基于智能优化算法的快速公交（BRT）线网规划与发车频率优化研究
|
摘要
目前,我国快速公交建设已经进入从导入期到成长期的发展阶段。快速公交系统规划、建设、运营管理逐渐得到了包括城市规划部门和公交运营部门在内的全社会范围的广泛关注。近年来新兴的智能优化算法的发展和应用,为解决快速公交系统的规划和发车频率优化提供了新的思路。本文在传统的普通公交系统的规划和发车频率优化的基础上,考虑到快速公交有别于普通公交的一些技术特性,应用智能优化新技术,针对快速公交系统的线网规划、战略层面的发车频率优化、战术层面的发车频率优化、战术层面的组合线路发车优化等问题进行了研究,概括起来,本文的工作主要包括以下几部分:
1)考虑快速公交线网规划问题的特点,建立了一类直达乘客量最大化的BRT网络规划问题数学模型。并设计了求解该模型的禁忌算法,对算例进行仿真计算。该算法采用自然数编码,通过起、终点的配对及路线的生成以及路线车辆数的分配两个阶段构造初始解,设计了线路选取和车辆分配两种邻域分别对BRT线路以及发车频率进行操作。结合惩罚函数和邻域操作两种方法来处理各种约束。对有20个站点的BRT网络的线路规划进行了仿真试验。并通过调整算法的技术参数、确定参数重复计算等手段对仿真结果进行深入分析。
2)针对快速公交客流在一个运营日中客流分布呈现“双驼峰”的特点,适时地调整分时段的发车频率,以保证运能的合理配置。在战略规划的层面上,主要从快速公交作为一个低收费的公共服务的角度分析问题,针对此类问题构建了兼顾公交公司和乘客双方利益的数学模型,并设计了求解该问题的遗传算法。遗传算法通过改进的交叉、变异操作设计等内容,对该类问题算例进行了仿真优化研究,同时还通过改变乘客等车时间权值,将优化结果与按客流比例发车情况下的结果进行对比分析等手段分析仿真影响因素和仿真效果。
3)从快速公交公司作为一个独立运营经济实体角度出发,研究了公交运营规划的战术层面上发车频率优化设计问题,这样就考虑了快速公交与其他交通方式的客流竞争关系。根据票价、车辆速度和发车频率计算网络的交通广义出行费用,采用改进的logit分配法对路段的客流进行分配。对存在竞争关系的BRT发车频率优化问题构建了数学模型,设计了求解该模型的禁忌算法。禁忌算法采用自然数编码,把每天公交车的运行时间分成多个时间段。每一条公交线每时段的发车频率代表一个子解,所有子解组合成BRT发车频率优化问题的解。把违反站点最大通行能力约束和违反最大时间等待乘客比例约束作为惩罚项加入到目标函数中。采用发车频率之间的移动和时段发车频率独立移动两种邻域操作。并且通过算法灵敏度分析,优化前后的结果对比,问题灵敏度分析等内容对仿真结果进行深入研究。
4)针对高峰时段经常出现的标准线路和大站快线组合发车的情况,考虑到与其他交通方式,主要是普通公交的客流竞争关系,从公交公司经营者的角度,在公交运营战术规划的层面上进行组合发车频率的优化。针对该类问题,建立了在保证一定服务水平的前提下追求公交公司经营利益的最大化的数学模型。结合禁忌算法和模拟退火算法二者的优点,提出了求解该模型的一种基于禁忌规则的模拟退火算法。在算法设计中,采用0-1编码表示快速线路站点集合,用自然数编码表示标准线路、快速线路的发车频率。根据BRT线路组合优化的特点,设计了单点取反、2-swap交换和单点增减三种邻域状态生成函数及相应的2-swap禁忌表和单点禁忌表,对组合线路算例进行优化仿真研究,并与单一算法的研究结果进行对比分析。
Presently the Bus Rapid Transit in China has shifted into the growing-up stage from the beginning. The plan, construction and operation of BRT have been the focus of the many sectors including urban plan bureau and public transit corporation. In recent years, intelligent optimization algorithms have been newly developed and applied in solving the problems of BRT plan and frequency optimization. In this dissertation, the difference between BRT and traditional transit being considered, there are the researches on BRT network optimization, frequency optimization of stratagem, frequency optimization of tactics,combined routes optimization, etc.
The main contents are as follows.
1. A kind of BRT networks plan models for nonstop passenger flow maximization based on the problem characteristics is given. A tabu search algorithm as the solution is designed. The algorithm applies the coding by natural number to OD match, routes generation and vehicle numbers assignment to get original solution. And routes choosing and vehicle assignment respectively do with BRT routes and frequency with penalty function and neighborhood operation to resolve restrictions. In this part, a network planning with 20-stop BRT is simulated. Algorithm parameter regulation and repetition calculation are done for analyses.
2. The BRT passenger flow distribution in one day is as Double-Peak, and the frequency in different periods must be adjusted for reasonable configuration of transportation capacity from the angel of stratagem planning, so a model considering the benefits of operator and passengers is built and the improved Genetic Algorithm for the problem is given. Simulation optimization based on the genetic algorithm is designed through betterment crossover and mutation operation. A simulation optimization research is given in which the effect of waiting time weight value to the result is as an analysis.
3. From the angle of Transit Company as an economic entity, the competition between BRT and other transit mode is considered. Based on the calculation of cost function by ticket price, vehicle speed and frequency, an improved logit assignment method is applied to optimize the frequency and maximize the transit company benefit to keep the passengers’satisfaction service level. A mathematical model and solution algorithm based on tabu algorithm is designed for the transit dispatching with competition. In the tabu algorithm, nature coding is designed to divide one day into multiple periods so as to cut the solution set to parts according to the periods. And constrains of shift between different frequencies and unique shift are operated as two neighborhoods. Without change of fundamental parameters, vehicle speed and ticket price are changed to influence the simulation results.
4. For the standard routes and pass-by bus combination, considering the competition from other modes, especially traditional transit, it is to optimize the frequency and maximize the transit company benefit for keeping the passengers’satisfation service level. Based on the characteristics of the problem, simulated annealing algorithm is combined with tabu search algorithm to optimize the frequency of BRT line combination. The combined tabu-simulated-annealing algorithm applies 0-1 coding to represent pass-by stops set and natural number to represent standard routes and frequency. According to BRT combined routes characteristic, the neighbor states of back single point, 2-swap exchange and add-cut single point are designed with 2-swap tabu table and single point tabu table. Then optimization simulation research is given for combined routes.
1)考虑快速公交线网规划问题的特点,建立了一类直达乘客量最大化的BRT网络规划问题数学模型。并设计了求解该模型的禁忌算法,对算例进行仿真计算。该算法采用自然数编码,通过起、终点的配对及路线的生成以及路线车辆数的分配两个阶段构造初始解,设计了线路选取和车辆分配两种邻域分别对BRT线路以及发车频率进行操作。结合惩罚函数和邻域操作两种方法来处理各种约束。对有20个站点的BRT网络的线路规划进行了仿真试验。并通过调整算法的技术参数、确定参数重复计算等手段对仿真结果进行深入分析。
2)针对快速公交客流在一个运营日中客流分布呈现“双驼峰”的特点,适时地调整分时段的发车频率,以保证运能的合理配置。在战略规划的层面上,主要从快速公交作为一个低收费的公共服务的角度分析问题,针对此类问题构建了兼顾公交公司和乘客双方利益的数学模型,并设计了求解该问题的遗传算法。遗传算法通过改进的交叉、变异操作设计等内容,对该类问题算例进行了仿真优化研究,同时还通过改变乘客等车时间权值,将优化结果与按客流比例发车情况下的结果进行对比分析等手段分析仿真影响因素和仿真效果。
3)从快速公交公司作为一个独立运营经济实体角度出发,研究了公交运营规划的战术层面上发车频率优化设计问题,这样就考虑了快速公交与其他交通方式的客流竞争关系。根据票价、车辆速度和发车频率计算网络的交通广义出行费用,采用改进的logit分配法对路段的客流进行分配。对存在竞争关系的BRT发车频率优化问题构建了数学模型,设计了求解该模型的禁忌算法。禁忌算法采用自然数编码,把每天公交车的运行时间分成多个时间段。每一条公交线每时段的发车频率代表一个子解,所有子解组合成BRT发车频率优化问题的解。把违反站点最大通行能力约束和违反最大时间等待乘客比例约束作为惩罚项加入到目标函数中。采用发车频率之间的移动和时段发车频率独立移动两种邻域操作。并且通过算法灵敏度分析,优化前后的结果对比,问题灵敏度分析等内容对仿真结果进行深入研究。
4)针对高峰时段经常出现的标准线路和大站快线组合发车的情况,考虑到与其他交通方式,主要是普通公交的客流竞争关系,从公交公司经营者的角度,在公交运营战术规划的层面上进行组合发车频率的优化。针对该类问题,建立了在保证一定服务水平的前提下追求公交公司经营利益的最大化的数学模型。结合禁忌算法和模拟退火算法二者的优点,提出了求解该模型的一种基于禁忌规则的模拟退火算法。在算法设计中,采用0-1编码表示快速线路站点集合,用自然数编码表示标准线路、快速线路的发车频率。根据BRT线路组合优化的特点,设计了单点取反、2-swap交换和单点增减三种邻域状态生成函数及相应的2-swap禁忌表和单点禁忌表,对组合线路算例进行优化仿真研究,并与单一算法的研究结果进行对比分析。
Presently the Bus Rapid Transit in China has shifted into the growing-up stage from the beginning. The plan, construction and operation of BRT have been the focus of the many sectors including urban plan bureau and public transit corporation. In recent years, intelligent optimization algorithms have been newly developed and applied in solving the problems of BRT plan and frequency optimization. In this dissertation, the difference between BRT and traditional transit being considered, there are the researches on BRT network optimization, frequency optimization of stratagem, frequency optimization of tactics,combined routes optimization, etc.
The main contents are as follows.
1. A kind of BRT networks plan models for nonstop passenger flow maximization based on the problem characteristics is given. A tabu search algorithm as the solution is designed. The algorithm applies the coding by natural number to OD match, routes generation and vehicle numbers assignment to get original solution. And routes choosing and vehicle assignment respectively do with BRT routes and frequency with penalty function and neighborhood operation to resolve restrictions. In this part, a network planning with 20-stop BRT is simulated. Algorithm parameter regulation and repetition calculation are done for analyses.
2. The BRT passenger flow distribution in one day is as Double-Peak, and the frequency in different periods must be adjusted for reasonable configuration of transportation capacity from the angel of stratagem planning, so a model considering the benefits of operator and passengers is built and the improved Genetic Algorithm for the problem is given. Simulation optimization based on the genetic algorithm is designed through betterment crossover and mutation operation. A simulation optimization research is given in which the effect of waiting time weight value to the result is as an analysis.
3. From the angle of Transit Company as an economic entity, the competition between BRT and other transit mode is considered. Based on the calculation of cost function by ticket price, vehicle speed and frequency, an improved logit assignment method is applied to optimize the frequency and maximize the transit company benefit to keep the passengers’satisfaction service level. A mathematical model and solution algorithm based on tabu algorithm is designed for the transit dispatching with competition. In the tabu algorithm, nature coding is designed to divide one day into multiple periods so as to cut the solution set to parts according to the periods. And constrains of shift between different frequencies and unique shift are operated as two neighborhoods. Without change of fundamental parameters, vehicle speed and ticket price are changed to influence the simulation results.
4. For the standard routes and pass-by bus combination, considering the competition from other modes, especially traditional transit, it is to optimize the frequency and maximize the transit company benefit for keeping the passengers’satisfation service level. Based on the characteristics of the problem, simulated annealing algorithm is combined with tabu search algorithm to optimize the frequency of BRT line combination. The combined tabu-simulated-annealing algorithm applies 0-1 coding to represent pass-by stops set and natural number to represent standard routes and frequency. According to BRT combined routes characteristic, the neighbor states of back single point, 2-swap exchange and add-cut single point are designed with 2-swap tabu table and single point tabu table. Then optimization simulation research is given for combined routes.
引文
[1] 陈爱萍, 快速公交规划的基本问题研究:[硕士学位论文],西安;长安大学,2004
[2] 王海娟,孙尧,对城市交通拥堵问题及其对策的思考, 北京汽车,2002(2):12-14
[3] 朱俭松,大城市客运交通发展方向,北京:中国建筑工业出版社,1998
[4] 李 云 燕 , 徐 康 明 , 快 速 公 交 系 统 成 长 为 一 种 新 型 交 通 模 式 ,http://blog.sina.com.cn/u/591971ab010003k0
[5] 原永静,快速公交系统(BRT)站点布局优化问题研究:[硕士学位论文],西安;长安大学,2005
[6] 王延娟,快速公交系统线路组合问题研究:[硕士学位论文],西安;长安大学,2005
[7] 雷军,重庆巴士快速交通项目研究报告:[硕士学位论文],重庆;重庆大学,2005
[8] 张志荣,都市捷运:规划与设计,台北:台北市三民书局,2001
[9] 张志荣,都市捷运:发展与运用,天津:天津大学出版社,2002
[10] 魏中华,任福田,中国城市快速公交系统(BRT)发展探讨,城市规划年会论文集,2004
[11] 李骏,快速公交与城市用地互动关系的探索和研究:[硕士学位论文],杭州:浙江大学,2005
[12] 于星涛,快速公交系统规划研究-以济南市为例:[硕士学位论文],上海:同济大学,2006
[13] 金凡,快速公交(BRT)在中国的发展,国外城市规划,2006,21(3):3-28
[14] 贾倩,BRT 在中国城市交通中的地位与发展战略探讨,城市公共交通,2005(3):19-23
[15] 戴帅,魏中华,BRT 在大城市公交系统中的功能定位分析,道路交通与安全,2006, 6(7):31-34
[16] 王风武,对中国发展快速公交的认识,城市交通,2006,4(6):26-28
[17] 赵杰,快速公交的规划和应用前景,城市车辆,2006,12(6):25-26
[18] 邹哲,徐康明,李科,快速公共汽车运营系统-面向可持续发展的城市交通发展战略选择,城市,2003,6(4):24-27
[19] 孟庆和,李大龙,快速公交的特点及应用,农业装备与车辆工程,2006,24(8):42-52
[20] 李玉辉,戈春珍,胡金成,快速公交系统(BRT)在我国的发展研究,辽宁交通科技,2006, 12(4):75-77
[21] 陈明明,牛惠民,快速公交系统及评价问题的研究,兰州交通大学学报(自然科学版) ,2006,25(4):113-117
[22] 罗大明,季晓京,北京南中轴路快速公交(BRT)智能公交系统总体设计概要,交通运输系统工程与信息,2005,5(2):97-98
[23] 闫雅彬,北京 BRT 的建设与发展,城市车辆,2006,10(2):26-27
[24] 周毅,关于中国 BRT 的探讨,交通世界,2006,42(10):68-69
[25] 国务院发展研究中心,长安大学 BRT 研究中心,西安市发展快速公交系统技术报告,2005
[26] 王骏阳,库里蒂巴与可持续发展规划,国外城市规划,2000,10(4):9-12
[27] 赵杰,胡子祥,刘丽亚,国外发展快速公交的经验及对我国城市交通发展的启示,城市交通,2004,2(3):56-59
[28] 学会秘书处,BRT 专题介绍,城市公共交通,2005,5(10):23-26
[29] 杨兆升,城市智能公共交通系统理论与方法,北京:中国铁道出版社,2003
[30] Newell G..F,Some issues related to the optimal design of bus Transportation Science,1979,13:20-35.
[31] 高自友,张好智,孙会君,城市交通网络设计问题中双层规划模型,方法及应用,交通运输系统工程与信息,2004,4(1):35-44
[32] Scheele S.A , Supply Model for Public Transit Services.Transportation Research-B,1980(14):133-146
[33] Koutsopoulos H.N,Odoni A,Determination of Headways as a Function of Time Varying Characteristics on a Transit Network. In Cmputer Scheduling of Public Transport 2,North-Holland,Amsterdam,1985:391-414
[34] Shih M.C , Mahmassani H.S , Vehicle Sizing Model for Bus Transit Networks.Transportation Research Record,1995:35-41
[35] 孙芙灵,公交调度中发车间隔的确定方法的探讨,西安公路交通大学学报,1997,2(6):44-48
[36] 杨超,李彬,城市公共交通线网优化的图论模型与算法,同济大学学报.1998,1(5):29-32
[37] 王炜,数学规划方法在公交网络优化中的应用,系统工程,1999,8(3):42-49
[38] 常玉林,胡启洲,城市公交线网优化的线性模型,中国公路学报,2005,18(1):95-98
[39] Lamnkin,Saatmans,The Design of Routes,Transportation Research,1967
[40] Hirsch,Dantzig,The Fixed Charge Problem,Rand Co,1968
[41] 陈茜,牛学勤,陈学武,王炜,公交线路发车频率优化模型,公路交通科技,2004,21(2):103-105
[42] 吕鹏,张文夫,公交车调度,工程数学学报,2002,19(F02):75-80
[43] D.Dubois,G.Bel,M.Llibre,A Set of Methods in Transportation Network Synthesis and Analysis,The Journal of the Operational Research Society, 1979:797-808
[44] 王炜,城市道路交通规划理论:[博士学位论文],南京;东南大学,1989
[45] 刘清,衷仁保,朱志勇,谢磊,实现城市公交线网优化的数学模型和广义A*算法,系统工程理论与实践,1992,10(2):12-17
[46] Zhu w,Trip frequency scheduling for terminal quening routers,Proceedings of 7th IFAC/IFORS Symposium on Transportation Systems,1994:70-77
[47] Baaj M.H,Mahmassani H.S,Hybrid route generation heuristic algorithm for the design of transit networks,Transportation Research C3,1995:31-50
[48] 单连龙,高自友,城市公交系统连续平衡网络设计的双层规划模型及求解算法,系统工程理论与实践,2000,15(7):85-93
[49] Ali Haghani,Mohamadreza Banihashemi,Heuristic approaches for solving large-scale bus transit vehicle scheduling problem with route time constraints,Transportation Research Part A,2002:309-333.
[50] 于滨,杨忠振,程春田,左志,公交线路发车频率优化的双层规划模型及其解法,吉林大学学报,2006,36(5):664-668
[51] 闫小勇,牛学勤,公交网络多路径选择启发式算法研究,城市交通,2005,3(3):23-26
[52] 刑文训,谢金星,现代优化计算方法,北京:清华大学出版社,1999
[53] Glover F ,Future paths for integer programming and links to artificial intelligence ,Computers and Operations Research,1986(13):533-549
[54] Cavique L,Rego C,Themido I.,Subgraph ejection chains and tabu search for the crew scheduling problem,Journal of the operational Research Society,1999:608-616
[55] Shen Y,Tabu Search for Bus and Train Driver Scheduling With TimeWindows[D],2001 PhD thesis,University of Leeds,UK
[56] Wei Fan,Randy B,Machemehl,A tabu search based heuristic method for the transit route network design problem , CASPT 2004 9th International Conference on Computer-Aided Scheduling of Public Transport,San Diego,California,2004
[57] 白子建,赵淑芝,田振中,公共交通网络优化的禁忌算法设计与实现,吉林大学学报(工学版),2006,36(3):40-44
[58] 沈吟东,倪郁东,基于禁忌搜索的公交调度计划系统,城市公共交通,2006,24(9):21-24
[59] Kirkpatrick S,Gelatt C D,Vecchi M P,Optimization by simulated annealing,Science,1983:671-680
[60] Kirkpatrick S,Gelatt C D ,Vecchi M P, Optimization by simulated annealing,Science,1983:377-383
[61] 蔡延光,钱积新,多重运输调度问题的模拟退火算法,系统工程理论与实践,1998,18(10):11-15
[62] 林柏梁,杨富社,出行费用最小化的公交网络优化模型,中国公路学报,1999,12(1),79-83
[63] Fang Zhao,Ike Ubaka,Optimization of Transit Network to Minimize Transfers and Optimize Route Directness,Journal of Public Transportation,2004(1):63-82
[64] 李铭,李旭宏,公交枢纽内始发线路优化配置模型及其模拟退火算法,可持续发展的中国交通,2005 全国博士生学术论坛
[65] Holland J.H,Adaptation in natural and artificial systems,MI:University of Michigan Press,1985
[66] Davis L,Handbook of genetic algorithm,New York:Van Nostrand Reinhold,1991
[67] Androulakis I.P,Venkatasubramanlan V,A genetic algorithm framework for process design and optimization,Computer Chen Engng,1991,15(4):217-228
[68] 刘勇,康立山,陈毓屏,非数值并行算法-遗传算法,北京:科学出版社,1998
[69] Brindle A , Genetic algorithms for function optimization , Ph DDissertation.Alberta:University of Alberta,1981
[70] Chakroborty P,Subrahmanyam P.S ,Optimal scheduling urban transit systems using genetic algorithms,Journal of Transportation Engineering,1995 :544-553
[71] Pattnaik S.B,Mohan S,Tom V.M,Urban Bus Transit Route Network Design Using Genetic Algorithm,Journal of Transportation Engineering,1998,124(4):368-375
[72] 孙艳丰,基于遗传算法的城市交通运输网优化问题研究,系统工程理论与实践,2000(3):34-37
[73] 钱大琳,离散非平衡公交网络优化模型及其求解算法,北方交通大学学报,2001(1):56-58
[74] 陈洪仁,分层限制的公交线网优化模型,哈尔滨建筑大学学报,2001(1):80-83
[75] 汤可夫,吴大为,基于改进遗传算法的公交线网整体优化方法,重庆交通学院学报,2004(4):22-25
[76] Ngamchai lovell,Agrawal Mathew Optimal Time Transfer in Bus Transit Route Network Design Using a Genetic Algorithm,Transportation Engineering,2003(5):510521
[77] 董刚,公交调度模型及算法,青岛科技大学学报,2004,25(3):1921
[78] Paul Forsyth,Anthony Wren,An ant system for bus driver scheduling, the 7th International Workshop on Computer-Aided Scheduling of Public Transport,Boston,1997
[79] 韩印,蚂蚁算法在智能公交网络优化中的应用研究,计算机工程与应用,2005,41(30):189191
[80] 王海星,申金升,智能蚁群算法解决公交区域调度问题研究,北京邮电大学学报,2006,29(2):3034
[81] 孙先仿,范跃祖,晏磊,张飞舟,智能交通系统中的运营车辆优化调度研究,北京航空航天大学学报,2002,6(2):1921
[82] 任传祥,张海,范跃祖,合遗传-模拟退火算法在公交智能调度中的应用,系统仿真学报,2005,17(9):20752077
[83] 于滨,城市公交系统模型与算法研究:[博士学位论文],大连;大连理工大学,2006
[84] Fang Zhao,Xiaogang Zeng,Simulated Annealing–Genetic Algorithm for Transit Network Optimization ,2006:57-68
[85] 于景飞,大城市常规公交线网优化方法研究及应用:[硕士学位论文],合肥;合肥工业大学,2005
[86] 李琼星,城市公交线网规划研究:[硕士学位论文] ,长沙;湖南大学,2002
[87] Hasselstro D,Public Transportation Planning- A Mathematical Programming Approach, Doctor Disstertation,University of Goteborg,Sweden,1981.
[88] Baaj M.H,Mahmassani H.S,Hybrid Route Generation Heuristic Algorithm for the Design of Transit Networks,Transportation Research-C,1995:1-50
[89] Dubois D,Bel G,Libre M,A Set of Methods in Transportation Network Synthesis and Analysis Journal of Operational Research Society,1979:797-808
[90] Ceder A,Wilson N.H.M,Bus Network Design , Transp. Res. Part B, 1986,20(1):331-344
[91] 杨兆升,城市智能公共交通系统理论与方法,北京:中国铁道出版社,2002
[92] 季利平,城市快速公交线网规划研究:[硕士学位论文] ,呼和浩特;内蒙古农业大学,2006
[93] 陈钦水,城市地面快速公交网络系统规划研究:[硕士学位论文] ,西安;西安建筑科技大学,2004
[94] 魏涛,快速公交系统通行能力分析:[硕士学位论文] ,长沙;长沙交通学院,2006
[95] 牟达,大连市快速公交规划及其效果评价:[硕士学位论文] ,大连;大连理工大学,2006
[96] 王炜,杨新苗,陈学武,城市公共交通系统规划方法与管理技术,北京:科学出版社,2002
[97] 刘灿齐,城市交通规划学,北京:人民交通出版社,2001
[98] Glover F,Tabu Search Part I,ORSA Journal on Computing,1989(1):190-206
[99] Glover F,Tabu Search Part II,ORSA Journal on Computing,1989(2):4-32
[100] Glover F,Luguna M.,Tabu Search Basel Switzerland,Science Publishers,1993
[101] 刘自发,基于智能优化算法的配电网络规划与优化运行研究:[博士学位论文] ,天津;天津大学,2005
[102] William H.K,Zhou Jing,Sheng Zhao-han,A capacity restraint transit assignment with elastic line frequency,Transportation Research Part B,2002,36(10):919-938.
[103] Jan Rong-hong , Chen Shiow-ling , Branch-and-bound algorithm for reliability-oriented task assignment in bus network systems , Journal of Information Science and Engineering,1994,10(1):81-97
[104] Maurizio Bielli , Massimiliano Caramia , Pasquale Carotenuto , Genetic algorithms in bus network optimization,Transportation Research Part C,2002,10(1):19-34
[105] Diaz R.B,Schneck D.C,Bus rapid transit technologies in the Americas,Transportation Research Record,2000:3-9
[106] Levinson H.S,Zimmerman S,Clinger J,Bus rapid transit:Synthesis of case studies,Transportation Research Record,2003:1-11
[107] Last A,Leak S.E,Transportation:a bus model,Traffic Engineering and Control,1976:14-20
[108] Current J,ReVelle C.S,Cohon J.L,The maximum covering shortest path problem:a multi-objective network design and routing formulation,European Journal of Operational Research,1985:189-199
[109] Furth P.G.,Optimal bus stop spacing through dynamic programming and geographic modeling.Transportation Research Record,2000:15-22
[110] 杨新苗,王炜,尹红亮,武勇,公交调度峰值曲线的优化方法,东南大学学报(自然科学版) ,2001,31(3):40-43
[111] Chien,Steven I,Optimization of bus stop locations for improving transit accessibility,Transportation planning and Technology,2004(6):211-227
[112] Herbert S.L,Scott R,Eric B,TCRP Report 90:Bus Rapid Transit,Transportation Research Board,2003
[113] Anthony A,Saka.Model for Determing Optimum Bus-Stop Spacing in Urban Areas,Journal of Transportation Engineering,2001,127(3):195-199
[114] Holland,J.H,Adaptation in natural and artificial systems:An introductory analysis with applications to biology,MI:The University of Michigan Press,1975
[115] Booker L.B,Goldberg D.E, Holland J.H,Classifier Systems and Genetic Algorithms,Articifial Interlligence,1989:235-282
[116] M ichalewiez Z,Janidow C, Brawezyd J,A Modified Genetic Algorithm for Optimal Control Problem ,Computers Math Application ,1992 (12):83-94
[117] Davis L,Handbook of genetic algorithms,Van Nostrand Reinhold,New York,1991
[118] Michalewica Z,Genetic algorithms + data structure = evolution programs,3rd edition,New York:springer-Verlag,1996
[119] 王鹏飞,智能公交之车辆人员排班算法的研究与应用:[硕士学位论文],济南;山东大学,2004
[120] 徐康明,波哥大快速公交系统创收支平衡,2003 年 2 月:原稿 By GeorgeG.Wynne,Director,International Programs
[121] Transportation Research Board,National Research Council ,Bus Rapid Transit Case Sudies in Bus Rapid Transit,Washington DC,2003:48-53
[122] 王凌,智能优化算法及其应用,北京:清华大学出版社,2002
[123] Hanafi S,On the Convergence of Tabu Search,Journal of Heuristic,2000,7:47-58
[124] WEN Fu-shuan,Chang C.S, A tabu search approach for fault section estimation and state identification of unobserved protective relays in power systems,Proceedings of 1996 international conference on intelligent systems applications to power systems,Korea Seoul,1996:341-347
[125] Glover F,Kochenberger G.A ,Alidaee B,Adaptive memory tabu search for binary quadratic programs,Management Science,1998,44(3):336-345
[126] 康立山,谢云,非数值并行算法-模拟退火算法,北京:科学出版社,1998
[127] 姚新,陈国良,模拟退火算法及其应用,计算机研究与发展,1990
[128] 刘岩,韩承德,王义和,模拟退火的背景与单调升温的模拟退火算法,计算机研究与发展,1996,33(1):4-10
[129] 王凌,郑大钟,模拟退火算法求解 Flow Shop 问题的研究,中国控制与决策学术年会,沈阳:东北大学出版社,1997
[130] Park M,Kim Y,A systematic procedure for setting parameters in simulated annealing algorithms,Computers & Operations Research,1998,25(3):207-217
[2] 王海娟,孙尧,对城市交通拥堵问题及其对策的思考, 北京汽车,2002(2):12-14
[3] 朱俭松,大城市客运交通发展方向,北京:中国建筑工业出版社,1998
[4] 李 云 燕 , 徐 康 明 , 快 速 公 交 系 统 成 长 为 一 种 新 型 交 通 模 式 ,http://blog.sina.com.cn/u/591971ab010003k0
[5] 原永静,快速公交系统(BRT)站点布局优化问题研究:[硕士学位论文],西安;长安大学,2005
[6] 王延娟,快速公交系统线路组合问题研究:[硕士学位论文],西安;长安大学,2005
[7] 雷军,重庆巴士快速交通项目研究报告:[硕士学位论文],重庆;重庆大学,2005
[8] 张志荣,都市捷运:规划与设计,台北:台北市三民书局,2001
[9] 张志荣,都市捷运:发展与运用,天津:天津大学出版社,2002
[10] 魏中华,任福田,中国城市快速公交系统(BRT)发展探讨,城市规划年会论文集,2004
[11] 李骏,快速公交与城市用地互动关系的探索和研究:[硕士学位论文],杭州:浙江大学,2005
[12] 于星涛,快速公交系统规划研究-以济南市为例:[硕士学位论文],上海:同济大学,2006
[13] 金凡,快速公交(BRT)在中国的发展,国外城市规划,2006,21(3):3-28
[14] 贾倩,BRT 在中国城市交通中的地位与发展战略探讨,城市公共交通,2005(3):19-23
[15] 戴帅,魏中华,BRT 在大城市公交系统中的功能定位分析,道路交通与安全,2006, 6(7):31-34
[16] 王风武,对中国发展快速公交的认识,城市交通,2006,4(6):26-28
[17] 赵杰,快速公交的规划和应用前景,城市车辆,2006,12(6):25-26
[18] 邹哲,徐康明,李科,快速公共汽车运营系统-面向可持续发展的城市交通发展战略选择,城市,2003,6(4):24-27
[19] 孟庆和,李大龙,快速公交的特点及应用,农业装备与车辆工程,2006,24(8):42-52
[20] 李玉辉,戈春珍,胡金成,快速公交系统(BRT)在我国的发展研究,辽宁交通科技,2006, 12(4):75-77
[21] 陈明明,牛惠民,快速公交系统及评价问题的研究,兰州交通大学学报(自然科学版) ,2006,25(4):113-117
[22] 罗大明,季晓京,北京南中轴路快速公交(BRT)智能公交系统总体设计概要,交通运输系统工程与信息,2005,5(2):97-98
[23] 闫雅彬,北京 BRT 的建设与发展,城市车辆,2006,10(2):26-27
[24] 周毅,关于中国 BRT 的探讨,交通世界,2006,42(10):68-69
[25] 国务院发展研究中心,长安大学 BRT 研究中心,西安市发展快速公交系统技术报告,2005
[26] 王骏阳,库里蒂巴与可持续发展规划,国外城市规划,2000,10(4):9-12
[27] 赵杰,胡子祥,刘丽亚,国外发展快速公交的经验及对我国城市交通发展的启示,城市交通,2004,2(3):56-59
[28] 学会秘书处,BRT 专题介绍,城市公共交通,2005,5(10):23-26
[29] 杨兆升,城市智能公共交通系统理论与方法,北京:中国铁道出版社,2003
[30] Newell G..F,Some issues related to the optimal design of bus Transportation Science,1979,13:20-35.
[31] 高自友,张好智,孙会君,城市交通网络设计问题中双层规划模型,方法及应用,交通运输系统工程与信息,2004,4(1):35-44
[32] Scheele S.A , Supply Model for Public Transit Services.Transportation Research-B,1980(14):133-146
[33] Koutsopoulos H.N,Odoni A,Determination of Headways as a Function of Time Varying Characteristics on a Transit Network. In Cmputer Scheduling of Public Transport 2,North-Holland,Amsterdam,1985:391-414
[34] Shih M.C , Mahmassani H.S , Vehicle Sizing Model for Bus Transit Networks.Transportation Research Record,1995:35-41
[35] 孙芙灵,公交调度中发车间隔的确定方法的探讨,西安公路交通大学学报,1997,2(6):44-48
[36] 杨超,李彬,城市公共交通线网优化的图论模型与算法,同济大学学报.1998,1(5):29-32
[37] 王炜,数学规划方法在公交网络优化中的应用,系统工程,1999,8(3):42-49
[38] 常玉林,胡启洲,城市公交线网优化的线性模型,中国公路学报,2005,18(1):95-98
[39] Lamnkin,Saatmans,The Design of Routes,Transportation Research,1967
[40] Hirsch,Dantzig,The Fixed Charge Problem,Rand Co,1968
[41] 陈茜,牛学勤,陈学武,王炜,公交线路发车频率优化模型,公路交通科技,2004,21(2):103-105
[42] 吕鹏,张文夫,公交车调度,工程数学学报,2002,19(F02):75-80
[43] D.Dubois,G.Bel,M.Llibre,A Set of Methods in Transportation Network Synthesis and Analysis,The Journal of the Operational Research Society, 1979:797-808
[44] 王炜,城市道路交通规划理论:[博士学位论文],南京;东南大学,1989
[45] 刘清,衷仁保,朱志勇,谢磊,实现城市公交线网优化的数学模型和广义A*算法,系统工程理论与实践,1992,10(2):12-17
[46] Zhu w,Trip frequency scheduling for terminal quening routers,Proceedings of 7th IFAC/IFORS Symposium on Transportation Systems,1994:70-77
[47] Baaj M.H,Mahmassani H.S,Hybrid route generation heuristic algorithm for the design of transit networks,Transportation Research C3,1995:31-50
[48] 单连龙,高自友,城市公交系统连续平衡网络设计的双层规划模型及求解算法,系统工程理论与实践,2000,15(7):85-93
[49] Ali Haghani,Mohamadreza Banihashemi,Heuristic approaches for solving large-scale bus transit vehicle scheduling problem with route time constraints,Transportation Research Part A,2002:309-333.
[50] 于滨,杨忠振,程春田,左志,公交线路发车频率优化的双层规划模型及其解法,吉林大学学报,2006,36(5):664-668
[51] 闫小勇,牛学勤,公交网络多路径选择启发式算法研究,城市交通,2005,3(3):23-26
[52] 刑文训,谢金星,现代优化计算方法,北京:清华大学出版社,1999
[53] Glover F ,Future paths for integer programming and links to artificial intelligence ,Computers and Operations Research,1986(13):533-549
[54] Cavique L,Rego C,Themido I.,Subgraph ejection chains and tabu search for the crew scheduling problem,Journal of the operational Research Society,1999:608-616
[55] Shen Y,Tabu Search for Bus and Train Driver Scheduling With TimeWindows[D],2001 PhD thesis,University of Leeds,UK
[56] Wei Fan,Randy B,Machemehl,A tabu search based heuristic method for the transit route network design problem , CASPT 2004 9th International Conference on Computer-Aided Scheduling of Public Transport,San Diego,California,2004
[57] 白子建,赵淑芝,田振中,公共交通网络优化的禁忌算法设计与实现,吉林大学学报(工学版),2006,36(3):40-44
[58] 沈吟东,倪郁东,基于禁忌搜索的公交调度计划系统,城市公共交通,2006,24(9):21-24
[59] Kirkpatrick S,Gelatt C D,Vecchi M P,Optimization by simulated annealing,Science,1983:671-680
[60] Kirkpatrick S,Gelatt C D ,Vecchi M P, Optimization by simulated annealing,Science,1983:377-383
[61] 蔡延光,钱积新,多重运输调度问题的模拟退火算法,系统工程理论与实践,1998,18(10):11-15
[62] 林柏梁,杨富社,出行费用最小化的公交网络优化模型,中国公路学报,1999,12(1),79-83
[63] Fang Zhao,Ike Ubaka,Optimization of Transit Network to Minimize Transfers and Optimize Route Directness,Journal of Public Transportation,2004(1):63-82
[64] 李铭,李旭宏,公交枢纽内始发线路优化配置模型及其模拟退火算法,可持续发展的中国交通,2005 全国博士生学术论坛
[65] Holland J.H,Adaptation in natural and artificial systems,MI:University of Michigan Press,1985
[66] Davis L,Handbook of genetic algorithm,New York:Van Nostrand Reinhold,1991
[67] Androulakis I.P,Venkatasubramanlan V,A genetic algorithm framework for process design and optimization,Computer Chen Engng,1991,15(4):217-228
[68] 刘勇,康立山,陈毓屏,非数值并行算法-遗传算法,北京:科学出版社,1998
[69] Brindle A , Genetic algorithms for function optimization , Ph DDissertation.Alberta:University of Alberta,1981
[70] Chakroborty P,Subrahmanyam P.S ,Optimal scheduling urban transit systems using genetic algorithms,Journal of Transportation Engineering,1995 :544-553
[71] Pattnaik S.B,Mohan S,Tom V.M,Urban Bus Transit Route Network Design Using Genetic Algorithm,Journal of Transportation Engineering,1998,124(4):368-375
[72] 孙艳丰,基于遗传算法的城市交通运输网优化问题研究,系统工程理论与实践,2000(3):34-37
[73] 钱大琳,离散非平衡公交网络优化模型及其求解算法,北方交通大学学报,2001(1):56-58
[74] 陈洪仁,分层限制的公交线网优化模型,哈尔滨建筑大学学报,2001(1):80-83
[75] 汤可夫,吴大为,基于改进遗传算法的公交线网整体优化方法,重庆交通学院学报,2004(4):22-25
[76] Ngamchai lovell,Agrawal Mathew Optimal Time Transfer in Bus Transit Route Network Design Using a Genetic Algorithm,Transportation Engineering,2003(5):510521
[77] 董刚,公交调度模型及算法,青岛科技大学学报,2004,25(3):1921
[78] Paul Forsyth,Anthony Wren,An ant system for bus driver scheduling, the 7th International Workshop on Computer-Aided Scheduling of Public Transport,Boston,1997
[79] 韩印,蚂蚁算法在智能公交网络优化中的应用研究,计算机工程与应用,2005,41(30):189191
[80] 王海星,申金升,智能蚁群算法解决公交区域调度问题研究,北京邮电大学学报,2006,29(2):3034
[81] 孙先仿,范跃祖,晏磊,张飞舟,智能交通系统中的运营车辆优化调度研究,北京航空航天大学学报,2002,6(2):1921
[82] 任传祥,张海,范跃祖,合遗传-模拟退火算法在公交智能调度中的应用,系统仿真学报,2005,17(9):20752077
[83] 于滨,城市公交系统模型与算法研究:[博士学位论文],大连;大连理工大学,2006
[84] Fang Zhao,Xiaogang Zeng,Simulated Annealing–Genetic Algorithm for Transit Network Optimization ,2006:57-68
[85] 于景飞,大城市常规公交线网优化方法研究及应用:[硕士学位论文],合肥;合肥工业大学,2005
[86] 李琼星,城市公交线网规划研究:[硕士学位论文] ,长沙;湖南大学,2002
[87] Hasselstro D,Public Transportation Planning- A Mathematical Programming Approach, Doctor Disstertation,University of Goteborg,Sweden,1981.
[88] Baaj M.H,Mahmassani H.S,Hybrid Route Generation Heuristic Algorithm for the Design of Transit Networks,Transportation Research-C,1995:1-50
[89] Dubois D,Bel G,Libre M,A Set of Methods in Transportation Network Synthesis and Analysis Journal of Operational Research Society,1979:797-808
[90] Ceder A,Wilson N.H.M,Bus Network Design , Transp. Res. Part B, 1986,20(1):331-344
[91] 杨兆升,城市智能公共交通系统理论与方法,北京:中国铁道出版社,2002
[92] 季利平,城市快速公交线网规划研究:[硕士学位论文] ,呼和浩特;内蒙古农业大学,2006
[93] 陈钦水,城市地面快速公交网络系统规划研究:[硕士学位论文] ,西安;西安建筑科技大学,2004
[94] 魏涛,快速公交系统通行能力分析:[硕士学位论文] ,长沙;长沙交通学院,2006
[95] 牟达,大连市快速公交规划及其效果评价:[硕士学位论文] ,大连;大连理工大学,2006
[96] 王炜,杨新苗,陈学武,城市公共交通系统规划方法与管理技术,北京:科学出版社,2002
[97] 刘灿齐,城市交通规划学,北京:人民交通出版社,2001
[98] Glover F,Tabu Search Part I,ORSA Journal on Computing,1989(1):190-206
[99] Glover F,Tabu Search Part II,ORSA Journal on Computing,1989(2):4-32
[100] Glover F,Luguna M.,Tabu Search Basel Switzerland,Science Publishers,1993
[101] 刘自发,基于智能优化算法的配电网络规划与优化运行研究:[博士学位论文] ,天津;天津大学,2005
[102] William H.K,Zhou Jing,Sheng Zhao-han,A capacity restraint transit assignment with elastic line frequency,Transportation Research Part B,2002,36(10):919-938.
[103] Jan Rong-hong , Chen Shiow-ling , Branch-and-bound algorithm for reliability-oriented task assignment in bus network systems , Journal of Information Science and Engineering,1994,10(1):81-97
[104] Maurizio Bielli , Massimiliano Caramia , Pasquale Carotenuto , Genetic algorithms in bus network optimization,Transportation Research Part C,2002,10(1):19-34
[105] Diaz R.B,Schneck D.C,Bus rapid transit technologies in the Americas,Transportation Research Record,2000:3-9
[106] Levinson H.S,Zimmerman S,Clinger J,Bus rapid transit:Synthesis of case studies,Transportation Research Record,2003:1-11
[107] Last A,Leak S.E,Transportation:a bus model,Traffic Engineering and Control,1976:14-20
[108] Current J,ReVelle C.S,Cohon J.L,The maximum covering shortest path problem:a multi-objective network design and routing formulation,European Journal of Operational Research,1985:189-199
[109] Furth P.G.,Optimal bus stop spacing through dynamic programming and geographic modeling.Transportation Research Record,2000:15-22
[110] 杨新苗,王炜,尹红亮,武勇,公交调度峰值曲线的优化方法,东南大学学报(自然科学版) ,2001,31(3):40-43
[111] Chien,Steven I,Optimization of bus stop locations for improving transit accessibility,Transportation planning and Technology,2004(6):211-227
[112] Herbert S.L,Scott R,Eric B,TCRP Report 90:Bus Rapid Transit,Transportation Research Board,2003
[113] Anthony A,Saka.Model for Determing Optimum Bus-Stop Spacing in Urban Areas,Journal of Transportation Engineering,2001,127(3):195-199
[114] Holland,J.H,Adaptation in natural and artificial systems:An introductory analysis with applications to biology,MI:The University of Michigan Press,1975
[115] Booker L.B,Goldberg D.E, Holland J.H,Classifier Systems and Genetic Algorithms,Articifial Interlligence,1989:235-282
[116] M ichalewiez Z,Janidow C, Brawezyd J,A Modified Genetic Algorithm for Optimal Control Problem ,Computers Math Application ,1992 (12):83-94
[117] Davis L,Handbook of genetic algorithms,Van Nostrand Reinhold,New York,1991
[118] Michalewica Z,Genetic algorithms + data structure = evolution programs,3rd edition,New York:springer-Verlag,1996
[119] 王鹏飞,智能公交之车辆人员排班算法的研究与应用:[硕士学位论文],济南;山东大学,2004
[120] 徐康明,波哥大快速公交系统创收支平衡,2003 年 2 月:原稿 By GeorgeG.Wynne,Director,International Programs
[121] Transportation Research Board,National Research Council ,Bus Rapid Transit Case Sudies in Bus Rapid Transit,Washington DC,2003:48-53
[122] 王凌,智能优化算法及其应用,北京:清华大学出版社,2002
[123] Hanafi S,On the Convergence of Tabu Search,Journal of Heuristic,2000,7:47-58
[124] WEN Fu-shuan,Chang C.S, A tabu search approach for fault section estimation and state identification of unobserved protective relays in power systems,Proceedings of 1996 international conference on intelligent systems applications to power systems,Korea Seoul,1996:341-347
[125] Glover F,Kochenberger G.A ,Alidaee B,Adaptive memory tabu search for binary quadratic programs,Management Science,1998,44(3):336-345
[126] 康立山,谢云,非数值并行算法-模拟退火算法,北京:科学出版社,1998
[127] 姚新,陈国良,模拟退火算法及其应用,计算机研究与发展,1990
[128] 刘岩,韩承德,王义和,模拟退火的背景与单调升温的模拟退火算法,计算机研究与发展,1996,33(1):4-10
[129] 王凌,郑大钟,模拟退火算法求解 Flow Shop 问题的研究,中国控制与决策学术年会,沈阳:东北大学出版社,1997
[130] Park M,Kim Y,A systematic procedure for setting parameters in simulated annealing algorithms,Computers & Operations Research,1998,25(3):207-217