,张晓森.用计算机绘制列车运行图.北京交通大学学报,1994,4：537-541
[28]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.北京交通大学学报,1997,21(3)：274-279
[29]张星臣,胡安洲,杨浩.铁路运输储备能力合理分配的计算机模拟研究.铁道学报,1997,19(5)：1-6
[30]聂磊,郭富娥.计算机编制高速铁路列车运行图的研究.中国铁道科学,1997,18(1)：101-110
[31]周磊山,胡思继.计算机编制网状线路列车运行图方法研究.铁道学报,1998,20(5)：15-21
[32]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.北方交通大学报,2002,26(5)：9-12
[33]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.中国铁道科学,2002,23(5)：9-12
[34]许红,马建军,龙建成等.城市轨道交通列车运行图编制的数学模型及方法.北 京交通大学学报,2006,30(3)：10-14
[35]汪波,杨浩,牛丰等.周期运行图编制模型与算法研究.北京交通大学学报,2007,29(5)：1-6
[36]高强周.城市轨道交通列车运行图设计实现与评价.北京交通大学硕士论文,2008
[37]谢美全,聂磊.周期性列车运行图编制模型研究.铁道学报,2009,31(4)：7-13
[38]杨意坚,何宇强.基于Max-plus方法的列车运行图稳定性评价.铁道学报,2009,31(4)：14-19
[39]陈军华.基于稳定性的客运专线运行图编制与评价问题研究.北京交通大学博士学位论文,2009
[40]祝建平,周磊山,乐逸祥.基于协作交互的列车运行图网络化编制系统.中国铁道科学,2010,31(1)：139-144
[41]孟令云,杨肇夏,李海鹰等.基于列车运行线分布的客运专线列车运行图动态性能分析.中国铁道科学,2010,31(2)：90-95
[42]赵宇刚,毛保华,蒋玉琨.基于列车运行时间偏离的地铁列车运行图缓冲时间研究.中国铁道科学,2011,32(1)：118-121
[43]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.中国铁道科学,1994,15(14)：60-66
[44]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.铁道学报,1995,17(3)：15-20
[45]彭其渊,杨明伦,倪少权.单线区段货物始发列车方案的优化模型及求解方法.西南交通大学学报,1995,30(2)：177-181
[46]彭其渊,朱松年,阎海峰.列车运行图可调整度评价系统研究.西南交通大学学报,1998,33(4)：367-371
[47]朱健梅.基于实用的技术站直通列车接续方案计算方法研究.西南交通大学学报,1999,34(3)：365-368
[48]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.铁道学报,2001,23(1)：1-8
[49]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.铁道运输与经济,2002,24(6)：41-43
[50]陈彦如,彭其渊,蒋阳升.复线列车运行调整满意优化模型研究.铁道学报,2003,25(3)：8-12
[51]刘爱江,许长枫,何大可.基于遗传算法的列车运行图初始布点配对模型.铁道计算机应用,2003,12(1)：13-16
[52]董守清,王进勇,闫海峰.双线铁路列车运行调整的禁忌搜索算法.中国铁道科学,2005,26(4)：114-119
[53]王利华.双线自动闭塞区段最大量铺画货物列车运行线的研究.铁道运输与经济,2007,29(5)：78-80
[54]章优仕,金炜东.基于离散事件拓扑图模型的单线列车运行调整迭代修复算法,系统仿真学报,2009,21(21)：7003-7007
[55]孙焰,李致中.单线区段货物列车运行图的一种优化方法.铁道学报,1991,15(4)：60-71
[56]孙焰,李致中.单线区间列车最优运行次序的排序模型及解法.铁道学报,]993,15(1)：62-71
[57]符卓.旅客列车运行方案图优化编制方法的研究,1996,18(4)：10-17
[58]史峰.定序单线列车运行图的原始——对偶算法.铁道学报,1996,18(1)：8-20
[59]孙焰,李致中.列车运行图最优初始布点方法.长沙铁道学院学报,1997,15(4)：80-87
[60]李夏苗,查伟雄,李轶平.以客运为主繁忙干线区段列车运行调整计划的优化.铁道学报,1999,21(6)：11-14
[61]查伟雄,陈治亚,李夏苗.复线列车运行调整理论与方法的研究.铁道学报,2000,22(1)：13-16
[62]肖龙文,谢如鹤.单线区段列车运行图的自动化调整方法.交通运输工程学报,2004,4(3)：25-29
[63]史峰,黎新华,秦进等.单线列车运行图铺划的时间循环迭代优化方法.铁道学报,2005,27(1)：1-5
[64]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.长沙：中南大学,2005
[65]周文梁,史峰,陈彦等.客运专线网络列车开行方案与运行图综合优化方法.铁道学报,2011,33(2)：1-7
[66]Φ.Π.柯契涅夫.铁路行车组织.高家驹,杨明伦等译.中国铁道出版社,1985
[67]E.A.索尼科夫.编组站工作强化.王鹤鸣译.中国铁道出版社,1987
[68]B.И.巴利奇,B.Φ.戈列恰纽克, И.Г.卡佐夫斯基,B.A.库特拉捷夫. 货物运输调整.王鹤鸣,郝克智,宋建业,梁万荣译.中国铁道出版社, 1992
[69]司马舸.日本自动化驼峰技术站的发展.中国铁路,1984,(12)：17-21
[70]O.Gulboden.Optimal planning of marshalling yard by operation research. PROC,1963:226-233
[71]Arjang A. Assad. Modeling of rail networks:Toward a routing/makeup model. Trans. Res. B.,1980,14(1):101-114
[72]M.A. Turnquist, M.S.Daskin. Queuing models of classification and connection delay in rail yards. Transp. Sci.,1982, (16):207-230
[73]S. Yagar,F.F. Saccomanno and Q. Shi. An efficient sequencing model for humping in a rail yard. Trans. Res.-A.,1983,17(4):251-262
[74]T.Gainic, J.Ferland, J. Rousseav. A tactical planning model for rail freight transportation. Trans. Sci.,1984, (18):165-183
[75]M. H. Keaton. Designing optimal railroad operating plans:Lagrangian relaxation and heuristic approaches. Trans. Res.-B.,1989,(23):415-431
[76]R. David, Martinelli and Huanliang Teng. Optimization of railway operations using neural networks. Trans. Res.-C.,1995,4(1):33-49
[77]O.K.Kwon. Routing and Scheduling Temporal and Heterogeneous freight car traffic on rail networks. Trans. Res.-E.,1997,34(2):101-115
[78]J.F.Cordeau. A Survey of Optimization Models for Train Routing and Scheduling.Transpotation Science,1998,32(4):380-404
[79]E.Dahlhaus.The train marshalling problem. Discrete Applied Mathematics,2000, 103:41-54
[80]J.F.Cordeau, Guy Desaulniers.Simultaneous locomotive and car assignment at VIA Rail Canada. Trans. Res.-B.,2001,35:767-787
[8]]刘军.基于知识的编组站作业整体仿真策略的研究.北方交通大学学报,1992,16(3)： 40-45
[82]何世伟,朱松年.一类涉及资源配置优化的排序问题及算法.铁道运输与经济,1996,4：75-79
[83]李文权.铁路区段站日工作计划优化模型及其算法的研究.西南交通大学博士学位论文,1997
[84]钟雁,张全寿.铁路编组站调车作业计划决策支持系统的研究.铁道学报,1994,16(4)：76-82
[85]曹家明.双线铁路行车调度调整得优化方法.西南交通大学学报,1995,30(5)： 520-526
[86]徐杰.区段站阶段计划自动编制模型和算法研究.西南交通大学博士学位论文,2003
[87]王慈光.技术站静态配流网络模型.交通运输工程与信息学报,2003,1(2)：67-71
[88]范征.丰台西编组站调度决策支持系统的研究——阶段计划解体照顾编、出发.西南交通大学硕士学位论文,1993
[89]牛惠民,胡安洲.双向编组站车流接续的综合优化.铁道学报,1998,20(60)：16-21
[90]彭其渊,赵军,韩雪松.技术站广义配流问题模型与算法.2010,31(2)：108-114
[91]吕红霞.基于蚁群算法的客运站到发线运用计划编制方法.2008,43(2)：153-158
[92]王世东,郑力,张智海等.技术站阶段计划自动编制的数学模型及算法.中国铁道科学,2008,29(2)：120-124
[93]王明慧,赵强.技术站智能调度系统阶段计划优化模型及算法研究.铁道学报,2005,27(6)：1-9
[94]王正彬,杜文,吴柏青等.基于解编顺序的阶段计划车流推算模型及算法.西南交通大学学报,2008,43(1)：91-95
[95]申永生,何世伟,王保华等.免疫算法求解技术站阶段计划配流问题研究.铁道学报,2009,31(4)：1-6
[96]刘霆,何世伟,王保华等.编组站调度计划随机机会约束规划模型及算法研究.铁道学报,2007,29(4)：12-17
[97]袁庆达,杜文,黎青松.区段站阶段计划的优化模型和算法.西南交通大学学报,2000,35(3)：250-254
[98]赵军,彭其渊,文超等.技术站广义动态配流问题的局部邻域搜索算法.西南交通大学学报,2010,45(3)：486-492
[99]黎浩东.铁路编组站鲁棒性阶段计划编制研究.北京交通大学硕士学位论文,2008
[100]郭寒英,石红国.求解编组站静态配流问题的一种改进算法.铁道运输与经济,2004,26(5)：74-76
[101]薛锋.双向编组站静态配流的优化.西南交通大学大学学报,2008,43(2)：159-164
[102]Dell'Amico,M., Martello, S. The k-cardinality assignment problem. Discrete Applied Mathematics,1997,76:103-121
[103]Klein M. A primal method for minimum cost flows with application to the assignment and transportation problem. Management Science,1967,14(1):205-220.
[104]David W., Pentico. Assignment problems:A golden anniversary survey European Journal of Operational Research,2007,176(2):774-793
[105]Rainer E., Burkard. Selected topics on assignment problems.Discrete Applied Mathematics,2002,123(1):257-302
[106]白国仲.C指派问题.系统工程理论与实践.2003,23(3)：107-111
[107]傅家良.运筹学方法与模型.上海：复旦大学出版社,2006
[108]《现代应用数学手册》编委会编.现代应用数学手册(运筹学与最优化理论卷).北京：清华大学出版社,1998
[109]甘应爱.运筹学.第三版.北京：清华大学出版社,2003
[110]谢政.图论的算法与复杂性理论.第二版.长沙：国防科技大学出版社,2003
[111]邢文训,谢金星.现代优化计算方法.北京：清华大学出版社,2001
[112]陈志平,徐宗本.计算机数学.北京：科学出版社,2001
[113]马良,项培军.蚂蚁算法在组合优化中的应用.管理科学学报,2001,4(2)：32-37
[114]王晓东.计算机算法设计与分析.北京：电子工业出版社,2003
[115]王凌.智能优化及其应用.北京：清华大学出版社,施普林格出版社,2001
[116]王岩冰,郑明春,刘弘.回溯算法的形式模型.计算机研究与发展,2008,38(9)：1066-1079
[117]高雷阜.最优化理论与方法.沈阳：东北大学出版社,2005
[118]史亮,聂长海,徐宝文.基于解空间树的组合测试数据生成.计算机学报,2006,29(6)：849-957
[119]王向东.数学分析的概念与方法(上册).上海：上海科学技术文献出版社,1989
[120]卢开澄.组合数学.北京：清华大学出版社,1991
[121]朱清新,杨凡,钟黔川等.计算机算法.北京：人民邮电出版社,2008
[122]王红梅.算法设计与分析.北京：清华大学出版社,2006
[123]屈婉玲.组合数学.北京：北京大学出版社,1991
[124]杨振生.组合数学及其算法.合肥：中国科学技术大学出版社,1997
[125]黄友锐.智能优化算法及其应用.北京：国防工业出版社,2008
[126]王慈光.用表上作业法求解技术站配流问题的研究.铁道学报,2002,2(4)：1-5
[127]薛锋.编组站调度系统配流协同优化理论与方法研究.西南交通大学博士学位 论文,2009
[128]陈云飞,刘玉树,范洁等.广义分配问题的一种小生境遗传蚁群优化算法.北京理工大学学报,2005,25(6)：490-494
[129]谭立刚,杨肇夏.编组站模拟系统中到达流生成的方法,北方交通大学学报,1998,22(6)： 43-47
[130]张军,胡晓敏,罗旭耀等译.蚁群优化.北京：清华大学出版社,2007
[131]李士勇,陈永强,李研.蚁群算法及其应用.哈尔滨：哈尔滨工业大学出版社,2004
[132]段海滨.蚁群算法原理及其应用.北京：科学出版社,2005
[133]吴庆洪,张纪会,徐心和.具有变异特征的蚁群算法.计算机研究与发展,1999,36(10)：1240-1245
[134]郭耀煌等.运筹学原理与方法.成都：西南交通大学出版社,1994
[135]吴祈宗.运筹学与最优化方法.北京：机械工业出版社,2003
[136]丁建立,陈增强.遗传算法与蚁群算法融合.计算机研究与发展,2003,40(9)：1531-1536
[137]高尚,杨静宇.群智能算法及其应用.北京：中国水利水电出版社,2006
[138]玄光南,陈润伟.遗传算法与工程优化.北京：清华大学出版社,2004
[139]黄席樾,向长城,殷礼胜.现代智能算法理论及应用.北京：科学出版社,2009
[140]Dorigo M, Gambardella L M. Ant colony system:a cooperative learning approach to the travelling salesman problem.IEEE Transaction on Evolutionary Computation,1997,1 (1):53-66
[141]Dorigo M, Maniezzo V, Colorni A. Ant System:optimization by a colony of cooperating agents.IEEE Transaction on Systems, Man and Cybernetics Part B, 1996,26(1):29-41
[142]Caro G D, Dorigo M. AntNet:Distributed stigmergetic control for communications networks. Journal of Artificial Intelligence Research,1998. 9:317-365
[143]D. Costa and A. Hertz. Ants can colour graphs. Journal of the Operational Research Society,1997,48:295-305
[144]Dorigo M, Caro G D, Gambardella L M. Ant algorithms for discrete optimization. Artificial Life,1999,5(2):137-172
[145]Gambardella L M,Taillard E D, Dorigo M. Ant colonies for the quadratic assignment problem. Journal of the Operational Research Society, 1999,50(2):167-176
[146]Z.J. Lee, C.Y. Lee, S.F. Su. An immunity-based ant colony optimization algorithm for solving weapon-target assignment problem, Applied Soft Computing,2002,2 (1):39-47
[147]Maniezzo V, Carbonaro A. An ANTS heuristic for the frequency assignment problem. Future Generation Computer Systems,2000,16(8):927-935
[148]Maniezzo V, Colorni A. The Ant System applied to the quadratic assignment problem. IEEE Transactions on Data and Knowledge Engineering,11(5):769-778,1999
[149]C. Blum. Ant colony optimization:introduction and recent trends, Physics of Life Reviews,2005,2 (4):353-373
[150]Dorigo M, Gambardella L M. Ant colonies for the traveling salesman problem. BioSystems,1997,43(2):73-81
[151]Dorigo M. Optimization, Learning and Natural Algorithms (in Italian). PhD thesis, Dipartimento di Elettronica, Politecnico di Milano, Italy,1992
[152]M. Dorigo, E. Bonabeau, G. Theraulaz. Ant algorithms and stigmergy. Future Generation Computer Systems,16(8):851-871,2000
[153]M. Dorigo, G. Di Caro, L. M. Gambardella. Ant algorithms for discrete optimization. Artificial Life,1999,5(2):137-172
[154]崔逊学.多目标进化算法及其应用.北京：国防工业出版社,2006
[155]雷德明,严新平.多目标智能优化算法及其应用.北京：科学出版社,2009
[156]段海滨,王道波,朱家强等.蚁群算法理论及应用研究的进展.控制与决策,2004,19(12)：1321-1326
[157]胡毓达.实用多目标最优化.上海：上海科学技术出版社,1990
[158]高尚,杨静.线性整数规划的蚁群算法.南京理工大学学报,2005,10(29)：120-123
[159]丁力平,谭建荣,冯毅雄等.基于Pareto蚁群算法的拆卸线平衡多目标优化.计算机集成制造系统,2009,15(7)：1407-1413
[160]龚本灿,李腊元.基于启发式变异的蚁群算法.计算机工程,2008,34(8)：35-37
[161]朱庆保,杨志军.基于变异和动态信息素更新的蚁群优化算法.软件学报,2004,15(2)：186-191
[162]S.K.Chaharsooghi,Amir H.Meimand Kermani. An effective ant colony optimization algorithm for multi-objective resource allocation problem. Applied Mathematics and Computation,200 (2008):167-177
[163]Thomas S, Holger H H. MAX-MIN ant system. Future Generation Computer Systems,2000,16 (8):889-914
[164]Wooyeon Yu, Pius J. Egbelu. Scheduling of inbound and outbound trucks in cross docking systems with temporary storage. European Journal of Operational Research,2008(184):377-396
[165]Peng-Yeng Yin, Jing-Yu Wang.Ant colony optimization for the nonlinear resource allocation problem.Applied Mathematics and Computation,2006,174:1438-1453
[166]Dorigo M, Gambardella L M. Ant colonies for the travelling salesman problem. BioSystems,1997,43:73-81
[167]D. Merkle, M. Middendorf, H. Schmeck, Ant colony optimization for resource constrained project scheduling, IEEE Transactions on EvolutionaryComputation, 2002,6:333-346
[168]Yuvraj Gajpal, Prakash Abad. An ant colony system (ACS) for vehicle routing problem with simultaneous delivery and pickup. Computers & Operations Research,36 (2009):3215-3223
[169]V. Maniezzo, A. Colorni, The ant system applied to the quadratic assignment problem, IEEE Transactions on Knowledge and Data Engineering,1999,11 (5):769-778
[170]W.J. Gutjahr. A graph-based Ant System and its convergence. Future Generation Computer Systems,16 (2000):873-888
[171]Konak, A., Kulturel-Konak, S., Norman, B. A., Smith, A. E.. A new mixed integer programming formulation for facility layout design using flexible bays. Operations Research Letters,2006,34:660-672
[172]B. Bullnheimer, R.F. Hartl, C. Strauss, A new rank based version of the ant systema computational study, Central European J. Oper. Res. Econom.7 (1999):25-38
[173]M. Dorigo, V. Manieszo, A. Colorni. The Ant System:Optimization by a Colony of Cooperating Agents. IEEE Transactions on Systems, Man and Cybernetics Part B,1996,26(1):29-41
[174]Snezana Mitrovic-Minic, Abraham P. Punnen. Local search intensified:Very large-scale variable neighborhood search for the multi-resource generalized assignment problem, Discrete Optimization,6 (2009):370-377
[175]Lourenco, H. R., Martin, O., Stuzle, T. Iterated local search. Handbook of Metahearistics,2002,57:321-353.
[176]T.C. Koopmans, M.J. Beckmann, Assignment problems and the location of economic activities, Econometrica,1957,25 (1):53-76
[177]P. Y. Yin, J. Y.Wang.An colony optimization for the nonlinear resource allocation problem, Applied Mathematics and Computation,174 (2006):1438-1453
[178]C. Blum. Ant colony optimization:introduction and recent trends, Physics of Life Reviews,2005,2(4):353-373
[179]高随祥.图论与网络流理论.北京：高等教育出版社,2009
[180]邓永录,梁之舜.随机点过程及其应用.北京：科学出版社,1992
[181]李致中.铁路运输管理的数学模型及算法.武汉：华中理工大学出版社,1995
[182]王小东.铁路双向编组站配流问题的研究.兰州交通大学博士学位论文,2009
[183]张全寿,张仲义,刘峰等.编组站货车实时信息系统.北京：中国铁道出版社,1997
[184]刘军.铁路技术站作业计划滚动式智能化编制方法研究.北方交通大学博士学位论文,1993
[185]孙焰,李致中.列车运行图的均衡性标准.长沙铁道学院学报,1993,11(2)：63-68
[186]何世伟.铁路枢纽作业计划的优化编制——技术站作业计划与枢纽日班计划的模型及算法研究.西南交通大学博士学位论文,1996
[187]班长青.铁路列车运行图的编制方法.北京：人民铁道出版社,1964
[188]程维生,张勇智.计算机编制列车运行图在我国的应用与展望.铁道运输与经济,1995(6)：28-29
[189]郭富娥,杨旭辉.计算机编制双线列车运行图的研究.铁道运输与经济,1998(4)：14-19
[190]胡思继,郑时德.关于我国铁路组织按图行车现状和问题的研究.北方交通大学学报,1987(2)：70-78
[191]王慈光.对有序组合树法的改进.西南交通大学学报,2006,41(5)：561-565
[192]符卓.方便旅客旅行的列车到发点优化确定方法.长沙铁道学院学报,1998,16(3)：30-33
[193]凌铿.应用电子计算机编制复线区段列车运行图.铁道运输与经济,1981(1)：80-83
[2]胡思继.铁路行车组织.北京：中国铁道出版社,2004
[3]马桂贞.铁路站场及枢纽.成都：西南交通大学出版社,2003
[4]彭其渊,闫海峰,石子明.计算机编制列车运行图的理论与方法.成都：西南交通大学出版社,2004
[5]王慈光.运输模型及优化.第二版.成都：西南交通大学出版社,2010：98-107
[6]郭富娥.论利用电子计算机编制列车运行图.计算机应用,1992,1：35-38
[7]胡思继.列车运行组织及通过能力理论.北京：中国铁道出版社,1993
[8]胡思继.列车运行图编制理论.北京：中国铁道出版社,2007
[9]彭其渊,吕红霞.计算机编制列车运行图实验教程.成都：西南交通大学出版社,2007
[10]郭富娥.日本近期开发的列车运行图编制系统.中国铁路,1995,8：38-40
[11]A. Caprara, M. Fischetti, P. Modeling and solving the train timetabling problem, Oper. Res.2002,50:851-861
[12]Shaw-Ching Chang, Yu-Chi Chung. From timetabling to train regulation—a new train operation model Information and Software Technology,Volume 47,Issue 9,15 June,2005:575-585
[13]Ji-Won Chung, Seog-Moon Oh, In-Chan Choi. A hybrid genetic algorithm for train sequencing in the Korean railway. Omega,2007,37 (3):555-565
[14]Yusin Lee, Chuen-Yih Chen. A heuristic for the train pathing and timetabling problem.Transportation Research Part B:Methodological,2009,43:837-851
[15]Xuesong Zhou, Ming Zhong. Single-track train timetabling with guaranteed optimality:Branch-and-bound algorithms with enhanced lower bounds. Transportation Research Part B:Methodological,2007,41(3):320-341
[16]Andrea D'Ariano, Dario Pacciarelli, Marco Pranzo. A branch and bound algorithm for scheduling trains in a railway network. European Journal of Operational Research,2007,183(2):644-657
[17]Enrique Castillo, Inmaculada Gallego, Jose Maria Urena, et al. Timetabling optimization of a mixed double- and single-tracked railway network. Applied Mathematical Modelling,2011,35(2):859-878
[18]Yu Hern Chang, Ching Cheng Shen. A multiobjective model for passenger train services planning application to Taiwan's high-speed rail line. Transportation Research Part B:Methodological,2000,34(3):91-106
[19]Valentina Cacchiani, Alberto Caprara, Paolo Toth. Scheduling extra freight trains on railway network. Transportation Research Part B:Methodological,2010, 44:215-231
[20]Caprara A., Michele M., Toth p.,et al. A Lagrangian heuristic algorithm for a real-world train timetabling problem. Discrete Applied Mathematics,2006,154(5): 738-753
[21]柳进.计算机绘制列车运行图的设计方法.铁道运输与经济,1997,5：30-38
[22]郭富娥.计算机编制双线列车运行图的研究.铁道运输与经济,1998,5：26-27
[23]郭富娥.高速线与既有线列车运行图衔接问题的研究.高速铁路,2000,7：25-27
[24]凌熙,杨浩,王亮斌.基于MAS的列车运行图智能编制系统建模方法研究,铁道运输与经济,2009,31(7)：81-84
[25]杨肇夏,孔庆钤.微计算机编制双线自动闭塞方向货物列车运行图的研究,铁道学报,1985,(4)：63-72
[26]周磊山.计算机快速处理铁路列车运行图的新方法,铁道运输与经济,1992,(7)：27-30
[27]李菊,张晓森.用计算机绘制列车运行图.北京交通大学学报,1994,4：537-541
[28]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.北京交通大学学报,1997,21(3)：274-279
[29]张星臣,胡安洲,杨浩.铁路运输储备能力合理分配的计算机模拟研究.铁道学报,1997,19(5)：1-6
[30]聂磊,郭富娥.计算机编制高速铁路列车运行图的研究.中国铁道科学,1997,18(1)：101-110
[31]周磊山,胡思继.计算机编制网状线路列车运行图方法研究.铁道学报,1998,20(5)：15-21
[32]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.北方交通大学报,2002,26(5)：9-12
[33]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.中国铁道科学,2002,23(5)：9-12
[34]许红,马建军,龙建成等.城市轨道交通列车运行图编制的数学模型及方法.北 京交通大学学报,2006,30(3)：10-14
[35]汪波,杨浩,牛丰等.周期运行图编制模型与算法研究.北京交通大学学报,2007,29(5)：1-6
[36]高强周.城市轨道交通列车运行图设计实现与评价.北京交通大学硕士论文,2008
[37]谢美全,聂磊.周期性列车运行图编制模型研究.铁道学报,2009,31(4)：7-13
[38]杨意坚,何宇强.基于Max-plus方法的列车运行图稳定性评价.铁道学报,2009,31(4)：14-19
[39]陈军华.基于稳定性的客运专线运行图编制与评价问题研究.北京交通大学博士学位论文,2009
[40]祝建平,周磊山,乐逸祥.基于协作交互的列车运行图网络化编制系统.中国铁道科学,2010,31(1)：139-144
[41]孟令云,杨肇夏,李海鹰等.基于列车运行线分布的客运专线列车运行图动态性能分析.中国铁道科学,2010,31(2)：90-95
[42]赵宇刚,毛保华,蒋玉琨.基于列车运行时间偏离的地铁列车运行图缓冲时间研究.中国铁道科学,2011,32(1)：118-121
[43]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.中国铁道科学,1994,15(14)：60-66
[44]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.铁道学报,1995,17(3)：15-20
[45]彭其渊,杨明伦,倪少权.单线区段货物始发列车方案的优化模型及求解方法.西南交通大学学报,1995,30(2)：177-181
[46]彭其渊,朱松年,阎海峰.列车运行图可调整度评价系统研究.西南交通大学学报,1998,33(4)：367-371
[47]朱健梅.基于实用的技术站直通列车接续方案计算方法研究.西南交通大学学报,1999,34(3)：365-368
[48]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.铁道学报,2001,23(1)：1-8
[49]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.铁道运输与经济,2002,24(6)：41-43
[50]陈彦如,彭其渊,蒋阳升.复线列车运行调整满意优化模型研究.铁道学报,2003,25(3)：8-12
[51]刘爱江,许长枫,何大可.基于遗传算法的列车运行图初始布点配对模型.铁道计算机应用,2003,12(1)：13-16
[52]董守清,王进勇,闫海峰.双线铁路列车运行调整的禁忌搜索算法.中国铁道科学,2005,26(4)：114-119
[53]王利华.双线自动闭塞区段最大量铺画货物列车运行线的研究.铁道运输与经济,2007,29(5)：78-80
[54]章优仕,金炜东.基于离散事件拓扑图模型的单线列车运行调整迭代修复算法,系统仿真学报,2009,21(21)：7003-7007
[55]孙焰,李致中.单线区段货物列车运行图的一种优化方法.铁道学报,1991,15(4)：60-71
[56]孙焰,李致中.单线区间列车最优运行次序的排序模型及解法.铁道学报,]993,15(1)：62-71
[57]符卓.旅客列车运行方案图优化编制方法的研究,1996,18(4)：10-17
[58]史峰.定序单线列车运行图的原始——对偶算法.铁道学报,1996,18(1)：8-20
[59]孙焰,李致中.列车运行图最优初始布点方法.长沙铁道学院学报,1997,15(4)：80-87
[60]李夏苗,查伟雄,李轶平.以客运为主繁忙干线区段列车运行调整计划的优化.铁道学报,1999,21(6)：11-14
[61]查伟雄,陈治亚,李夏苗.复线列车运行调整理论与方法的研究.铁道学报,2000,22(1)：13-16
[62]肖龙文,谢如鹤.单线区段列车运行图的自动化调整方法.交通运输工程学报,2004,4(3)：25-29
[63]史峰,黎新华,秦进等.单线列车运行图铺划的时间循环迭代优化方法.铁道学报,2005,27(1)：1-5
[64]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.长沙：中南大学,2005
[65]周文梁,史峰,陈彦等.客运专线网络列车开行方案与运行图综合优化方法.铁道学报,2011,33(2)：1-7
[66]Φ.Π.柯契涅夫.铁路行车组织.高家驹,杨明伦等译.中国铁道出版社,1985
[67]E.A.索尼科夫.编组站工作强化.王鹤鸣译.中国铁道出版社,1987
[68]B.И.巴利奇,B.Φ.戈列恰纽克, И.Г.卡佐夫斯基,B.A.库特拉捷夫. 货物运输调整.王鹤鸣,郝克智,宋建业,梁万荣译.中国铁道出版社, 1992
[69]司马舸.日本自动化驼峰技术站的发展.中国铁路,1984,(12)：17-21
[70]O.Gulboden.Optimal planning of marshalling yard by operation research. PROC,1963:226-233
[71]Arjang A. Assad. Modeling of rail networks:Toward a routing/makeup model. Trans. Res. B.,1980,14(1):101-114
[72]M.A. Turnquist, M.S.Daskin. Queuing models of classification and connection delay in rail yards. Transp. Sci.,1982, (16):207-230
[73]S. Yagar,F.F. Saccomanno and Q. Shi. An efficient sequencing model for humping in a rail yard. Trans. Res.-A.,1983,17(4):251-262
[74]T.Gainic, J.Ferland, J. Rousseav. A tactical planning model for rail freight transportation. Trans. Sci.,1984, (18):165-183
[75]M. H. Keaton. Designing optimal railroad operating plans:Lagrangian relaxation and heuristic approaches. Trans. Res.-B.,1989,(23):415-431
[76]R. David, Martinelli and Huanliang Teng. Optimization of railway operations using neural networks. Trans. Res.-C.,1995,4(1):33-49
[77]O.K.Kwon. Routing and Scheduling Temporal and Heterogeneous freight car traffic on rail networks. Trans. Res.-E.,1997,34(2):101-115
[78]J.F.Cordeau. A Survey of Optimization Models for Train Routing and Scheduling.Transpotation Science,1998,32(4):380-404
[79]E.Dahlhaus.The train marshalling problem. Discrete Applied Mathematics,2000, 103:41-54
[80]J.F.Cordeau, Guy Desaulniers.Simultaneous locomotive and car assignment at VIA Rail Canada. Trans. Res.-B.,2001,35:767-787
[8]]刘军.基于知识的编组站作业整体仿真策略的研究.北方交通大学学报,1992,16(3)： 40-45
[82]何世伟,朱松年.一类涉及资源配置优化的排序问题及算法.铁道运输与经济,1996,4：75-79
[83]李文权.铁路区段站日工作计划优化模型及其算法的研究.西南交通大学博士学位论文,1997
[84]钟雁,张全寿.铁路编组站调车作业计划决策支持系统的研究.铁道学报,1994,16(4)：76-82
[85]曹家明.双线铁路行车调度调整得优化方法.西南交通大学学报,1995,30(5)： 520-526
[86]徐杰.区段站阶段计划自动编制模型和算法研究.西南交通大学博士学位论文,2003
[87]王慈光.技术站静态配流网络模型.交通运输工程与信息学报,2003,1(2)：67-71
[88]范征.丰台西编组站调度决策支持系统的研究——阶段计划解体照顾编、出发.西南交通大学硕士学位论文,1993
[89]牛惠民,胡安洲.双向编组站车流接续的综合优化.铁道学报,1998,20(60)：16-21
[90]彭其渊,赵军,韩雪松.技术站广义配流问题模型与算法.2010,31(2)：108-114
[91]吕红霞.基于蚁群算法的客运站到发线运用计划编制方法.2008,43(2)：153-158
[92]王世东,郑力,张智海等.技术站阶段计划自动编制的数学模型及算法.中国铁道科学,2008,29(2)：120-124
[93]王明慧,赵强.技术站智能调度系统阶段计划优化模型及算法研究.铁道学报,2005,27(6)：1-9
[94]王正彬,杜文,吴柏青等.基于解编顺序的阶段计划车流推算模型及算法.西南交通大学学报,2008,43(1)：91-95
[95]申永生,何世伟,王保华等.免疫算法求解技术站阶段计划配流问题研究.铁道学报,2009,31(4)：1-6
[96]刘霆,何世伟,王保华等.编组站调度计划随机机会约束规划模型及算法研究.铁道学报,2007,29(4)：12-17
[97]袁庆达,杜文,黎青松.区段站阶段计划的优化模型和算法.西南交通大学学报,2000,35(3)：250-254
[98]赵军,彭其渊,文超等.技术站广义动态配流问题的局部邻域搜索算法.西南交通大学学报,2010,45(3)：486-492
[99]黎浩东.铁路编组站鲁棒性阶段计划编制研究.北京交通大学硕士学位论文,2008
[100]郭寒英,石红国.求解编组站静态配流问题的一种改进算法.铁道运输与经济,2004,26(5)：74-76
[101]薛锋.双向编组站静态配流的优化.西南交通大学大学学报,2008,43(2)：159-164
[102]Dell'Amico,M., Martello, S. The k-cardinality assignment problem. Discrete Applied Mathematics,1997,76:103-121
[103]Klein M. A primal method for minimum cost flows with application to the assignment and transportation problem. Management Science,1967,14(1):205-220.
[104]David W., Pentico. Assignment problems:A golden anniversary survey European Journal of Operational Research,2007,176(2):774-793
[105]Rainer E., Burkard. Selected topics on assignment problems.Discrete Applied Mathematics,2002,123(1):257-302
[106]白国仲.C指派问题.系统工程理论与实践.2003,23(3)：107-111
[107]傅家良.运筹学方法与模型.上海：复旦大学出版社,2006
[108]《现代应用数学手册》编委会编.现代应用数学手册(运筹学与最优化理论卷).北京：清华大学出版社,1998
[109]甘应爱.运筹学.第三版.北京：清华大学出版社,2003
[110]谢政.图论的算法与复杂性理论.第二版.长沙：国防科技大学出版社,2003
[111]邢文训,谢金星.现代优化计算方法.北京：清华大学出版社,2001
[112]陈志平,徐宗本.计算机数学.北京：科学出版社,2001
[113]马良,项培军.蚂蚁算法在组合优化中的应用.管理科学学报,2001,4(2)：32-37
[114]王晓东.计算机算法设计与分析.北京：电子工业出版社,2003
[115]王凌.智能优化及其应用.北京：清华大学出版社,施普林格出版社,2001
[116]王岩冰,郑明春,刘弘.回溯算法的形式模型.计算机研究与发展,2008,38(9)：1066-1079
[117]高雷阜.最优化理论与方法.沈阳：东北大学出版社,2005
[118]史亮,聂长海,徐宝文.基于解空间树的组合测试数据生成.计算机学报,2006,29(6)：849-957
[119]王向东.数学分析的概念与方法(上册).上海：上海科学技术文献出版社,1989
[120]卢开澄.组合数学.北京：清华大学出版社,1991
[121]朱清新,杨凡,钟黔川等.计算机算法.北京：人民邮电出版社,2008
[122]王红梅.算法设计与分析.北京：清华大学出版社,2006
[123]屈婉玲.组合数学.北京：北京大学出版社,1991
[124]杨振生.组合数学及其算法.合肥：中国科学技术大学出版社,1997
[125]黄友锐.智能优化算法及其应用.北京：国防工业出版社,2008
[126]王慈光.用表上作业法求解技术站配流问题的研究.铁道学报,2002,2(4)：1-5
[127]薛锋.编组站调度系统配流协同优化理论与方法研究.西南交通大学博士学位 论文,2009
[128]陈云飞,刘玉树,范洁等.广义分配问题的一种小生境遗传蚁群优化算法.北京理工大学学报,2005,25(6)：490-494
[129]谭立刚,杨肇夏.编组站模拟系统中到达流生成的方法,北方交通大学学报,1998,22(6)： 43-47
[130]张军,胡晓敏,罗旭耀等译.蚁群优化.北京：清华大学出版社,2007
[131]李士勇,陈永强,李研.蚁群算法及其应用.哈尔滨：哈尔滨工业大学出版社,2004
[132]段海滨.蚁群算法原理及其应用.北京：科学出版社,2005
[133]吴庆洪,张纪会,徐心和.具有变异特征的蚁群算法.计算机研究与发展,1999,36(10)：1240-1245
[134]郭耀煌等.运筹学原理与方法.成都：西南交通大学出版社,1994
[135]吴祈宗.运筹学与最优化方法.北京：机械工业出版社,2003
[136]丁建立,陈增强.遗传算法与蚁群算法融合.计算机研究与发展,2003,40(9)：1531-1536
[137]高尚,杨静宇.群智能算法及其应用.北京：中国水利水电出版社,2006
[138]玄光南,陈润伟.遗传算法与工程优化.北京：清华大学出版社,2004
[139]黄席樾,向长城,殷礼胜.现代智能算法理论及应用.北京：科学出版社,2009
[140]Dorigo M, Gambardella L M. Ant colony system:a cooperative learning approach to the travelling salesman problem.IEEE Transaction on Evolutionary Computation,1997,1 (1):53-66
[141]Dorigo M, Maniezzo V, Colorni A. Ant System:optimization by a colony of cooperating agents.IEEE Transaction on Systems, Man and Cybernetics Part B, 1996,26(1):29-41
[142]Caro G D, Dorigo M. AntNet:Distributed stigmergetic control for communications networks. Journal of Artificial Intelligence Research,1998. 9:317-365
[143]D. Costa and A. Hertz. Ants can colour graphs. Journal of the Operational Research Society,1997,48:295-305
[144]Dorigo M, Caro G D, Gambardella L M. Ant algorithms for discrete optimization. Artificial Life,1999,5(2):137-172
[145]Gambardella L M,Taillard E D, Dorigo M. Ant colonies for the quadratic assignment problem. Journal of the Operational Research Society, 1999,50(2):167-176
[146]Z.J. Lee, C.Y. Lee, S.F. Su. An immunity-based ant colony optimization algorithm for solving weapon-target assignment problem, Applied Soft Computing,2002,2 (1):39-47
[147]Maniezzo V, Carbonaro A. An ANTS heuristic for the frequency assignment problem. Future Generation Computer Systems,2000,16(8):927-935
[148]Maniezzo V, Colorni A. The Ant System applied to the quadratic assignment problem. IEEE Transactions on Data and Knowledge Engineering,11(5):769-778,1999
[149]C. Blum. Ant colony optimization:introduction and recent trends, Physics of Life Reviews,2005,2 (4):353-373
[150]Dorigo M, Gambardella L M. Ant colonies for the traveling salesman problem. BioSystems,1997,43(2):73-81
[151]Dorigo M. Optimization, Learning and Natural Algorithms (in Italian). PhD thesis, Dipartimento di Elettronica, Politecnico di Milano, Italy,1992
[152]M. Dorigo, E. Bonabeau, G. Theraulaz. Ant algorithms and stigmergy. Future Generation Computer Systems,16(8):851-871,2000
[153]M. Dorigo, G. Di Caro, L. M. Gambardella. Ant algorithms for discrete optimization. Artificial Life,1999,5(2):137-172
[154]崔逊学.多目标进化算法及其应用.北京：国防工业出版社,2006
[155]雷德明,严新平.多目标智能优化算法及其应用.北京：科学出版社,2009
[156]段海滨,王道波,朱家强等.蚁群算法理论及应用研究的进展.控制与决策,2004,19(12)：1321-1326
[157]胡毓达.实用多目标最优化.上海：上海科学技术出版社,1990
[158]高尚,杨静.线性整数规划的蚁群算法.南京理工大学学报,2005,10(29)：120-123
[159]丁力平,谭建荣,冯毅雄等.基于Pareto蚁群算法的拆卸线平衡多目标优化.计算机集成制造系统,2009,15(7)：1407-1413
[160]龚本灿,李腊元.基于启发式变异的蚁群算法.计算机工程,2008,34(8)：35-37
[161]朱庆保,杨志军.基于变异和动态信息素更新的蚁群优化算法.软件学报,2004,15(2)：186-191
[162]S.K.Chaharsooghi,Amir H.Meimand Kermani. An effective ant colony optimization algorithm for multi-objective resource allocation problem. Applied Mathematics and Computation,200 (2008):167-177
[163]Thomas S, Holger H H. MAX-MIN ant system. Future Generation Computer Systems,2000,16 (8):889-914
[164]Wooyeon Yu, Pius J. Egbelu. Scheduling of inbound and outbound trucks in cross docking systems with temporary storage. European Journal of Operational Research,2008(184):377-396
[165]Peng-Yeng Yin, Jing-Yu Wang.Ant colony optimization for the nonlinear resource allocation problem.Applied Mathematics and Computation,2006,174:1438-1453
[166]Dorigo M, Gambardella L M. Ant colonies for the travelling salesman problem. BioSystems,1997,43:73-81
[167]D. Merkle, M. Middendorf, H. Schmeck, Ant colony optimization for resource constrained project scheduling, IEEE Transactions on EvolutionaryComputation, 2002,6:333-346
[168]Yuvraj Gajpal, Prakash Abad. An ant colony system (ACS) for vehicle routing problem with simultaneous delivery and pickup. Computers & Operations Research,36 (2009):3215-3223
[169]V. Maniezzo, A. Colorni, The ant system applied to the quadratic assignment problem, IEEE Transactions on Knowledge and Data Engineering,1999,11 (5):769-778
[170]W.J. Gutjahr. A graph-based Ant System and its convergence. Future Generation Computer Systems,16 (2000):873-888
[171]Konak, A., Kulturel-Konak, S., Norman, B. A., Smith, A. E.. A new mixed integer programming formulation for facility layout design using flexible bays. Operations Research Letters,2006,34:660-672
[172]B. Bullnheimer, R.F. Hartl, C. Strauss, A new rank based version of the ant systema computational study, Central European J. Oper. Res. Econom.7 (1999):25-38
[173]M. Dorigo, V. Manieszo, A. Colorni. The Ant System:Optimization by a Colony of Cooperating Agents. IEEE Transactions on Systems, Man and Cybernetics Part B,1996,26(1):29-41
[174]Snezana Mitrovic-Minic, Abraham P. Punnen. Local search intensified:Very large-scale variable neighborhood search for the multi-resource generalized assignment problem, Discrete Optimization,6 (2009):370-377
[175]Lourenco, H. R., Martin, O., Stuzle, T. Iterated local search. Handbook of Metahearistics,2002,57:321-353.
[176]T.C. Koopmans, M.J. Beckmann, Assignment problems and the location of economic activities, Econometrica,1957,25 (1):53-76
[177]P. Y. Yin, J. Y.Wang.An colony optimization for the nonlinear resource allocation problem, Applied Mathematics and Computation,174 (2006):1438-1453
[178]C. Blum. Ant colony optimization:introduction and recent trends, Physics of Life Reviews,2005,2(4):353-373
[179]高随祥.图论与网络流理论.北京：高等教育出版社,2009
[180]邓永录,梁之舜.随机点过程及其应用.北京：科学出版社,1992
[181]李致中.铁路运输管理的数学模型及算法.武汉：华中理工大学出版社,1995
[182]王小东.铁路双向编组站配流问题的研究.兰州交通大学博士学位论文,2009
[183]张全寿,张仲义,刘峰等.编组站货车实时信息系统.北京：中国铁道出版社,1997
[184]刘军.铁路技术站作业计划滚动式智能化编制方法研究.北方交通大学博士学位论文,1993
[185]孙焰,李致中.列车运行图的均衡性标准.长沙铁道学院学报,1993,11(2)：63-68
[186]何世伟.铁路枢纽作业计划的优化编制——技术站作业计划与枢纽日班计划的模型及算法研究.西南交通大学博士学位论文,1996
[187]班长青.铁路列车运行图的编制方法.北京：人民铁道出版社,1964
[188]程维生,张勇智.计算机编制列车运行图在我国的应用与展望.铁道运输与经济,1995(6)：28-29
[189]郭富娥,杨旭辉.计算机编制双线列车运行图的研究.铁道运输与经济,1998(4)：14-19
[190]胡思继,郑时德.关于我国铁路组织按图行车现状和问题的研究.北方交通大学学报,1987(2)：70-78
[191]王慈光.对有序组合树法的改进.西南交通大学学报,2006,41(5)：561-565
[192]符卓.方便旅客旅行的列车到发点优化确定方法.长沙铁道学院学报,1998,16(3)：30-33
[193]凌铿.应用电子计算机编制复线区段列车运行图.铁道运输与经济,1981(1)：80-83
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