摘要
乘务员运用计划的编制是交通运输领域中各种运输方式都需要面临的重要问题,其实质是在给定运行时刻表及运输工具的接续关系后,制定各类乘务人员的工作计划。在航空运输及城市交通运输领域,乘务员的运用费用在直接生产费用中仅次于燃料费用。随着我国高速铁路的建设和发展,乘务员的工作要求越来越高,其运用费用在生产运营总费用中的比重逐渐加大,乘务计划在运营管理中的作用也越趋明显,计划的编制水平将成为影响高速铁路乘务员运用效率的关键因素。
乘务计划的编制过程通常划分为乘务交路计划编制和乘务排班计划编制两个子问题。乘务交路计划主要根据列车运行计划和动车组交路计划来确定值乘区段的接续关系,并确定所需要的最少乘务员数。乘务排班计划则是在综合考虑乘务员休息、培训等的基础上,确定乘务员在一定周期内每天工作的具体安排,并保证乘务员(组)之间工作量的均衡,其编制工作一般是在乘务交路计划的基础上进行。本文在参考国内外研究成果的基础上,研究我国高速铁路乘务计划编制问题,建立了相关问题的优化模型,结合现代优化计算方法,设计了各问题的有效求解算法。论文的主要研究工作如下：
1.分析了高速铁路乘务制度选择、乘务计划分类、计划编制影响因素、编制流程及常用建模方法等相关基础理论,为乘务计划编制问题优化模型的建立奠定了理论基础；对智能优化算法中比较具有代表性的模拟退火算法和蚁群算法的基本原理、应用流程、参数设计、主要特点及常用改进进行了归纳和总结,为乘务计划编制问题相关模型求解算法的设计奠定了基础。
2.分析了乘务交路计划编制问题的特点,将其划分为值乘区段集合覆盖和乘务交路段匹配两个子问题。考虑到乘务计划中便乘的存在及不同模型的求解难度,选用集合覆盖模型对问题进行表述,并对该形式下可行乘务交路段的费用计算方法进行讨论,建立了以最小化乘务交路段总费用为目标的集合覆盖模型,设计了求解模型的改进蚁群算法。根据成对列车运行计划中以乘务员换乘站到发的乘务交路段数相等的特点,建立了乘务交路段匹配的指派问题模型,进一步分析了其与TSP问题的共性,设计了求解的蚁群算法。
3.研究了两种不同形式的高速铁路乘务排班计划编制问题,即单一循环乘务排班计划和给定周期乘务排班计划。对单一循环乘务排班计划,建立了以乘务交路接续总时间最短和乘务交路接续冗余时间分布最均衡为目标的优化模型。分析得出问题的实质是一个带有里程约束的TSP问题,进而根据问题的特点,设计了基于动态启发式信息的蚁群优化算法；对于给定周期乘务排班计划,将其编制过程划分为乘务交路段集合分解和非极大排班方案调整两个阶段,分别建立了优化模型并设计了求解算法。
4.在分析高速铁路乘务计划原有编制流程优、缺点的基础上,以系统整体最优为目标,从优化模型的建立及求解和编制流程的改进两个方面对乘务计划的综合优化问题进行了研究。综合考虑乘务计划编制过程中各阶段的优化目标及约束条件,建立了乘务计划综合优化模型,并设计了蚁群算法；针对乘务交路计划编制问题模型迭代式求解的特点,设计了多种交互控制策略对乘务计划编制流程进行改进。
5.通过分析蚁群算法的特点及乘务计划编制过程中各子问题的结构,对蚁群算法进行改进,设计了基于双重信息素和启发式信息的蚁群优化算法,以及基于动态启发式信息的蚁群优化算法,应用于求解乘务计划编制过程中相关问题的求解。
上述研究不仅对于提高高速铁路乘务计划的编制水平、实现乘务计划编制的智能化具有实际意义,同时对我国高速铁路乘务计划编制决策支持系统的研究与设计也具有参考价值。
Crew planning problem is one of the most important problems that every transportation mode has to face. The essence of this problem is making the working plan of crews after given the running scheduling and the continuation relationship of conveyance. In the field of air transportation and urban transportation, the use of crew costs in the direct production cost just less than fuel cost. As the construction and development of China high-speed railway, the working requirement of crews become more and more harsh, and the proportion of its cost in the total cost also increasing gradually, thus the effect of crew plan in the operation and management of high-speed railway become increasingly significant. The quality of the crew plan will be the key factor that influences the using efficiency of crew members of high-speed railway.
Crew planning problem usually divide into two sub-problems, which are crew scheduling problem and crew rostering problem. The target of crew scheduling problem is to decide the connection between all segments according to the train working diagram and the EMU plan, and minimize the crew member used in this stage. In contrast, the goal of crew rostering problem is to decide the working schedule of crew members in certain period, and balance the workload of all crew members. The weaving of crew rostering problem usually based on the result of crew scheduling problem. Based on the research results at home and abroad, this dissertation studies the crew planning problem of China high-speed railway, build the optimization models of related problems, and designed effective algorithms for each model combined with modern optimization algorithms. The main research works of the dissertation are as follows:
1. The choosing of institution, classification, influence factor, weaving flow and commonly used model techniques of crew planning problem of China high-speed railway are analyzed to found the theory foundation for further study. The basic principles, application flow, parameter design methods, main characteristics and commonly used improving strategies of simulated annealing algorithm and ant colony algorithm are summarized to build the algorithm foundation for solving the related optimization models founded in the study process of crew planning problem.
2. The weaving of crew scheduling plan is divided into two stages on the basis of analyzing the characteristic of crew scheduling problem. The set covering model is chose to formulate the problem with the consideration of the existence of deadhead and the difficulty for solving different models. The optimization model aimed at minimize the total cost of crew segments is founded and the ant colony algorithm is designed for solving the model. The assignment model for the matching of crew segments is build according to the characteristic that the segments departure from or arrive at the same relief station are equally in train working diagram in pairs. Furthermore, this problem is described as traveling salesman problem and an ant colony algorithm for solving this problem is designed.
3. Two different forms of crew rostering problem are studied. For the single-circulation crew rostering problem, an optimization model is build with the objectives of minimize the connection time and balance of redundant time in connection time. By further analyze, we conclude that the essence of this problem is a traveling salesman problem with restrictions of travel distance. Ant colony algorithm based on dynamic heuristic information is designed according to the characteristic of this problem. For the crew rostering problem with given periodic, the weaving procedure is divide into two stage, optimization model and solving algorithm are studied for each stage, respectively.
4. Based on the advantage and disadvantage of the weaving flow of crew plan, and aimed at global optimization, this dissertation studies the integrated optimization of crew planning problem from two different points of view which are modeling optimization and weaving flow optimization. Build optimization model of crew planning problem by consider the objectives and constraints of each stage simultaneously, and then designed ant colony algorithm. For the algorithm designed for solving the crew scheduling problem improve the solution iteratively, this dissertation designed various control strategies to improve the weaving flow of crew planning problem.
5. Two improved ant colony algorithms are designed on the basis of analyzing the characteristic of ant colony algorithm and the structure of the sub-problems in crew planning problem. Then, the ant colony algorithm with double pheromone and heuristic information and the ant colony algorithm with dynamic heuristic information are used to solving relative problems.
The research above has not only practical significance for improving the quality of crew plan of high-speed railway and realize the intelligent weaving of crew plan, but also has reference value for the research and design of decision support system for the crew planning problem of China high-speed railway.
引文
[1]Nadia Souai, Jacques Teghem. Genetic algorithm based approach for the integrated airline crew-pairing and rostering problem[J]. European Journal of Operational Research.2009,199(3):674～683
[2]赵鹏.高速铁路动车组和乘务员运用的研究[D].北方交通大学博士学位论文.1998
[3]Caprara A, Fischetti M, Toth P, Vigo D. Algorithms for Railway Crew Management[J]. Mathematical Programming.1997,79:125～141
[4]Martin Desrochers. A Column Generation Approach to the Urban Transit Crew Sc heduling Problem[J]. Transportation Science, Vol.23, No.1,1989
[5]孙远运,刘刚,马均培.客运专线运营调度系统总体架构设计[J],2009,45(32)：215-221
[6]逯宗田,袁娟.客运专线运营调度系统软件架构探讨[J].2007,43(12)：29-31
[7]刘隽.基于分散自律体系的多Agent客运专线运营调度系统[D].铁道科学研究院博士学位论文.2006,7
[8]付强.高速铁路综合调度系统研究[D].西南交通大学硕士学位论文.2005,4
[9]赵鹏,富井规雄.基于概率局域搜索的动车组平日运用计划编制算法[J].系统工程理论与实践,2004,24(2)：123-129
[10]耿敬春,肖荣国,倪少权,等.客运专线动车组周期性运用计划编制的研究[J].铁道学报,2006,28(4)：17-21
[11]张杰,陈韬,施福根.客运专线动车组运用计划的计算机编制[J].西南交通大学学报,2006,41(5)：635-640
[12]陈华群.动车组运用计划编制系统相关问题研究[D].西南交通大学硕士学位论文.2007,4
[13]孙雪姣,葛正义,张春.高速铁路动车组检修计划方案的探讨[J].铁道建筑,2004,(12)：73-75
[14]王莹,刘军,苗建瑞.基于列生成算法的动车组检修计划优化[J].中国铁道科学,2010,31(2)：115-120
[15]陈韬,吕红霞,王艳艳.客运专线车站作业计划编制系统的研究[J].铁道运输与经济,2009,31(8)：12-15
[16]Arabeyre, J., Fearnley, J., Steiger, F., Teather, W. The airline crew scheduling problem: A survey[J]. Transportation Science,1969,3:140～163
[17]Beasley, J. E. and Cao, B. A tree search algorithm for the crew scheduling problem[J]. European Journal of Operational Research,1996,94:517～526
[18]Beasley, J. E. and Cao, B. A dynamic programming based algorithm for the crew scheduling problem[J]. Computers Ops Res.1998,25:567～582
[19]Shangyao Yan, Yu-Ping Tu. A network model for airline cabin crew scheduling[J]. European Journal of Operational Research,2002,140:531～540
[20]Shangyao Yan, Jei-Chi Chang. Airline cockpit crew scheduling[J]. European Journal of Operational Research,2002,136:501～511
[21]David Levine. Application of a hybrid genetic algorithm to airline crew scheduling[J]. Computers Ops Res,1996,23:547～558
[22]Gershkoff, I. Optimizing flight crew schedules[J]. Interfaces,1989,19(4):29-43
[23]Sydney C.K. Chu, Edmond C. H. Chan. Crew scheduling of light rail transit in Hong Kong from modeling to implementation[J]. Computers Ops Res,1998,25: 887～894
[24]Sydney C.K. Chu. Generating, scheduling and rostering of shift crew-duties, Applications at the Hong Kong International Airport[J]. European Journal of Operational Research,2007,177:1764～1778
[25]Martin Lagerholm, Carsten Peterson, Bo Soderberg. Airline crew scheduling using Potts mean field techniques[J]. European Journal of Operational Research, 2000,120:81～96
[26]Lavoie, S., Minoux, M., and Odier, E. A new approach for crew pairing problems by coloumn generation with an opplication to air transportation[J]. European Journal of Operational Research,1988,35:45～58
[27]Shaw Ching Chang. A new aircrew-scheduling model for short-haul routes[J]. Journal of Air Transport Management,2002,8:249～260
[28]Dusan Teodorovic, Panta Lucic. A fuzzy set theory approach to the aircrew rostering problem[J]. Fuzzy Sets and Systems,1998,95,261～271
[29]Herbert Dawid, Johannes Konig, Christine Strauss. An enhanced rostering model for airline crews[J]. Computers & Operations Research,2001,28,671～688
[30]Panta Lucic, Dusan Teodorovic. Simulated annealing for the multi-objective aircrew rostering problem[J]. Transportation Research Part A,1999,33:19～45
[31]Michel Gamache, Alain Hertz, Jerome Olivier Ouellet. A graph coloring model for a feasibility problem in monthly crew scheduling with preferential bidding[J]. Computers & Operations Research,2007,34:2384～2395
[32]Dennis Huisman. A column generation approach for the rail crew re-scheduling problem[J]. European Journal of Operational Research 2007,180,163～173.
[33]Anne Merciar, Jean-Francois Cordeau, Francois Soumis. A computational study of Benders decomposition for the integrated aircraft routing and crew scheduling problem[J]. Computers & Operations Research 2005,32:1451～1476
[34]Anne Mercier, Francois Soumis. An integrated aircraft routing, crew scheduling and flight retiming model[J]. Computers & Operations Research,2007,34: 2251～2265
[35]S. Yan, T.-T. Tung, Y.-P. Tu. Optimal construction of airline individual crew pairings[J]. Computers & Operations Research,2002,29:341～363
[36]Yufeng Guo, Taieb Mellouli, Leena Suhl, Markus P.Thiel. A partially integrated airline crew scheduling approach with time-dependent crew capacities and multiple home bases[J]. European Journal of Operational Research,2006,171: 1169～1181
[37]Claude P. Medard, Nidhi Sawhney. Airline crew scheduling from planning to operations[J]. European Journal of Operational Research,2007,183:1013～1027
[38]Dennis Huisman, Albert P. M. Wagelmans. A solution approach for dynamic vehicle and crew scheduling[J]. European Journal of Operational Research,2006, 172:453～471
[39]Goran Stojkovic, Francois Soumis, Jacques Desrosiers, Marius M. Solomon. An optimization model for a real-time flight scheduling problem[J]. Transportation Research Part A,2002,36:779～788
[40]Christos Goumopoulos, Efthymios Housos. Efficient trip generation with a rule modeling system for crew scheduling problems[J]. The Journal of Systems and Software,2004,69:43～56
[41]H. Timucin Ozdemir, Chilukuri K. Mohan. Flight graph based genetic algorithm for crew scheduling in airlines[J]. Information Sciences,2001,133:165～173
[42]Guy Desaulniers. Managing large fixed costs in vehicle routing and crew scheduling problems solved by column generation[J]. Computers & Operations Research,2007,34:1221～1239
[43]Gunther Zapfel, Michael Bogl. Multi-period vehicle routing and crew scheduling with outsourcing options[J]. Int. J. Production Economics,2008,113:980～996
[44]Marta Mesquita, Ana Paias. Set partitioning, covering-based approaches for the integrated vehicle and crew scheduling problem[J]. Computers & Operations Research,2008,35:1562～1575
[45]Hai D. Chu, Eric Gelman, Ellis L. Johnson. Solving large scale crew scheduling problems[J]. European Journal of Operational Research,1997,97:260～268
[46]B.L. Hollis, M.A. Forbes, B.E. Douglas. Vehicle routing and crew scheduling for metropolitan mail distribution at Australia Post[J]. European Journal of Operational Research,2006,173:133～150
[47]Angelo Monfrogliot. Hybrid heuristic algorithms for set covering[J]. Computers Ops Res,1998,25(6):441～455
[48]段华斌,陈林.关于机车交路与乘务员乘务方式的探讨[J].内燃机车,2003,(2)：21-22,29
[49]马国忠,张展杰,吴海涛.长交路下铁路机车乘务模式研究[J].交通运输工程与信息学报,2007,5(4)：1-5,28
[50]王文元.机车乘务员一次乘务作业过程标准浅析[J].铁道技术监督,1999,2：15-18
[51]徐忠,袁双喜.实施长交路轮乘制机车交路方式的思考[J].华东交通大学学报,2004,21(6)：30-33
[52]丁子全.青藏线格拉段机车乘务制度采用随乘制设计探讨[J].铁道机车车辆2002年增刊
[53]姚汤伟.客运机车“乘务加强机班”模式的实践[J].铁道运输与经济,2005,29(5)：33-35
[54]侯海波.关于机车乘务员乘务方式改革的探讨[J].铁道技术监督,2004,8：19-20
[55]张春明.实行机车长交路轮乘制的实践[J].铁道运输与经济,2004,26(4)：34-35
[56]赵鹏,胡安洲,杨浩.机车乘务员运用计划的优化编制[J].铁道学报,1998,20(4)：8-12
[57]赵鹏,姚凤金,张洪亮.综合调度仿真系统中的机车乘务计划的编制[J].铁道运输与经济,2005,27(3)：74-76
[58]于得水.客运专线乘务计划编制系统的设计与实现[D].西南交通大学硕士学位论文.2004
[59]夏平.客运专线乘务员运用计划编制研究[D].北京交通大学硕士学位论文.2007.
[60]程岩岩.我国铁路乘务调度计划编制方法的研究与设计[D].北京交通大学硕士学位论文.2007
[61]王莹,刘军,苗建瑞.客运专线乘务交路计划编制的优化模型与算法[J].铁道学报,2009,31(1)：15-19
[62]银大伟.乘务计划编制系统的研究与设计[D].西南交通大学硕士学位论文.2008,6
[63]李献忠,徐瑞华.基于乘务广义费用的城市轨道交通排班[J].同济大学学报(自然科学版),2007,35(6)：750-754
[64]李文慧.匈牙利方法在铁路列车乘务组分派问题中的应用[J].兰州交通大学学报(自然科学版),2007,26(3)：55-57
[65]李献忠,徐瑞华.城市轨道交通乘务值乘方式的模糊综合评价法[J].学术专论,2006,9：41-43
[66]陈林,王诚东.客运专线乘务组织模式及交路方案设置的构想[J].交通运输工程与信息学报,2010,8(1)：30-34
[67]王媛媛,周成晨,倪少权.基于蚁群算法的客运专线乘务交路计划编制方法研究[J].铁路计算机应用,2009,18(7)：11-14
[68]纪殿瑜,王建英,霍黎明.乘务计划编制系统研究[J].铁路计算机应用,2009,18(10)：29-31
[69]阎永光,黄斌.广深线城际列车乘务组排班计划编制方法探讨[J].交通运输工程与信息学报,2010,8(1)：25-29
[70]李青,张军,张学军.解决排班问题的多目标优化模型及算法研究[J].北京航空航天大学学报,2003,29(9)：821-824
[71]孙宏.航空公司飞机排班问题：模型及算法研究[D].西南交通大学博士学位论文.2003
[72]饶云波.航空公司乘务员排班系统的优化算法[D].电子科技大学硕士学位论文.2006
[73]李志荣,张兆宁.基于蚁群算法的航班着陆排序[J].交通运输工程与信息学报,2006,4(2)：66-69
[74]王元崑.基于蚁群算法的大型航空公司机群排班系统的设计与实现[D].中国民航大学硕士学位论文.2007
[75]魏云飞.遗传算法在人员排班问题上的应用研究[D].浙江工业大学硕士学位论文.2005
[76]赵焕省.航班机组排班算法及应用技术研究[D].南京航空航天大学硕士学位论文.2007,1
[77]铁科院联合体.客运专线运营调度系统集成投标文件,第三卷.2005
[78]张骥翼,杨宏图.从日本铁路看中国铁路客运专线运营调度系统的建设[J].铁 道运输与经济,2006,28(9)：29-31,34
[79]王莹.动车组运用计划和乘务计划的优化方法研究[D].北京交通大学博士学位论文.2009,2
[80]王甦男.旅客运输.第二版[M].北京：中国铁道出版社,2003
[81]杨浩,何世伟.铁路运输组织学.第一版[M].北京：中国铁道出版社,2001
[82]李力.高速铁路旅客列车开行方案研究[D].西南交通大学硕士学位论文.2010
[83]杨晓.客运专线旅客列车开行方案研究[D].北京交通大学硕士学位论文.2008
[84]赵鹏,张迦南.铁路动车组的运用问题研究[J].北京交通大学学报,2009,33(3)：6-10,16
[85]耿敬春.京沪高速铁路动车组运用计划编制相关问题研究[D].西南交通大学硕士学位论文.2009,11
[86]铁道部运输局.既有线提速200KM/h行车组织[M].北京：中国铁道出版社,2007,1
[87]韩伯领,田长海,王钰滨.客运专线综合维修天窗形式比较[J].中国铁道科学,2009,30(5)：95-99
[88]彭进,崔之川.铁路客运组织.第一版[M].北京：中国铁道出版社,2007
[89]C. Barnhart and G. Laporte (Eds.).Handbook in OR & MS[M], Vol.14,2007: 129～187
[90]卢开澄,卢华明.图论及其应用[M].北京：清华大学出版社,1995,8
[91]邢文训,谢金星.现代优化计算方法[M].北京：清华大学出版社,2005
[92]Hertz A, de Werra D. The tabu search metaheuristic:how we use it[J]. Annals of Mathematics and Artificial Intelligence,1990,1:111121
[93]Hurink J, Jurisch B, Thole M. Tabu search for the job-shop scheduling problem with multi-purpose machines[J]. OR Spektrum,1994,15:205～215
[94]黄友锐.智能优化算法及其应用[M].北京：国防工业出版社,2008
[95]王凌.智能优化算法及其应用[M].北京：清华大学出版社,2001
[96]沈冰.模拟退火算法在板式家具优化下料中的研究与应用[D].东北林业大学硕士学位论文.2007,4
[97]宋静波.基于混合模拟退火算法的航空公司勤务排班算法研究[D].南京航空航天大学硕士学位论文.2009,1
[98]刘晓莹.基于改进模拟退火算法的给水管网改扩建优化规划[D].合肥工业大学硕士学位论文.2009,4
[99]高珊.基于改进的模拟退火算法的自主移动机器人路径规划的研究[D].中国海洋大学硕士学位论文.2009,6
[100]辛振铭.一种改进的模拟退火算法在TSP问题中的研究与应用[D].东北师范大学硕士学位论文.2010,5
[101]何敬宇.模拟退火算法在边坡稳定分析中的应用研究[D].内蒙古工业大学硕士学位论文.2007,4
[102]潘攀.基于模拟退火算法的接近式紫外光刻误差修正的研究[D].中国科学技术大学硕士学位论文.2010,5
[103]姜蓉.基于模拟退火算法的贷款组合优化研究[D].湖南大学硕士学位论文.2003,10
[104]杜维.基于模拟退火算法的地图点状要素注记配置研究[D].武汉大学硕士学位论文.2005,5
[105]玄光男,程润伟.遗传算法与工程优化[M].北京：清华大学出版社,2004
[106]张文修,梁怡.遗传算法的数学基础[M].西安：西安交通大学出版社,2000
[107]张顶学.遗传算法与粒子群算法的改进及应用[D].华中科技大学博士学位论文.2007,11
[108]DorigoM. Optimization Learning and Natural Algorithms[D]. Ph.D. Thesis. Department of Electronics, Politecnico diMilano, Italy,1992.
[109]Dorigo, M., & Gambardella, L.M. Ant colonies for the traveling salesman problem[J]. BioSystems,1997a,43(2):73～81
[110]Dorigo, M., Maniezzo, V., Colorni, A. Ant System: Optimization by a colony of cooperating agents[J]. IEEE Transactions on Systems, Man, and Cybernetics-Part B,1996,26:29～41
[111]段海滨.蚁群算法原理及其应用[M].北京：科学出版社,2005
[112]马良,朱刚,宁爱兵.蚁群优化算法[M].北京：科学出版社,2008,2
[113]李士勇.蚁群优化算法及其应用[M].哈尔滨：哈尔滨工业大学大学出版社,2005
[114]闻育.复杂多阶段动态决策的蚁群优化方法及其在交通系统控制中的应用[D].浙江大学博士学位论文.2004,4
[115]张军.蚁群优化[M].北京：清华大学出版社,2007
[116]江迎春.改进的蚁群算法在TSP问题上的应用[D].中南民族大学硕士学位论文.2009,5
[117]徐红梅,陈义保,刘加光,王燕涛.蚁群算法中参数设置的研究[J].山东理工大学学报(自然科学版),2008,22(1)：7-11
[118]刘彦鹏.蚁群优化算法的理论研究及其应用[D].浙江大学博士学位论文.2007,4
[119]程世娟.改进蚁群算法及其在结构系统可靠性优化中的应用[D].西南交通大学博士学位论文.2009,4
[120]高小永.基于多目标蚁群算法的土地利用优化配置[D].武汉大学博士学位论文.2010,5
[121]高尚.蚁群算法理论、应用及其与其它算法的混合[D].南京理工大学博士学位论文.2005
[122]Bullnheimer, B., Hartl, R. F., & Strauss, C. A new rank-based version of the Ant System:A computational study[J]. Central European Journal for Operations Reasearch and Economics,1999c,7(1):25-38
[123]Stiitzle, T., & Hoos, H. H. Improving the Ant System:A detailed report on the MAX-MIN Ant System[R]. Technical report AIDA-96-12, FG Intellektik, FB Informatik, TU Darmstadt, Germany,1996
[124]杨剑锋.蚁群算法及其应用研究[D].浙江大学博士学位论文.2007,4
[125]吕勇.蚁群优化算法及在网络路由中的应用研究[D].浙江大学博士学位论文.2005,10
[126]李伟.改进型蚁群算法及其应用研究[D].太原理工大学硕士学位论文.2008
[127]Wu B. An introduction to neural networks and their applications in manufacturing[J]. Journal of Intelligent Manufacturing,1992,3:391-403
[128]杨行峻,郑君里.人工神经网络[M].北京：高等教育出版社,1992
[129]张青贵.人工神经网络导论[M].北京：中国水利水电出版社,2004
[130]曾建潮.微粒群算法[M].北京：科学出版社,2004
[131]王凌,刘波.微粒群优化与调度算法[M].北京：清华大学出版社,2008
[132]寇晓丽.群智能算法及其应用研究[D].西安电子科技大学博士学位论文.2009,1
[133]卜月华.图论及其应用[M].南京：东南大学出版社,2002
[134]北京铁路局.CRH3型动车组司机一次乘务作业标准(试行).2008,7
[135]张先迪,李正良.图论及其应用[M].北京：高等教育出版社,2005,2
[136]钱颂迪.运筹学[M].北京：清华大学出版社,1990,1
[137]陈宝林.最优化理论与算法[M].北京：清华大学出版社,2005
[138]黄红选,韩继业.数学规划[M].北京：清华大学出版社,2006,3
[139]王宇嘉.多目标粒子群优化算法的全局搜索策略研究[D].上海交通大学博士学位论文.2008,12
[140]徐玖平,李军.多目标决策的理论与方法[M].北京：清华大学出版社,2005,3
[141]沈佳铭,洪亮,石春琦,等.一种可重构的24bit∑△调制器的设计[J].微电子学与计算机,2007,24(4)：159-162
[142]梁耀,覃征,杨利英,黄茹.指派问题的变异蚁群算法求解[J].微电子学与计算机,2005,22(6)：80-83
[143]卢开澄,卢华明.组合数学[M].北京：清华大学出版社,2002
[144]郑丽英.计算机算法设计与分析[M].北京：中国铁道出版社,2009,6
[145]周培德.计算几何：算法设计与分析[M].北京：清华大学出版社,2005,4
[146]章庆辉Y3V3-free图的哈密尔顿问题[D].山东师范大学硕士学位论文.2006,10
[147]宁万涛Johnson图的连通度、割集和哈密尔顿圈[D].兰州大学硕士学位论文.2008,5