需求响应公交及其路径优化研究综述

doi:10.11959/j.issn.2096-6652.202116

摘要/Abstract

摘要：

随着新基建等技术的泛在应用，需求响应公交（DRT）正成为未来城市交通发展的趋势。为了进一步厘清DRT的国内外研究现状，首先，梳理和分析了DRT的分类和实现DRT运营所必需的生产要素；其次，阐述了DRT模式的产生过程和运营实践；再次，从优化目标、约束选择、求解算法3个维度对DRT优化问题进行分析总结，尤其对元启发式算法进行了详细总结；最后，在面向 DRT 的应用场景、模型构建、算法求解、常规公交与DRT协同优化等方面提出了展望，针对DRT未来可能的研究方向和研究热点提出了建议。

关键词: 公共交通, 需求响应公交, 路径优化, 求解算法

Abstract:

With the widespread application of new infrastructure and other technologies, demand responsive transit (DRT) is becoming the trend of urban traffic development in the future.In order to further clarify the research status of DRT at home and abroad, firstly, the classification of DRT and the operational production factors were analyzed.Secondly, the production process and operation practice of DRT mode were described.Thirdly, the DRT optimization problem was summarized and analyzed from the three dimensions including optimization objectives, constraint selection and solving algorithm, especially the meta heuristic algorithm.Finally, the prospect of DRT scenarios, model construction, algorithm solution, and the collaborative optimization were proposed.Several hotspots and possible directions of future research were suggested.

Key words: public transport, demand responsive transit, route optimization, solving algorithm

中图分类号:

U491.2

冯帅,刘小明. 需求响应公交及其路径优化研究综述[J]. 智能科学与技术学报, 2021, 3(2): 161-171.

Shuai FENG,Xiaoming LIU. A survey of research on demand responsive transit and its route optimization[J]. Chinese Journal of Intelligent Science and Technology, 2021, 3(2): 161-171.

图/表 13

图1

图2

图3

表1

图4

图5

图6

图7

图8

表2

表3

图9

表4

与DRT问题主要求解算法相关的研究"

参考文献	模型	求解算法	优化目标	数据来源
[62]	单接驳点和多接驳点的 DRT 路径优化模型	改进后的禁忌搜索算法	乘客出行成本和公交运营成本最小，系统潜在客流吸引最大	北京某职住分离区域数据
[63]	城市公交应急疏散VRP模型	精确算法和禁忌搜索算法	总疏散出行时间最短	长春中心区路网数据
[64]	混合整数规划模型	改进的禁忌搜索算法	综合成本最小	某公司实际业务场景数据
[65]	取送一体化VRP模型	禁忌搜索启发式算法	服务总成本最小	设计算例
[66]	需求响应接驳公交线路优化模型	混合模拟退火算法	乘客出行成本和公司运营成本最小，同时满足最大乘客定制需求	设计算例
[67]	混合需求条件下的线路协调优化模型	模拟退火算法	系统总费用最低	设计算例
[68]	以车站数量和位置均衡为优化目标的灵活车站模型	模拟退火算法	运营成本最小，乘客出行时间最短	调查问卷数据
[69]	考虑企业运营成本和可靠性的优化模型	基于遗传算法的优化算法	车辆可变成本和固定成本之和最小	设计算例
[70]	DRT多停车场多车辆VRP模型	基于遗传算法的三段式混合编码方式方法	运营总里程最小	兰州城关区部分交通网络数据
[71]	基于共享汽车的最佳DRT模型	基于遗传算法的两阶段启发式算法	总旅行时间最短	重庆案例研究
[72]	乘客需求可拆分的优化模型	蚁群优化算法	DRT网络覆盖率最大，车辆总收益最大	成都定制公交系统
[73]	DAR优化模型	蚁群优化算法	车队规模最大	仿真数据
[74]	组合VRP模型	改进的粒子群优化算法	合乘出租司机收益最大，乘客服务率最高，乘客费用最低	仿真数据
[75]	两阶段调度优化模型	改进的粒子群优化算法	乘客出行成本与运营成本之和最小	陕西省西咸新区272路公交数据
[76]	协同组合优化模型	改进的混合粒子群优化算法	企业成本最小	汕尾东部地区至火车站实例

表4

参考文献 76

[33]	WU L R . Real-time tour planning for flexible route bus considering passengers’ waiting behavior[D]. Dalian:Dalian University of Technology, 2014.
[34]	邱丰, 李文权, 沈金星 . 可变线路式公交的两阶段车辆调度模型[J]. 东南大学学报(自然科学版), 2014,44(5): 1078-1084.
	QIU F , LI W Q , SHEN J X . Two-stage model for flex-route transit scheduling[J]. Journal of Southeast University (Natural Science Edition), 2014,44(5): 1078-1084.
[35]	丁帅 . 灵活型公交接驳系统运行线路优化研究[D]. 济南:山东大学, 2016.
	DING S . The route optimization research of flexible feeder transit system[D]. Jinan:Shandong University, 2016.
[36]	LI X G , QUADRIFOGLIO L . 2-vehicle zone optimal design for feeder transit services[J]. Public Transport, 2011,3(1): 89-104.
[37]	孙继洋, 黄建玲, 陈艳艳 ,等. 面向多目标站的灵活型公交路径优化调度模型[J]. 交通运输系统工程与信息, 2019,19(6): 105-111.
	SUN J Y , HUANG J L , CHEN Y Y ,et al. Flexible bus route optimization scheduling model for multi-target stations[J]. Journal of Transportation Systems Engineering and Information Technology, 2019,19(6): 105-111.
[1]	宁滨 . 平行轨道交通系统[J]. 智能科学与技术学报, 2019,1(3): 215-218.
	NING B . Parallel rail transportation system[J]. Chinese Journal of Intelligent Science and Technology, 2019,1(3): 215-218.
[38]	KIRCHLER D , CALVO W R . A granular tabu search algorithm for the dial-a-ride problem[J]. Transportation Research Part B:Methodological, 2013,56: 120-135.
[39]	SUN B , WEI M , ZHU S L . Optimal design of demand-responsive feeder transit services with passengers’ multiple time windows and satisfaction[J]. Future Internet, 2018,10(3): 30.
[2]	吕宜生, 陈圆圆, 金峻臣 ,等. 平行交通:虚实互动的智能交通管理与控制[J]. 智能科学与技术学报, 2019,1(1): 21-33.
	LYU Y S , CHEN Y Y , JIN J C ,et al. Parallel transportation:virtual-real interaction for intelligent traffic management and control[J]. Chinese Journal of Intelligent Science and Technology, 2019,1(1): 21-33.
[40]	WANG Z W , YU J , HAO W ,et al. Designing high-freedom responsive feeder transit system with multitype vehicles[J]. Journal of Advanced Transportation, 2020(6): 1-20.
[41]	王健, 曹阳, 王运豪 . 考虑出行时间窗的定制公交线路车辆调度方法[J]. 中国公路学报, 2018,31(5): 143-150.
[3]	郑南宁 . 人工智能新时代[J]. 智能科学与技术学报, 2019,1(1): 1-3.
	ZHENG N N . The new era of artificial intelligence[J]. Chinese Journal of Intelligent Science and Technology, 2019,1(1): 1-3.
[41]	WANG J , CAO Y , WANG Y H . Customized bus route vehicle schedule method considering travel time windows[J]. China Journal of Highway and Transport, 2018,31(5): 143-150.
[42]	王正武, 陈涛, 宋名群 . 同时接送模式下响应型接驳公交运行路径与调度的协调优化[J]. 交通运输工程学报, 2019,19(5): 139-149.
[4]	LI X G , QUADRIFOGLIO L . Feeder transit services:choosing between fixed and demand responsive policy[J]. Transportation Research Part C:Emerging Technologies, 2010,18(5): 770-780.
[5]	ERRICO F , CRAINIC T G , MALUCELLI F ,et al. A survey on planning semi-flexible transit systems:methodological issues and a unifying framework[J]. Transportation Research Part C:Emerging Technologies, 2013,36: 324-338.
[42]	WANG Z W , CHEN T , SONG M Q . Coordinated optimization of operation routes and schedules for responsive feeder transit under simultaneous pick-up and delivery mode[J]. Journal of Traffic and Transportation Engineering, 2019,19(5): 139-149.
[43]	QUADRIFOGLIO L , DESSOUKY M M , ORDONEZ F . A simulation study of demand responsive transit system design[J]. Transportation Research Part A:Policy and Practice, 2008,42(4): 718-737.
[6]	DONG X T , REY D , WALLER S T . Dial-a-ride problem with users’ accept/reject decisions based on service utilities[J]. Transportation Research Record Journal of the Transportation Research Board, 2020,2674(4): 1-13.
[7]	DOU X P , MENG Q , LIU K . Customized bus service design for uncertain commuting travel demand[J]. Transportmetrica A:Transport Science, 2020(3): 1405-1430.
[44]	PEI M Y , LIN P Q , DU J ,et al. Operational design for a real-time flexible transit system considering passenger demand and willingness to pay[J]. IEEE Access, 2019,7: 180305-180315.
[45]	BRAMEL J , SIMCHI-LEVI D , . On the effectiveness of set covering formulations for the vehicle routing problem with time windows[J]. Operations Research, 1997,45(2): 157-325.
[8]	QIU G , SONG R , HE S W ,et al. Clustering passenger trip data for the potential passenger investigation and line design of customized commuter bus[J]. IEEE Transactions on Intelligent Transportation Systems, 2019,20(9): 3351-3360.
[9]	ZHENG Y , LI W Q , QIU F . A methodology for choosing between route deviation and point deviation policies for flexible transit services[J]. Journal of Advanced Transportation, 2018(4): 6292410.1-6292410.12.
[46]	QIU X Q , FEUERRIEGEL S , NEUMANN D . Making the most of fleets:a profit-maximizing multi-vehicle pickup and delivery selection problem[J]. European Journal of Operational Research, 2016,259(1): 155-168.
[47]	MOHAMMAD R , AHMED G . A branch-and-price algorithm for a vehicle routing with demand allocation problem[J]. European Journal of Operational Research, 2018,272(2): 523-538.
[10]	GIUFFRIDA N , PIRA M L , INTURRI G ,et al. On-demand flexible transit in fast-growing cities:the case of dubai[J]. Sustainability, 2020,12(11): 4455.
[11]	SUN J Y , HUANG J L , CHEN Y Y ,et al. Flexible bus route optimization for multitarget stations[J]. Mathematical Problems in Engineering, 2020:7183465.
[12]	BROOME K , WORRALL L , FLEMING J ,et al. Evaluation of flexible route bus transport for older people[J]. Transport Policy, 2012,21(4): 85-91.
[13]	COLE L M . Tomorrow’s transportation:new systems for the urban future[M].[S.l.]: U.S.Government Printing Office, 1968.
[48]	LYSGAARD J . Reachability cuts for the vehicle routing problem with time windows[J]. European Journal of Operational Research, 2006,175(1): 210-223.
[49]	MAK V , ERNST A T . New cutting-planes for the time- and/or precedence-constrained ATSP and directed VRP[J]. Mathematical Methods of Operations Research, 2007,66(1): 69-98.
[14]	PERRITT H H , PERRITT J . Americans with disabilities ACT (ADA) handbook[M].[S.l.]: Aspen Publishers Online, 2002.
[15]	RODIER C J , JOHNSTON R A , SHABAZIAN D R . Evaluation of advanced transit alternatives using consumer welfare[J]. Transportation Research Part C:Emerging Technologies, 1998,6(1-2): 141-156.
[50]	JEPSEN M , PETERSEN B , SPOORENDONK S ,et al. Subset-row inequalities applied to the vehicle-routing problem with time windows[J]. Operations Research, 2008,56(2): 497-511.
[51]	ALP E O . Integrated routing and scheduling of hazmat trucks with stops en route[J]. Transportation Science, 2007,41(1): 107-122.
[16]	BRAKE J , NELSON J D , WRIGHT S . Demand responsive transport:towards the emergence of a new market segment[J]. Journal of Transport Geography, 2004,12(4): 323-337.
[17]	卢小林, 张娴, 俞洁 ,等. 灵活型定制公交系统综合评价方法研究[J]. 公路交通科技, 2015,32(5): 135-140.
[52]	CIMEN M , SOYSAL M . Time-dependent green vehicle routing problem with stochastic vehicle speeds:an approximate dynamic programming algorithm[J]. Transportation Research Part D:Transport and Environment, 2017,54: 82-98.
[53]	NOVOA C , STORER R . An approximate dynamic programming approach for the vehicle routing problem with stochastic demands[J]. European Journal of Operational Research, 2009,196(2): 509-515.
[17]	LU X L , ZHANG X , YU J ,et al. Research of a comprehensive evaluation method for customized flexible transit system[J]. Journal of Highway and Transportation Research and Development, 2015,32(5): 135-140.
[18]	巫威眺 . 不确定环境下公交网络协同调度的鲁棒性及控制策略[D]. 广州:华南理工大学, 2015.
[54]	裴明阳 . 灵活公共交通系统营运调度模型与方法研究[D]. 广州:华南理工大学, 2020.
	PEI M Y . Operational design models for flexible transit systems[D]. Guangzhou:South China University of Technology, 2020.
[18]	WU W T . The robustness and control strategies of bus network schedule coordination with uncertainty[D]. Guangzhou:South China University of Technology, 2015.
[19]	LIU T , CEDER A A . Analysis of a new public-transport-service concept:customized bus in China[J]. Transport Policy, 2015: 63-76.
[55]	邱丰 . 可变线路式公交运营调度与模式优化研究[D]. 南京:东南大学, 2015.
	QIU F . Research on operation scheduling and mode optimization of flex-route buses[D]. Nanjing:Southeast University, 2015.
[20]	KOFFMAN D . Operational experiences with flexible transit services[J]. Transportation Research Board, 2004.
[21]	徐康明, 李佳玲, 冯浚 ,等. 定制公交服务初探[J]. 城市交通, 2013(5): 24-27.
[56]	贺韵竹 . 城市化进程中公交服务商业模式创新研究[D]. 大连:大连海事大学, 2020.
	HE Y Z . Innovation of business mode of public transit service during the process of a rapid urbanization[D]. Dalian:Dalian Maritime University, 2020.
[21]	XU K M , LI J L , FENG J ,et al. Discussion on subscription bus services[J]. Urban Transport of China, 2013(5): 24-27.
[22]	PARRAGH S N , DOERNER K F , HARTL R F . A survey on pickup and delivery problems[J]. Journal FürBetriebswirtschaft, 2008,58(1): 21-51.
[57]	LI H Q , CHANG X Y , ZHAO W C ,et al. The vehicle flow formulation and savings-based algorithm for the rollon-rolloff vehicle routing problem[J]. European Journal of Operational Research, 2017,257(3): 859-869.
[58]	李进, 张江华 . 基于碳排放与速度优化的带时间窗车辆路径问题[J]. 系统工程理论与实践, 2014,34(12): 3063-3072.
[23]	LAPORTE G . Fifty years of vehicle routing[J]. Transportation Science, 2009,43(4): 408-416.
[24]	CODATO G , FISCHETTI M . Combinatorial benders’ cuts for mixedinteger linear programming[J]. Operations Research, 2006,54(4): 756-766.
[58]	LI J , ZHANG J H . Vehicle routing problem with time windows based on carbon emissions and speed optimization[J]. Systems Engineering-Theory and Practice, 2014,34(12): 3063-3072.
[59]	LI H Q , ZHANG L , LYU T ,et al. The two-echelon time-constrained vehicle routing problem in linehaul-delivery systems[J]. Transportation Research Part B:Methodological, 2016,94: 169-188.
[25]	GéRALDINE H , CORDEAU J F , LAPORTE G . An integer L-shaped algorithm for the dial-a-ride problem with stochastic customer delays[J]. Discrete Applied Mathematics, 2011,159(9): 883-895.
[26]	TONG L , ZHOU L S , LIU J T ,et al. Customized bus service design for jointly optimizing passenger-to-vehicle assignment and vehicle routing[J]. Transportation Research Part C:Emerging Technologies, 2017,85: 451-475.
[60]	潘立军, 符卓 . 求解带时间窗车辆路径问题的插入检测法[J]. 系统工程理论与实践, 2012,32(2): 319-322.
	PAN L J , FU Z . Insertion detection method for vehicle routing problem with time windows[J]. Systems Engineering-Theory and Practice, 2012,32(2): 319-322.
[27]	申婵, 崔洪军 . 基于可靠性最短路的实时定制公交线路优化研究[J]. 交通运输系统工程与信息, 2019,19(6): 99-104.
	SHEN C , CUI H J . Optimization of real-time customized shuttle bus lines based on reliability shortest path[J]. Journal of Transportation Systems Engineering and Information Technology, 2019,19(6): 99-104.
[61]	刘霞, 齐欢 . 带时间窗的动态车辆路径问题的局部搜索算法[J]. 交通运输工程学报, 2008,8(5): 114-120.
	LIU X , QI H . Local search algorithm of dynamic vehicle routing problem with time window[J]. Journal of Traffic and Transportation Engineering, 2008,8(5): 114-120.
[28]	FU L P . Planning and design of flex-route transit services[J]. Transportation Research Record:Journal of the Transportation Research Board, 2002: 59-66.
[29]	郑汉, 张星臣, 王志美 . 混合车型需求响应公交服务定制问题研究[J]. 交通运输系统工程与信息, 2018,8(2): 157-163.
[62]	聂靖入 . 基于改进禁忌搜索算法的灵活公交接驳线路规划研究[D]. 北京:清华大学, 2017.
	NIE J R . Research on flexible feeder transit route planning based on improved tabu search algorithm[D]. Beijing:Tsinghua University, 2017.
[63]	崔建勋, 安实, 崔娜 . 基于时间扩展网络的区域疏散公交路径规划[J]. 华南理工大学学报(自然科学版), 2010,38(3): 64-69.
	CUI J X , AN S , CUI N . Route planning of public transit for regional evacuation based on time-expanded network[J]. Journal of South China University of Technology(Natural Science Edition), 2010,38(3): 64-69.
[64]	邱媛 . 基于一种改进的禁忌搜索算法的时间相关电动车车辆路径问题研究[D]. 南京:南京大学, 2020.
	QIU Y . An improved tabu search for time-dependent electric vehicle routing problem[D]. Nanjing:Nanjing University, 2020.
[65]	BRUNI M E , GUERRIERO F , BERALDI P . Designing robust routes for demand-responsive transport systems-sciencedirect[J]. Transportation Research Part E:Logistics and Transportation Review, 2014,70(1): 1-16.
[66]	彭巍, 周和平, 高攀 . 面向城际轨道交通的定制化接驳公交线路优化[J]. 长沙理工大学学报(自然科学版), 2017,14(4): 49-54,82.
[29]	ZHENG H , ZHANG X C , WANG Z M . Design of demand-responsive service by mixed-type vehicles[J]. Journal of Transportation Systems Engineering and Information Technology, 2018,8(2): 157-163.
[30]	范文豪 . 需求响应式接驳公交路径优化模型研究[D]. 南京:东南大学, 2017.
[66]	PENG W , ZHOU H P , GAO P . The route optimization research of customized feeder transit system oriented on intercity railway system[J]. Journal of Changsha University of Science and Technology (Natural Science), 2017,14(4): 49-54,82.
[67]	王正武, 宋名群 . 多换乘点响应型接驳公交运行线路的协调优化[J]. 中国公路学报, 2019,32(9): 164-172.
	WANG Z W , SONG M Q . Coordinated optimization of operation routes for responsive feeder transit systems with multiple transfer points[J]. China Journal of Highway and Transport, 2019,32(9): 164-174.
[68]	赵迪 . 陆侧网络不发达机场响应式公交接驳研究[D]. 北京:北京交通大学, 2019.
[30]	FAN W H . Research on routing optimization model of demand-responsive connector[D]. Nanjing:Southeast University, 2017.
[31]	GHANNADPOUR S F , NOORI S , TAVAKKOLI-MOGHADDAM R , ,et al. A multi-objective dynamic vehicle routing problem with fuzzy time windows:model,solution and application[J]. Applied Soft Computing, 2014,14: 504-527.
[68]	ZHAO D . Research on responsive bus connection for landside network underdeveloped airport[D]. Beijing:Beijing Jiaotong University, 2019.
[69]	何民, 李沐轩, 税文兵 ,等. 可靠性和舒适性对响应式定制公交线路设计的影响[J]. 公路交通科技, 2019,36(5): 145-151.
[32]	PAQUETTE J , CORDEAU J F , LAPORTE G . Quality of service in dial-a-ride operations[J]. Computers and Industrial Engineering, 2009,56(4): 1721-1734.
[33]	吴丽荣 . 考虑乘客等待行为的柔性路径公交车实时调度方法[D]. 大连:大连理工大学, 2014.
[69]	HE M , LI M X , SHUI W B ,et al. Influence of reliability and comfort on responsive custom bus route design[J]. Journal of Highway and Transportation Research and Development, 2019,36(5): 145-151.
[70]	王超, 马昌喜 . 基于遗传算法的定制公交多停车场多车线路优化[J]. 交通信息与安全, 2019,37(3): 109-117,127.
	WANG C , MA C X . Optimization of parking lot and multi-vehicle route of customized buses based on genetic algorithm[J]. Journal of Transport Information and Safety, 2019,37(3): 109-117,127.
[71]	SUN B , WEI M , WU W . An optimization model for demand- responsive feeder transit services based on ride-sharing car[J]. Information, 2019,10(12): 370.
[72]	李艳梅 . 定制公交系统线网构建方法研究[D]. 成都:西南交通大学, 2016.
	LI Y M . Network planning of customized city bus service[D]. Chengdu:Southwest Jiaotong University, 2016.
[73]	TRIPATHY T , NAGAVARAPU S C , AZIZIAN K ,et al. Solving dial-a-ride problems using multiple ant colony system with fleet size minimisation[J]. Advances in Intelligent Systems and Computing, 2017: 325-336.
[74]	吴芳, 李志成, 徐琛 . 出租车合乘制调度优化模型研究[J]. 兰州交通大学学报, 2009,28(1): 104-107.
	WU F , LI Z C , XU C . Study of the mode of combined-taxi optimal scheduling[J]. Journal of Lanzhou Jiaotong University, 2009,28(1): 104-107.
[75]	余静财 . 可变线路公交设置条件及车辆调度模型研究[D]. 西安:长安大学, 2019.
	YU J C . Research on setting conditions and vehicle scheduling model for the route deviation system[D]. Xi’an:Chang’an University, 2019.
[76]	陈兴博 . 需求响应式公交协同组合调度研究[D]. 广州:华南理工大学, 2019.
	CHEN X B . Research on demand responsive transit cooperative combination scheduling[D]. Guangzhou:South China University of Technology, 2019.

交通服务模式	自由度	时刻表	载客量	乘坐成本	舒适度	运营模式
常规公交	0	固定	高	低	低	基于固定公交线路
DRT	(0, 100%)	固定、不固定或无	可变化	中	高	可提前收集需求
私家车	100%	无	低	高	高	完全响应需求

参考文献	问题特点	目标类型	优化目标	模型及求解算法	测试数据来源
[29]	混合车型VRP问题	考虑企业运营成本	车辆运营里程最小和使用车辆最少	DRT调度等价分解模型；分布式列生成算法	模拟预约系统
[30]	单换乘点VRP问题	考虑企业运营成本	企业运营成本最小	VRP模型；改进的遗传算法	仿真实验
[31]	带有模糊时间窗的动态路径优化问题	考虑企业运营成本	企业运营成本最小	多目标模型；遗传算法和3个基本模块的策略	Solomon数据集
[33]	考虑乘客等待行为的DRT优化问题	考虑乘客服务质量	乘客满意度最高	数学模型；NSGA-II算法	随机生成算例
[34]	同时服务预约需求和实时需求的VRP问题	同时考虑企业运营成本和乘客服务质量	乘客时间成本和企业运营成本最小	DRT公交调度模型；模拟退火算法和启发式插入算法	仿真洛杉矶646路公交数据
[35]	单车型DRT路径优化问题	同时考虑企业运营成本和乘客服务质量	车队总运行时间和因车辆提前或延迟到达降低的乘客服务水平最小	VRP模型；禁忌搜索算法	在山东建筑大学区域进行仿真实验
[36]	两个区域的支线运输服务的最佳设计	同时考虑企业运营成本和乘客服务质量	乘客服务质量最高企业运营成本最小	连续逼近系统分析模型；插入启发式算法	仿真实验

参考文献	问题特点	主要约束	优化目标	模型及求解算法	测试数据来源
[37]	灵活型公交VRP调度问题	车载容量约束	车辆的运行时间和乘客出行时间最短	灵活型公交VRP调度模型；启发式算法	仿真案例
[38]	静态DAR问题	车载容量约束	乘客服务质量最高，企业运营成本最小	混合整数线性规划模型；粒度禁忌搜索算法	其他文献数据
[39]	需求响应运输服务优化问题	车载容量约束	总里程运营成本最小，乘客满意度最高	混合整数线性规划模型；改进的蝙蝠算法	南京案例
[40]	高自由度响应式公交优化问题	车载容量约束	系统总收益最大	混合整数规划模型；元启发式算法	长沙地铁1号线尚双塘站
[41]	考虑出行时间窗的 DRT 车辆调度问题	时间窗约束	多辆公交车总运营里程最短	调度优化模型；贪心算法和遗传算法	随机生成算例
[42]	DRT路径优化和车辆调度问题	时间窗约束	系统运营利润最大	优化模型；双遗传算法	随机生成算例
[43]	DRT系统设计问题	时间窗约束	时间窗最小	DRT调度模型；启发式算法	洛杉矶DRT数据
[44]	考虑乘客支付意愿的灵活路径公交系统优化问题	时间窗约束	系统总收益最大	实时随机型灵活公交运营系统模型；遍历方法和改进的禁忌搜索算法	广州87路公交数据