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Article(id=1149768952479400140, tenantId=1146029695717560320, journalId=1146123166801305609, issueId=1149768937925165147, articleNumber=null, orderNo=null, doi=10.12404/j.issn.1671-1815.2404608, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1718812800000, receivedDateStr=2024-06-20, revisedDate=1732377600000, revisedDateStr=2024-11-24, acceptedDate=null, acceptedDateStr=null, onlineDate=1752055879945, onlineDateStr=2025-07-09, pubDate=1748361600000, pubDateStr=2025-05-28, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1752055879945, onlineIssueDateStr=2025-07-09, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1752055879945, creator=13701087609, updateTime=1752055879945, updator=13701087609, issue=Issue{id=1149768937925165147, tenantId=1146029695717560320, journalId=1146123166801305609, year='2025', volume='25', issue='15', pageStart='6155', pageEnd='6586', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=0, createTime=1752055876475, creator=13701087609, updateTime=1768456822194, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1218559490207699090, tenantId=1146029695717560320, journalId=1146123166801305609, issueId=1149768937925165147, language=EN, specialIssueTitle=, coverIllustrator=, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1218559490211893395, tenantId=1146029695717560320, journalId=1146123166801305609, issueId=1149768937925165147, language=CN, specialIssueTitle=, coverIllustrator=, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=6520, endPage=6529, ext={EN=ArticleExt(id=1149768954459111641, articleId=1149768952479400140, tenantId=1146029695717560320, journalId=1146123166801305609, language=EN, title=Optimization of Urban Rail Transit Feeder Bus Scheduling Considering Passenger Flows Demand, columnId=1156262728772735295, journalTitle=Science Technology and Engineering, columnName=Papers·Traffics and Transportations, runingTitle=null, highlight=null, articleAbstract=

In order to meet the transfer and transportation requirements of passengers and to significantly mitigate the loss of passenger flow that exceeds the waiting tolerance threshold, the optimization method of feeder bus scheduling considering the arrival time and passenger flow loss of rail transit trains was studied. The distribution of passenger flow demand was characterized by the passenger transfer demand and the arrival times of rail transit within the study period. The transfer time was described by the alignment between the time passengers arrive at the station of the bus and the bus departure schedule, as well as the operational capacity of the buses. The constraints of bus departure intervals, passenger flow loss and transfer demands were considered, and the multi-objective optimization with the minimum passenger flow loss, bus number and passenger transfer waiting time was realized under the limited number of buses that can be scheduled. Due to the contradictions among the optimization objectives, the model was solved with Non-dominated Sorting Genetic Algorithm II (NSGA-II). Finally, taking the actual bus routes as an example, the results show that the optimized model takes into account the bus operation cost and the passenger transfer time cost, and can obtain the scheduling that meets the passenger flow demand and represents different priorities. When the number of feeder buses is the same, the total transfer waiting time of the optimized method is reduced by 8.0% compared with the uniform headway. The average factor under the uneven is 59.3%, which is better than the average factor of 50.2% under the uniform. The calculation results validate the effectiveness and rationality of the model and algorithm, effectively enhancing the match between the time and capacity of buses and urban rail transit.

, correspAuthors=Ming-ming CHEN, authorNote=null, correspAuthorsNote=null, copyrightStatement=null, copyrightOwner=null, extLink=null, articleAbsUrl=null, sourceXml=null, magXml=null, pdfUrl=null, pdf=null, pdfFileSize=null, pdfExtLink=null, richHtmlUrl=null, mobilePdfUrl=null, reviewReport=null, pdfFirstPage=null, abstractGraph=null, abstractGraphContent=null, abstractVideo=null, citation=null, cebUrl=null, magXmlContent=null, mapNumber=null, authorCompany=null, fund=null, authors=null, authorsList=Guang-hui ZHOU, Ming-ming CHEN, Ji-long LI, Si-jia WANG, Zhen WANG), CN=ArticleExt(id=1149768977452286248, articleId=1149768952479400140, tenantId=1146029695717560320, journalId=1146123166801305609, language=CN, title=考虑客流需求的城轨接运公交行车计划优化, columnId=1156262730664366426, journalTitle=科学技术与工程, columnName=论文·交通运输, runingTitle=null, highlight=null, articleAbstract=

为了满足城市轨道交通乘客换乘接运公交的需求,有效减少因超过候车容忍时间而出现的客流流失量,研究考虑轨道交通列车到站时间、客流流失量的接运公交行车计划优化方法。以研究时段内乘客换乘需求和轨道交通到站时间等标明客流需求分布,以乘客到达接运公交首站的时间与公交发车时刻衔接关系、接运公交运能等描述换乘时间。考虑公交发车时间间隔、客流流失量、客流换乘需求等约束,在可调度的公交车辆数有限情况下,实现客流流失量、公交车辆数和乘客换乘候车总时间最小的多目标优化。由于优化目标之间存在矛盾,可利用带精英策略的非支配排序遗传算法(non-dominated sorting genetic algorithm II, NSGA-Ⅱ)求解模型,得到该问题的Pareto解集。最后,以实际接运公交线路进行算例分析,结果表明:优化模型兼顾公交运营成本和乘客换乘时间成本,可得到满足客流需求且代表不同侧重点的行车计划方案;接运公交车辆数相同时,本文方法相对于均匀发车方案可使乘客换乘候车总时间优化效果增加8.0%;不均匀发车间隔下的平均满载率为59.3%,优于均匀发车间隔下的平均满载率50.2%。计算结果验证了模型和算法的有效性和合理性,有效提升接运公交和城市轨道交通时间和运能匹配度。

, correspAuthors=陈明明, authorNote=null, correspAuthorsNote=
* 陈明明(1982—),男,汉族,山西霍州人,博士,副教授。研究方向:公交运营与管理。E-mail:。
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周广汇(1999—),男,汉族,甘肃白银人, 硕士研究生。研究方向:公交运营与管理。E-mail:。

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周广汇(1999—),男,汉族,甘肃白银人, 硕士研究生。研究方向:公交运营与管理。E-mail:。

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周广汇(1999—),男,汉族,甘肃白银人, 硕士研究生。研究方向:公交运营与管理。E-mail:。

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IEEE Transactions on Evolutionary Computation, 2002, 6(2): 182-197., articleTitle=A fast and elitist multiobjective genetic algorithm: NSGA-II, refAbstract=null), Reference(id=1172924086847161046, tenantId=1146029695717560320, journalId=1146123166801305609, articleId=1149768952479400140, doi=null, pmid=null, pmcid=null, year=2023, volume=null, issue=null, pageStart=null, pageEnd=null, url=null, language=null, rfNumber=[18], rfOrder=29, authorNames=舒伟成, journalName=地铁首末站常规公交“1+N”时刻表优化模型及算法, refType=null, unstructuredReference=舒伟成. 地铁首末站常规公交“1+N”时刻表优化模型及算法[D]. 南昌: 华东交通大学, 2023., articleTitle=null, refAbstract=null), Reference(id=1172924086981378776, tenantId=1146029695717560320, journalId=1146123166801305609, articleId=1149768952479400140, doi=null, pmid=null, pmcid=null, year=2023, volume=null, issue=null, pageStart=null, pageEnd=null, url=null, language=null, rfNumber=[18], rfOrder=30, authorNames=Shu Weicheng, journalName=The “1+N” timetable optimization model and algorithm of Metro first and last stations, refType=null, unstructuredReference=Shu Weicheng. The “1+N” timetable optimization model and algorithm of Metro first and last stations[D]. Nanchang: East China Jiaotong University, 2023., articleTitle=null, refAbstract=null)], funds=[Fund(id=1172924084091503264, tenantId=1146029695717560320, journalId=1146123166801305609, articleId=1149768952479400140, awardId=GSSYLXM-04, language=CN, fundingSource=甘肃省教育厅双一流重大科研项目(GSSYLXM-04), fundOrder=null, country=null)], companyList=[AuthorCompany(id=1172924077103792657, tenantId=1146029695717560320, journalId=1146123166801305609, articleId=1149768952479400140, xref=1, ext=[AuthorCompanyExt(id=1172924077112181266, tenantId=1146029695717560320, journalId=1146123166801305609, articleId=1149768952479400140, companyId=1172924077103792657, language=EN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=1 School of Traffic and Transportation, Lanzhou Jiaotong University, Lanzhou 730070, China), AuthorCompanyExt(id=1172924077116375571, tenantId=1146029695717560320, journalId=1146123166801305609, articleId=1149768952479400140, 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Classification of matching values for operational capacity

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运能匹配程度 分类 匹配度取值
运能富余 浪费 [0,0.40)
富余 [0.40,0.75)
运能协调 好 [0.75,0.80)
较好 [0.80,0.90)
运能瓶颈 轻度 [0.90,1.00)
中度 [1.00,1.10)
重度 [1.10,+∞)
), ArticleFig(id=1172924082761908867, tenantId=1146029695717560320, journalId=1146123166801305609, articleId=1149768952479400140, language=CN, label=表1, caption=

运能匹配度取值分级

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运能匹配程度 分类 匹配度取值
运能富余 浪费 [0,0.40)
富余 [0.40,0.75)
运能协调 好 [0.75,0.80)
较好 [0.80,0.90)
运能瓶颈 轻度 [0.90,1.00)
中度 [1.00,1.10)
重度 [1.10,+∞)
), ArticleFig(id=1172924082866766471, tenantId=1146029695717560320, journalId=1146123166801305609, articleId=1149768952479400140, language=EN, label=Table 2, caption=

Model parameter values

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参数 取值 参数 取值
hmin/min 5 TSmin 11:00
hmax/min 14 Ql/人 200
Rmin/min 4 φ/% 66[13]
Rmax/min 15[13] eul/min 4
pmax/% 60[18] Nmax/辆 24
), ArticleFig(id=1172924082942263944, tenantId=1146029695717560320, journalId=1146123166801305609, articleId=1149768952479400140, language=CN, label=表2, caption=

模型参数取值

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参数 取值 参数 取值
hmin/min 5 TSmin 11:00
hmax/min 14 Ql/人 200
Rmin/min 4 φ/% 66[13]
Rmax/min 15[13] eul/min 4
pmax/% 60[18] Nmax/辆 24
), ArticleFig(id=1172924083034538636, tenantId=1146029695717560320, journalId=1146123166801305609, articleId=1149768952479400140, language=EN, label=Table 3, caption=

Arrival time and transfer demand of rail transit trains

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方向 列车
车次u		 到站
时间		 时间
gu/s		 换乘需求 d u l , m/人
接运线路1 接运线路2
上行 U1 11:00 0 12 6
U2 11:07 420 14 8
U3 11:14 840 10 7
U4 11:21 1 260 16 10
U5 11:28 1 680 9 14
U6 11:35 2 100 13 15
U7 11:42 2 520 21 17
U8 11:49 2 940 26 20
U9 11:56 3 360 20 19
U10 12:03 3 780 22 21
U11 12:10 4 200 17 23
U12 12:17 4 620 20 18
U13 12:24 5 040 21 13
U14 12:31 5 460 20 15
U15 12:38 5 880 16 11
U16 12:45 6 300 17 9
U17 12:52 6 720 20 9
U18 12:59 7 140 13 4
下行 V1 11:02 120 10 10
V2 11:09 540 8 4
V3 11:16 960 12 11
V4 11:23 1 380 11 8
V5 11:30 1 800 13 12
V6 11:37 2 220 11 14
V7 11:44 2 640 9 13
V8 11:51 3 060 20 22
V9 11:58 3 480 16 18
V10 12:05 3 900 20 21
V11 12:12 4 320 19 17
V12 12:19 4 740 16 16
V13 12:26 5 160 23 18
V14 12:33 5 580 16 17
V15 12:40 6 000 14 9
V16 12:47 6 420 11 10
V17 12:54 6 840 9 3
), ArticleFig(id=1172924083118424718, tenantId=1146029695717560320, journalId=1146123166801305609, articleId=1149768952479400140, language=CN, label=表3, caption=

轨道交通列车到站时间及换乘客流量

, figureFileSmall=null, figureFileBig=null, tableContent=
方向 列车
车次u		 到站
时间		 时间
gu/s		 换乘需求 d u l , m/人
接运线路1 接运线路2
上行 U1 11:00 0 12 6
U2 11:07 420 14 8
U3 11:14 840 10 7
U4 11:21 1 260 16 10
U5 11:28 1 680 9 14
U6 11:35 2 100 13 15
U7 11:42 2 520 21 17
U8 11:49 2 940 26 20
U9 11:56 3 360 20 19
U10 12:03 3 780 22 21
U11 12:10 4 200 17 23
U12 12:17 4 620 20 18
U13 12:24 5 040 21 13
U14 12:31 5 460 20 15
U15 12:38 5 880 16 11
U16 12:45 6 300 17 9
U17 12:52 6 720 20 9
U18 12:59 7 140 13 4
下行 V1 11:02 120 10 10
V2 11:09 540 8 4
V3 11:16 960 12 11
V4 11:23 1 380 11 8
V5 11:30 1 800 13 12
V6 11:37 2 220 11 14
V7 11:44 2 640 9 13
V8 11:51 3 060 20 22
V9 11:58 3 480 16 18
V10 12:05 3 900 20 21
V11 12:12 4 320 19 17
V12 12:19 4 740 16 16
V13 12:26 5 160 23 18
V14 12:33 5 580 16 17
V15 12:40 6 000 14 9
V16 12:47 6 420 11 10
V17 12:54 6 840 9 3
), ArticleFig(id=1172924083261031057, tenantId=1146029695717560320, journalId=1146123166801305609, articleId=1149768952479400140, language=EN, label=Table 4, caption=

Target value of Pareto solution set

, figureFileSmall=null, figureFileBig=null, tableContent=
解集
序号		 客流流失量
Z1/人		 接运公交车
辆数Z2/辆		 候车总时间
Z3/min		 候车平均
时间/min
1 105 22 4 020 4.0
2 131 20 4 218 4.2
3 150 19 4 329 4.3
4 169 18 4 440 4.4
5 200 16 4 884 4.9
), ArticleFig(id=1172924083361694357, tenantId=1146029695717560320, journalId=1146123166801305609, articleId=1149768952479400140, language=CN, label=表4, caption=

Pareto解集的目标值

, figureFileSmall=null, figureFileBig=null, tableContent=
解集
序号		 客流流失量
Z1/人		 接运公交车
辆数Z2/辆		 候车总时间
Z3/min		 候车平均
时间/min
1 105 22 4 020 4.0
2 131 20 4 218 4.2
3 150 19 4 329 4.3
4 169 18 4 440 4.4
5 200 16 4 884 4.9
), ArticleFig(id=1172924083420414614, tenantId=1146029695717560320, journalId=1146123166801305609, articleId=1149768952479400140, language=EN, label=Table 5, caption=

Optimization plan for bus transportation timetable (Pareto optimal solution 2)

, figureFileSmall=null, figureFileBig=null, tableContent=
接运公交线路1 接运公交线路2
发车
时刻		 发车
间隔/s		 车辆
编号		 发车
时刻		 发车
间隔/s		 车辆
编号
11:04 — 1 11:06 — 2
11:13 542 3 11:16 602 4
11:20 422 5 11:27 662 6
11:28 482 7 11:34 422 8
11:37 542 9 11:43 542 10
11:46 542 11 11:51 482 12
11:53 422 13 11:59 482 14
12:00 422 15 12:05 360 16
12:06 362 17 12:12 362 18
12:12 362 19 12:18 362 20
12:19 422 1 12:25 422 2
12:26 422 3 12:32 422 4
12:32 362 5 12:42 602 7
12:40 482 6 12:52 602 9
12:49 542 8 13:03 662 11
12:57 482 10 — — —
13:03 362 12 — — —
), ArticleFig(id=1172924083491717783, tenantId=1146029695717560320, journalId=1146123166801305609, articleId=1149768952479400140, language=CN, label=表5, caption=

接运公交行车时刻表优化方案(Pareto最优解2)

, figureFileSmall=null, figureFileBig=null, tableContent=
接运公交线路1 接运公交线路2
发车
时刻		 发车
间隔/s		 车辆
编号		 发车
时刻		 发车
间隔/s		 车辆
编号
11:04 — 1 11:06 — 2
11:13 542 3 11:16 602 4
11:20 422 5 11:27 662 6
11:28 482 7 11:34 422 8
11:37 542 9 11:43 542 10
11:46 542 11 11:51 482 12
11:53 422 13 11:59 482 14
12:00 422 15 12:05 360 16
12:06 362 17 12:12 362 18
12:12 362 19 12:18 362 20
12:19 422 1 12:25 422 2
12:26 422 3 12:32 422 4
12:32 362 5 12:42 602 7
12:40 482 6 12:52 602 9
12:49 542 8 13:03 662 11
12:57 482 10 — — —
13:03 362 12 — — —
), ArticleFig(id=1172924083751764634, tenantId=1146029695717560320, journalId=1146123166801305609, articleId=1149768952479400140, language=EN, label=Table 6, caption=

Comparison of optimization results for different departure plans

, figureFileSmall=null, figureFileBig=null, tableContent=
公交车
辆数/辆		 均匀发车
间隔/min		 客流流失量/人 换乘候车总时间/min
均匀发车 不均匀发车 均匀发车 不均匀发车
22 7 89 105 4 110 4 020
20 8 118 131 4 326 4 218
19 10 165 150 4 530 4 329
18 12 193 169 4 824 4 440
16 13 234 200 5 120 4 884
), ArticleFig(id=1172924083906953885, tenantId=1146029695717560320, journalId=1146123166801305609, articleId=1149768952479400140, language=CN, label=表6, caption=

不同发车方案优化结果对比

, figureFileSmall=null, figureFileBig=null, tableContent=
公交车
辆数/辆		 均匀发车
间隔/min		 客流流失量/人 换乘候车总时间/min
均匀发车 不均匀发车 均匀发车 不均匀发车
22 7 89 105 4 110 4 020
20 8 118 131 4 326 4 218
19 10 165 150 4 530 4 329
18 12 193 169 4 824 4 440
16 13 234 200 5 120 4 884
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考虑客流需求的城轨接运公交行车计划优化
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周广汇 1, 2 , 陈明明 1, 2, * , 李继龙 1, 2 , 王斯佳 1 , 王振 1
科学技术与工程 | 论文·交通运输 2025,25(15): 6520-6529
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科学技术与工程 | 论文·交通运输 2025, 25(15): 6520-6529
考虑客流需求的城轨接运公交行车计划优化
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周广汇1, 2 , 陈明明1, 2, * , 李继龙1, 2, 王斯佳1, 王振1
作者信息
  • 1 兰州交通大学交通运输学院, 兰州 730070
  • 2 兰州交通大学城市交通大数据分析与应用实验室, 兰州 730070

    • 周广汇(1999—),男,汉族,甘肃白银人, 硕士研究生。研究方向:公交运营与管理。E-mail:。

通讯作者:

* 陈明明(1982—),男,汉族,山西霍州人,博士,副教授。研究方向:公交运营与管理。E-mail:。
Optimization of Urban Rail Transit Feeder Bus Scheduling Considering Passenger Flows Demand
Guang-hui ZHOU1, 2 , Ming-ming CHEN1, 2, * , Ji-long LI1, 2, Si-jia WANG1, Zhen WANG1
Affiliations
  • 1 School of Traffic and Transportation, Lanzhou Jiaotong University, Lanzhou 730070, China
  • 2 Urban Transportation Big Data Analysis and Application Laboratory, Lanzhou Jiaotong University, Lanzhou 730070, China
出版时间: 2025-05-28 doi: 10.12404/j.issn.1671-1815.2404608
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摘要
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为了满足城市轨道交通乘客换乘接运公交的需求,有效减少因超过候车容忍时间而出现的客流流失量,研究考虑轨道交通列车到站时间、客流流失量的接运公交行车计划优化方法。以研究时段内乘客换乘需求和轨道交通到站时间等标明客流需求分布,以乘客到达接运公交首站的时间与公交发车时刻衔接关系、接运公交运能等描述换乘时间。考虑公交发车时间间隔、客流流失量、客流换乘需求等约束,在可调度的公交车辆数有限情况下,实现客流流失量、公交车辆数和乘客换乘候车总时间最小的多目标优化。由于优化目标之间存在矛盾,可利用带精英策略的非支配排序遗传算法(non-dominated sorting genetic algorithm II, NSGA-Ⅱ)求解模型,得到该问题的Pareto解集。最后,以实际接运公交线路进行算例分析,结果表明:优化模型兼顾公交运营成本和乘客换乘时间成本,可得到满足客流需求且代表不同侧重点的行车计划方案;接运公交车辆数相同时,本文方法相对于均匀发车方案可使乘客换乘候车总时间优化效果增加8.0%;不均匀发车间隔下的平均满载率为59.3%,优于均匀发车间隔下的平均满载率50.2%。计算结果验证了模型和算法的有效性和合理性,有效提升接运公交和城市轨道交通时间和运能匹配度。

公共交通  /  接运公交  /  行车计划  /  客流流失  /  非支配排序遗传算法  /  运能匹配

In order to meet the transfer and transportation requirements of passengers and to significantly mitigate the loss of passenger flow that exceeds the waiting tolerance threshold, the optimization method of feeder bus scheduling considering the arrival time and passenger flow loss of rail transit trains was studied. The distribution of passenger flow demand was characterized by the passenger transfer demand and the arrival times of rail transit within the study period. The transfer time was described by the alignment between the time passengers arrive at the station of the bus and the bus departure schedule, as well as the operational capacity of the buses. The constraints of bus departure intervals, passenger flow loss and transfer demands were considered, and the multi-objective optimization with the minimum passenger flow loss, bus number and passenger transfer waiting time was realized under the limited number of buses that can be scheduled. Due to the contradictions among the optimization objectives, the model was solved with Non-dominated Sorting Genetic Algorithm II (NSGA-II). Finally, taking the actual bus routes as an example, the results show that the optimized model takes into account the bus operation cost and the passenger transfer time cost, and can obtain the scheduling that meets the passenger flow demand and represents different priorities. When the number of feeder buses is the same, the total transfer waiting time of the optimized method is reduced by 8.0% compared with the uniform headway. The average factor under the uneven is 59.3%, which is better than the average factor of 50.2% under the uniform. The calculation results validate the effectiveness and rationality of the model and algorithm, effectively enhancing the match between the time and capacity of buses and urban rail transit.

public transport  /  feeder bus  /  vehicle scheduling  /  loss of passenger flow  /  non dominant sorting genetic algorithm  /  capacity matching
周广汇, 陈明明, 李继龙, 王斯佳, 王振. 考虑客流需求的城轨接运公交行车计划优化. 科学技术与工程, 2025 , 25 (15) : 6520 -6529 . DOI: 10.12404/j.issn.1671-1815.2404608
Guang-hui ZHOU, Ming-ming CHEN, Ji-long LI, Si-jia WANG, Zhen WANG. Optimization of Urban Rail Transit Feeder Bus Scheduling Considering Passenger Flows Demand[J]. Science Technology and Engineering, 2025 , 25 (15) : 6520 -6529 . DOI: 10.12404/j.issn.1671-1815.2404608
正文
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在城市公共交通系统中,城市轨道交通由于运量大、速度快、集约高效、节能环保等突出优点,逐渐成为城市公共交通系统的骨干,支撑和引领城市发展。但是城市轨道交通覆盖范围较小,可达性较低,不能满足乘客支线运输服务,因此,构建与城市轨道交通接驳的设施愈加重要。常规公交由于调度较为灵活,可以实现客流“门到门”的运输服务,能够快速疏散集聚客流,成为换乘方式首选。一些城市逐渐推进城市轨道交通和常规公交网络融合发展,强化轨道交通与常规公交的换乘协调、运营融合。因此,实现轨道交通与常规公交行车时刻表的协同,减少乘客换乘时间成本、换乘客流流失量和企业运营成本,满足客流需求,已经成为接运公交要解决的重要问题。
近年来,国内外学者和专家在接运公交方面有大量的研究并取得一定的成果,在接运公交基础理论、轨道交通与接运公交的运营协调优化等方面均进行了研究探索。姜晓红等[1]以公交企业运营成本、乘客换乘时间、乘客换乘失败惩罚等为目标,建立了同时优化时刻表与行车计划的双层规划模型,并以城乡公交为实例对所提的方法进行了分析和验证,较好的应用于实践。张天伟等[2]在详细分析公交车辆运行特征的基础上,充分考虑乘客出行成本和公交载客成本,建立公交时刻表优化模型,结合实际线路计算发车间隔和运营成本,扩充了行车时刻表问题研究的实际应用。
从发车策略和乘客换乘时间出发,龙雪琴等[3]、Gkiotsalitis[4]考虑乘客换乘候车时间、协同换乘次数对时刻表编制的影响,建立了公交调度模型。袁振洲等[5]、梁晓辉等[6]在考虑乘客滞留站点的前提下,以换乘候车时间和非换乘乘客候车时间最小为目标,建立了公交行车时刻表优化模型。Xiong等[7]构建混合整数规划模型求解轨道交通接运电动公交时刻表,实现了公交总成本最小化。范文博等[8]提出自适应发车策略,构建以期望广义系统成本最小化为目标的优化模型,解决固定发车间隔导致系统过饱和或低饱和等问题。杨亚璪等[9]在研究电动接运公交与轨道交通的乘客换乘关系的基础上,针对换乘等待时间长、成本高等问题,以候车时间成本、换乘失败成本、公交运营成本和充电成本之和最小为目标,提出一种面向高峰时段的接运电动公交的时刻表优化方法。部分学者研究了乘客出行过程中的整体需求,建立了接运公交路径优化模型,但未考虑公交时刻表对乘客出行需求的影响[10-11]。胡松等[12] 针对交通低出行需求场景下时空下供需不平衡问题,建立了一个实时预定公交动态调度系统,可估算乘客排队候车时间。
综合来看,现有研究在接运公交和电动接运公交运营调度都有一定的研究基础,研究重点在于考虑乘客换乘时间和公交成本的运营调度问题上,在接运公交行车时刻表研究时多假设所有客流都换乘公交,较少考虑因候车时间过长而产生的客流流失现象,且编制接运公交行车计划时较少考虑轨道交通和接运公交运能匹配。现充分考虑轨道交通到站时间和排队候车容忍时间,以接运公交车辆数、换乘客流流失量、换乘候车总时间最少为目标,建立基于运能协调的多目标优化模型,模型中以发车时间间隔、客流换乘需求等约束,设计带精英策略的非支配排序遗传算法(non-dominated sorting genetic algorithm II,NSGA-Ⅱ)求解得到模型的 Pareto 解集,为决策者提供不同偏好的行车计划方案。
1 问题描述
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接运公交具有将客流运输到轨道交通站点,及疏散客流的双重功能,可增大轨道交通的影响范围。以轨道交通站点为网络连接基点,轨道交通和接运公交换乘特征如图1所示,主要有以下几种:① 接运公交线路途经轨道交通站点,公交线路L4、L5分别经过轨道交通站点R3、R1,由于无法保证车辆满载率,在运力调配和行车间隔调度上难度较大。② 轨道交通站点与接运公交首末站衔接换乘,轨道交通站点R2、R3乘客出站后可分别换乘公交线路L1、L2、L3到达目的地,此时常规公交与轨道交通在同一枢纽站点运输客流,有利于统筹安排运力和行车间隔。轨道交通出现较大客流量时,接运公交快速疏散客流,缓解站点压力,有一定的实践价值,作为主要研究对象。
通常情况下,轨道交通和接运公交的换乘衔接受到客流量的影响,且由于服务强度和运行速度不同,实际运营的发车间隔也不同。轨道交通运行时间在某一时段是固定的,因此,要尽可能发挥接运公交的调度较为灵活的优势,以轨道交通发车时刻、客流需求编制接运公交行车计划,确保全过程出行的连续性和高效性。
1.1 换乘候车时间
假设不考虑乘客步行行为差异,乘客从轨道交通列车下车后步行至接运公交首站的时间为固定值,轨道交通和接运公交换乘衔接时空图如图2所示。设gu为轨道交通列车u到站时刻,eul表示轨道交通换乘接运公交走行时间, b l m表示接运公交线路l第m辆车首站发车时刻,引入0-1变量 δ u l , m, 轨道交通列车u的乘客换乘接运公交线路l第m辆车时为1,否则为0。针对乘客因候车时间长产生客流流失,引入“最大候车容忍时间”参数Rmax[13]。分析换乘时空图可知,乘客从轨道交通列车u下车后步行至接运公交线路l进行换乘,由于时间上的不连续,会出现换乘成功( δ u l , m=1)和换乘失败( δ u l , m=0)两种情况,具体说明如下:
(1) 如果gu+eul> b l m - 1,则换乘乘客到达公交站点时,接运公交线路l的第m-1辆车已开行,乘客只能等下一辆车,此时 δ u l , m=0。
(2) 如果gu+eul≤ b l m≤gu+eul+Rmax,则换乘乘客到达公交站点时间早于接运公交线路l的第m辆车发车时刻,乘客有机会换乘成功,此时 δ u l , m=1;若换乘客流超过公交容量限制,部分乘客无法换乘,继续等待下一辆车。
(3) 如果gu+eul+Rmax< b l m + 1,表示换乘候车时间已经超过最大候车容忍时间,部分乘客不会换乘第m+1辆车,选择换乘其他交通方式,则认为换乘失败,此时 δ u l , m=0。
1.2 运能匹配
为了直观体现轨道交通和接运公交运能协调程度,引入运能匹配度ρ,可定义为:研究时段内,轨道交通乘客换乘接运公交的客流量与接运公交运输能力的比值[14]。当ρ<1时,表示运能匹配程度较好,ρ越小,表示接运能力越强;但是,ρ的值过小表示接运公交接运能力远大于换乘需求量,会造成公交车辆资源浪费,基于匹配度取值的运能瓶颈分级如表1所示[14]。
多个专家学者通过评价体系验证运能匹配度分级在 0.7~0.95 时协调较好[15]。参考一些学者的经验并考虑运营时间段内换乘客流变化情况,运能匹配度理想区间取为[0.75,0.90),公式为
0.75≤ρ= Q 换 乘 u → l Q 总 l= ∑ u = 1 U C u β r u φ u l ∑ m = 1 M C l p m a x<0.9
φul= D u l , m D u
式中:Du为轨道交通车站下车的乘客数; D u l , m为轨道交通列车u换乘接运公交线路l的总乘客数;Cl、Cu分别为接运公交和轨道交通额定载客人数; βru为轨道交通列车u满载率;换乘比例φul与换乘客流量有关。当运能匹配度不在此范围内时,可根据公交运输能力调整行车计划。
综合考虑轨道交通换乘客流需求、公交车辆数,编制合理的接运公交行车计划可以减少乘客候车时间。为了更好地研究候车时间对车辆调度的影响,从轨道交通和接运公交运能协调的角度出发,构建与轨道交通到站时刻协调的接运公交行车计划模型,为轨道交通和接运公交时间协调、运能协调提供参考。
2 接运公交行车计划优化模型
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2.1 参数设置
为方便建模,规定城市轨道交通和接运公交线路的运行时段。模型中涉及的集合、参数和决策变量定义如下。
(1) 集合定义。L为接运公交线路集合,l∈L;U为城市轨道交通到站列车集合,u,v∈U;M为接运公交车辆集合,m,i,j,k∈M。
(2) 参数定义。 d u l , m为轨道交通列车u换乘接运公交线路l第m辆车的乘客数; d u l为轨道交通列车u换乘接运公交线路l失败的乘客数; r u l , m为轨道交通列车u换乘乘客仍在等待接运公交线路l第m辆车的乘客数; w u l , m为接运公交线路l第m辆车发车前,列车u换乘乘客中已离开排队队列的乘客数; q l t为研究时段t内接运公交线路l发出的公交车辆数;Nmax为能够调度的最大公交车辆数; hmin、hmax分别为接运公交线路l的最小、最大发车时间间隔; b l m z为接运公交线路l第m辆车在站点z发车时刻;pl、pmax为接运公交满载率、最大满载率; Rmin、Rmax为乘客换乘最小、最大候车容忍时间,min; φ为排队候车时间超过最大候车容忍时间乘客离开队列的概率;φul为乘客换乘比例; Ql为客流最大流失量;TSmin为研究时段开始时间。
(3) 决策变量。 δ u l , m为0-1变量, 轨道交通列车u的乘客换乘接运公交线路l第m辆车时为1,否则为0; a u l , m为0-1变量, 表示轨道交通列车u上的换乘乘客候车时间是否超过最大候车容忍时间,超过为1,否则为0; Hl,z为0-1变量,接运公交线路l经过站点z时其值为 1,否则为 0,表征接运公交路线与车站的衔接关系; ξ u , m l , z为0-1 变量,轨道交通列车u的乘客换乘接运公交线路l第m辆车,且公交目的地是接运公交车站z时,取值为 1,否则为 0。
2.2 模型假设
为了简化问题,做出如下假设:
(1) 假设所有公交车辆全程走行时间是固定的,公交车班次连续运行,不存在所有车辆都出行之后首班车无法返回的情况。
(2) 从城市轨道交通换乘至接运公交的客流是给定的,可由对历史客流数据统计分析获得。
(3) 乘客已知公交下一车次发车时间,如果候车时间超过最大候车容忍时间可选择其他方式。
(4) 接运公交线路的首末站在轨道交通站点附近,公交车型统一,只考虑轨道交通换乘至公交的客流。
2.3 目标函数
在研究时段内,当换乘候车时间超过最大候车容忍时间,部分乘客会选择换乘其他出行方式,为了减少客流流失,吸引更多客流,以产生的客流流失量Z1为一个优化目标,表达式为
Z1= ∑ u ∈ U ∑ l ∈ L ∑ m ∈ M( D u l , m- d u l , m)
公交企业购置的公交车辆有限,以较少的车辆运输乘客是企业重点考虑的问题。因此,选用接运公交车辆数Z2为一个优化目标,表达式为
Z2= ∑ l ∈ L ∑ t q l t
在全过程出行服务中,换乘候车时间是乘客换乘时重点考虑因素,以乘客换乘候车总时间Z3为一个优化目标,表达式为
Z3= ∑ l ∈ L ∑ u ∈ U ∑ m ∈ M( b l m-gu-eul) D u l δ u l , m
根据上述分析,从系统角度出发,分别以客流流失量最小、公交车辆数最小和乘客换乘换乘候车总时间最小为目标构建多目标优化模型,优化目标可表示为
minZ1=min ∑ u ∈ U ∑ l ∈ L ∑ m ∈ M( D u l , m- d u l , m)
minZ2=min ∑ l ∈ L ∑ t q l t
minZ3=min ∑ l ∈ L ∑ u ∈ U ∑ m ∈ M( b l m-gu-eul) D u l δ u l , m
2.4 约束条件
2.4.1 发车时间间隔
为满足换乘需求,保证接运公交运营符合实际情况,接运公交发车间隔要控制在一个区间,如式(9);接运公交每一车次按序发车,为避免出现串车,首站和中间站点发车时刻要有序,如式(10);在研究时段内,接运公交线路首班车必须在给定时间发车,且接运公交最后一辆车与研究时段轨道交通最后一列车接运成功,如式(11)、式(12);接运公交发车时刻和发车时间间隔均为整数变量,保证接运公交运营调度在实际中易于执行,如式(13)。
hmin≤hl= 60 C l p l D u l= b l m + 1- b l m≤hmax
b l m< b l m + 1, b l m z< b l ( m + 1 ) z
TSmin≤ b l 1≤TSmin+h1
b l m ( l a s t )≥gu(last)+eul
hl,h1, b l 1, b l m∈Z, ∀ l ∈ L , m ∈ M
2.4.2 车辆配置和客流流失量
在实际运行中,公交车辆是有限的,则运营时间段内可发出的公交车辆总数不能超过能够调度的最大公交车辆数,如式(14);公交每一个车次最多有一个后序车次和一个前序车次连接,定义xij表示接运公交车次i和j是否连接,如式(15);如果发车车次i和j可连接时,取值为 1,否则为0;为了控制客流流失量,设定最大候车容忍时间约束,在候车容忍时间区间内,客流不会流失,如式(16);为了吸引更多乘客,客流流失量要控制在企业可接受范围内,如式(17)。
$\begin{array}{l} \sum_{l \in L} \sum_{t} q_{l}^{t}=\sum_{l \in L} \sum_{t} \frac{t \max \left(D_{u}^{l}\right)}{C_{l} p_{l}} \leqslant N_{\max } \\ \sum_{j} x_{i j} \leqslant 1, \quad \forall i \in M \end{array}$
∑ ixij≤1, ∀ j ∈ M
Rmin≤ b l m-gu-eul≤Rmax
∑ u ∈ U ∑ l ∈ L ∑ m ∈ M( D u l , m- d u l , m)= ∑ u ∈ U ∑ l ∈ L ∑ m ∈ M r u l , m a u l , mφ≤Ql
2.4.3 客流需求
要判定产生的客流流失量,则要判断换乘接运公交线路的候车时间是否超过最大候车容忍时间,如式(18)、式(19);所有乘客有换乘成功和失败两种可能,所有换乘总客流是平衡的,如式(20);到达接运公交起点站的乘客必须等其之前到站的乘客上车后才能换乘,不存在插队问题,如式(21),式中M是一个足够大的正数;为保证较多的客流换乘接运公交,则到达公交首发站的乘客在超过最大候车容忍时间之前不会换乘其他交通方式,如式(22);式(23)为决策变量关系约束;式(24)表示m-1辆公交发车后,轨道交通第u列车换乘客流中继续等待第m辆公交的客流量。
a u l , m∈{0,1}, ∀u∈U,l∈L,m∈M
$\begin{array}{c} M\left(a_{u}^{l, m}-1\right) \leqslant b_{l}^{m}-g_{u}-e_{u l}-R \leqslant M a_{u}^{l, m}, \\ \forall u \in U, l \in L, m \in M \end{array}$
∑ m ∈ M d u l , m+ d u l= D u l , m
d u l , i≤M(1- δ v l , j), ∀i,j∈M,u,v∈U,g u<gv, b l i> b l j,l∈L
d u l≤M(1- δ v l , j), ∀u,v∈U,g u<gv,l∈L
δ u l , i≤ d u l , i, ∀u∈U,l∈L,i∈M
r u l , m= D u l , m , 　 u = 1,2 , 3 , … , U ; m = 1 D u l , m - ∑ k = 1 m - 1 ( d u l , k + w u l , k ) , 　 　 　 u = 1,2 , 3 , … , U ; m = 2,3 , … , M
轨道交通换乘客流出站后选择接运公交某一线路进行换乘,当接运公交线路l通过接运公交站点z时,换乘乘客才会选择该线路,如式(25);式(26)为0-1变量决策约束。
ξ u , m l , z≤Hl,z
xij, δ u l , m, ξ u , m l , z,Hl,z∈{0,1}, ∀m,i,j∈M,u∈U,l∈L
3 基于NSGA-Ⅱ的模型求解算法
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本文提出的接运公交行车计划优化模型为一个多目标优化模型,现有研究多采用启发式算法求解。部分研究学者已经证明常规公交行车计划优化问题是一个 NP-hard 问题,采用遗传算法(genetic algorithm,GA)求解 [16]。由于GA算法求解多目标问题多运用加权法的方式归一化,加权系数较难确定,实质上仍为单目标问题求解且需要使用适应度函数,无法真正体现多目标优化的优势。本文选用的优化目标之间存在一定冲突,难以找到多个目标均达到最优的方案。因此,GA算法不适合本文模型求解,可利用多目标优化算法生成多个互不支配的Pareto解供决策者选择。在GA算法的基础上,Kalyanmoy等[17]提出的带精英策略的快速非支配排序遗传算法(NSGA-Ⅱ)在解决多目标优化问题时能够求解得到分布均匀的 Pareto解集,被广泛应用在多目标问题求解上,可为本文模型求解算法。
NSGA-Ⅱ算法使用快速非支配排序和拥挤度算子来寻找一组非支配解,快速非支配排序可处理个体之间的支配关系,拥挤度算子、拥挤度比较算子增加种群的多样性。同时引入精英策略能够筛选并保持每一代的最优解,通过协调各目标间的相互关系,使得到的Pareto解集在目标空间中更加均匀。该算法是一种基于Pareto最优解的多目标优化算法,在解决此接运公交行车计划优化模型上更具有优势。基于NSGA-II的多目标优化算法求解步骤如下:
(1)种群初始化。种群规模N、交叉概率pc、变异概率pm、进化代数gen=1及最大进化代数maxgen等参数,随机挑选生成初始种群Pn。
(2)判断是否生成第一代种群,如果生成则令gen=2;否则对Pn中所有个体实行非支配排序,得到所有个体的非支配排序值,且进行选择、交叉和变异生成种群规模为N的子代种群Qn,并使进化代数gen=2。
(3)父代种群Pn和子代种群Qn进行合并,生成种群规模为2N的新种群Rn=Pn∪Qn。
(4)判断是否已生成新的父代种群,若没有则依次计算各目标函数的值,根据函数值对Rn进行快速非支配排序,并计算拥挤度。
(5)通过精英保留策略,在Rn中挑选优秀个体加入新父代种群 Pn+1,新父代种群Pn+1经过选择、交叉和变异操作后,计算子代种群Qn+1产生的目标函数值。
(6)若达到最大迭代次数maxgen,输出Pareto最优解集,算法结束;否则令gen=gen+1,转回步骤(3)。
根据带精英策略的NSGA-Ⅱ算法执行步骤,算法流程图如图3所示。
4 算例分析
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4.1 算例描述
本文中研究基于运能协调的接运公交行车计划,主要选取兰州市轨道交通1号线和2条始发接运公交线路为研究算例,验证模型和求解算法的有效性。选定的研究时段为11:00—13:00,该时段站点停靠35次列车。轨道交通发车间隔为7 min,站点停靠时间为2 min,乘客换乘走行时间为4 min。以14 min为单位统计每个时间段轨道交通换乘接运公交线路1、2的客流量,研究时段换乘的乘客为1 007人,客流分布如图4所示。
研究时间段接运公交采用固定时间、均匀发车间隔的发车方式,始发站布设在轨道交通站点附近且位于同一个公交车场,接运公交线路1、2从出发到返回车场全程走行时间分别为64、70 min,接运公交平均行驶速度为30 km/h,平均发车时间间隔为10 min。模型中接运公交线路部分参数参考文献[13,18],如表2所示。
参考《城市公交管理规范标准》中的规定,公交标准车型的额定载客人数Cl=40人/辆,高峰时段车辆平均满载率应低于 85%,平峰时段车辆平均满载率低于60%[18]。根据数据统计,研究时段内列车到站时间以及换乘接运公交的客流量如表3所示。
4.2 算例结果及分析
使用Python语言编程实现NSGA-Ⅱ算法,NSGA-Ⅱ算法中各参数设置为:种群规模N=100、最大进化代数maxgen=500、交叉概率pc=0.8、变异概率pm=0.2。当迭代至maxgen时停止运行,输出结果为运行至最大代数取得的 Pareto近似最优解,多次独立运行获得的Pareto近似最优解集如图5所示。为了便于区分各个解的优劣,可设定不同颜色判定,图5右侧8~24中的每一个值代表一种颜色,数值越小表示求得的解较优,满足各约束条件。
根据某一次运算结果求解发车时刻,计算Pareto解集中客流流失量、接运公交车辆数和乘客换乘时间。所有解中换乘候车平均时间都在容忍时间区间内,满足乘客需求,Pareto解集中的乘客流失量最少为105人,占乘客换乘需求总量的10.4%。从表4可以看出用NSGA-Ⅱ算法求解模型,可以在Pareto解集得到多个处于相互非支配地位的最优解,虽然不同益解对应的目标值有差异,但均能使多个目标整体效达到最优,且偏好不同目标的 Pareto解可为决策者提供不同方案。
由表4可知,当决策者侧重运营成本时,可以选择解5编制接运公交行车计划;当决策者偏向乘客候车时间成本及吸引换乘客流量时,可以选择解1编制接运公交行车计划。如果决策者综合权衡多个目标,可以选定解2~4的结果编制行车计划,根据情况实时调整。以解2给出接运公交行车时刻表方案,如表5所示,执行两个车次的车辆运行周转时间在发车时刻区间以内,不会出现车场无车可调的情况。
根据表5优化方案可知,当接运公交车辆数为20辆时,产生的客流流失量为131人,乘客换乘候车总时间为4 218 min,候车平均时间为4.2 min(252 s),接运公交线路1、2发出的车次数分别为17和15,部分车辆循环周转,执行了两个车次,研究时段内城市轨道交通最后一班列车的乘客均离开站点,该趟列车有换乘需求的乘客没有站点滞留情况,均通过换乘方式离开站点。
4.3 优化结果分析
4.3.1 最大公交车辆数灵敏度分析
构建的多目标优化模型中,接运公交车辆数的变化直接影响客流流失量和换乘候车总时间,将能够调度的公交车辆数在16~24辆之间调整,客流流失量、乘客换乘候车总时间变化如图6所示。
由图6可知,当公交车辆数为16辆时,客流流失量达到上限,如果最大公交车辆数少于16辆,客流流失量将会超过最大客流流失量Ql。随着公交车辆数的增加,客流流失量和换乘候车总时间逐渐减少,当公交车辆数为22辆时,客流流失量和换乘候车总时间的变化趋于平缓。如果继续增加公交车辆数,公交企业运营成本将会增加,但是客流流失量和换乘候车总时间降低幅度较小,此时可以权衡企业成本和乘客时间成本的前提下决策可调度的公交车辆数。
4.3.2 不同发车方案对比分析
公交企业在实际运营中多采用均匀发车间隔时刻表,为了验证本文提出的基于运能协调的不均匀发车间隔的有效性,根据客流需求和公交额定载客人数计算不同公交车辆数时的发车间隔,确定均匀发车间隔方案,将两种方法得到的目标值进行对比。以目标(6)~目标(8)和约束条件构建均匀发车间隔模型,发车间隔5 min≤hl≤14 min,根据时间间隔约束求解最大公交车辆数为16、18、19、20、22辆时的发车间隔,可知该范围下发车间隔分别为13、12、10、8、7 min。计算等发车间隔下的目标值,与表4中的解做对比,方案结果对比如表6所示。
两种发车方案对比分析如图7所示。由图7可知,如果采用均匀发车间隔,当Nmax>20时,对应的客流流失量较表 4中的解1和解2分别减少15.2%和10.0%,客流流失量少于本文提出的不均匀发车方案。由于车辆数较多的情况下,发车间隔较小,排队候车时间超过最大候车容忍时间乘客离开队列的概率φ在相应的减少,由式(3)可知客流流失量也在减少。但由式(14)计算相同车辆数下的平均满载率,均匀发车下的平均满载率为50.2%,不均匀发车间隔下的平均满载率为59.3%,优于均匀发车间隔下各公交车次平均满载率,这是由于均匀发车间隔未考虑轨道交通换乘客流到站时间和到站客流量,无法保证车辆最低满载率,造成公交运力浪费。
由图7可知,在公交车辆数相同时,采用不均匀发车间隔相较于均匀发车间隔方案最多可使乘客换乘候车总时间减少8.0%(车辆数为18辆),平均换乘候车时间也优于均匀发车间隔方案。由图6可知,公交车辆数达到一定上限,客流流失量不会随着车辆数增加而减少,此时对客流流失量的优化作用越来越少,更加说明本文方法的有效性。如果减少公交车辆数,两种方法的换乘候车总时间差值逐渐增大,进一步说明了不均匀发车间隔的优越性。
5 结论
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(1) 考虑轨道交通列车到站时间、运能协调和客流流失等因素,以换乘客流流失量最小、可调度的公交车辆数最小和乘客换乘候车总时间最小为目标,设定发车时间间隔、最大客流流失量、候车容忍时间等约束条件,构建城轨接运公交行车计划多目标优化模型,并通过NSGA-Ⅱ算法求解得到Pareto解集,筛选出不同偏好的行车计划方案供决策者选择,并进行方案对比。
(2) 通过算例结果可知,本文构建的行车计划模型可以兼顾公交运营成本和乘客换乘时间成本,采用不均匀发车间隔可以衔接轨道交通到站时间,在运能协调情况下根据客流需求实时调整接运公交行车计划,避免运营时段内因发车间隔过小增加企业运营成本,及发车间隔过大导致客流流失量增加,企业效益减小。
(3) 通过方案对比可知,公交车辆数相同的情况下,由于均匀发车方案未考虑换乘客流到站时间和公交车辆的有限性,致使车辆满载率较低,公交运力相比于本文优化方案浪费较大。同时,本文优化模型相对于均匀发车方案可使乘客换乘候车总时间减少8.0%。因此,从综合考虑公交车辆运营成本和乘客换乘候车时间成本出发,本文求解得到的行车计划方案效果较优。
考虑运能协调下的接运公交行车计划编制,所有公交车辆采用单一车型。如果考虑高峰时段、体育赛事等大客流爆发情景,即某时段内换乘客流计算得到的运能匹配度评定等级为“运能瓶颈”,标准公交车型的运力将无法满足需求,采用本文公交行车计划模型将不再适用该场景。针对客流爆发场景,将以最大程度疏散客流量为目标,引入多车型公交模式和应急接运调度模式,解决运能瓶颈下接运公交行车时刻表和多车型模式联合优化问题,此问题也将成为下一步研究方向。
基金
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  • 甘肃省教育厅双一流重大科研项目(GSSYLXM-04)
文献
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2025年第25卷第15期
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doi: 10.12404/j.issn.1671-1815.2404608
  • 接收时间：2024-06-20
  • 首发时间：2025-07-09
  • 出版时间：2025-05-28
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  • 收稿日期：2024-06-20
  • 修回日期：2024-11-24
基金
甘肃省教育厅双一流重大科研项目(GSSYLXM-04)
作者信息
    1 兰州交通大学交通运输学院, 兰州 730070
    2 兰州交通大学城市交通大数据分析与应用实验室, 兰州 730070

通讯作者:

* 陈明明(1982—),男,汉族,山西霍州人,博士,副教授。研究方向:公交运营与管理。E-mail:。
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红菇科 Russulaceae 3 23 11.00 小皮伞属 Marasmius 6 2.87
小菇属 Mycena 11 5.26
光柄菇属 Pluteus 5 2.39
红菇属 Russula 17 8.13
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