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Article(id=1149729550315204956, tenantId=1146029695717560320, journalId=1146123302524792850, issueId=1149729524209861062, articleNumber=null, orderNo=null, doi=10.3969/j.issn.1672-6073.2025.01.006, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1712937600000, receivedDateStr=2024-04-13, revisedDate=1727280000000, revisedDateStr=2024-09-26, acceptedDate=null, acceptedDateStr=null, onlineDate=1752046485736, onlineDateStr=2025-07-09, pubDate=null, pubDateStr=null, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1752046485736, onlineIssueDateStr=2025-07-09, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1752046485736, creator=13701087609, updateTime=1752046485736, updator=13701087609, issue=Issue{id=1149729524209861062, tenantId=1146029695717560320, journalId=1146123302524792850, year='2025', volume='38', issue='1', pageStart='1', pageEnd='176', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1752046479512, creator=13701087609, updateTime=1753780104827, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1157000875844653181, tenantId=1146029695717560320, journalId=1146123302524792850, issueId=1149729524209861062, language=EN, specialIssueTitle=, coverIllustrator=, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1157000875844653182, tenantId=1146029695717560320, journalId=1146123302524792850, issueId=1149729524209861062, language=CN, specialIssueTitle=, coverIllustrator=, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=44, endPage=52, ext={EN=ArticleExt(id=1149729550495560039, articleId=1149729550315204956, tenantId=1146029695717560320, journalId=1146123302524792850, language=EN, title=Optimization Study of Flexible Train Composition and Full-Length and Short-Turn Routings Based on NSGA-II, columnId=1152669340382966151, journalTitle=Urban Rapid Rail Transit, columnName=Forum of Rapid Rail Transit, runingTitle=null, highlight=null, articleAbstract=

In response to the diversified and uneven demand for passenger travel, with the goal of improving service levels, this study proposes an operational mode for urban rail transit, which involves online flexible train composition and fulllength and shortturn routings, and integrates NSGAII algorithm to optimize the operational scheme. Firstly, the study analyzes the turnaround scenarios of trains under flexible composition conditions and determines the relationship between turnaround time and departure intervals. Secondly, using passenger travel costs and train operating kilometers as objective functions, a mathematical model for the operational mode of urban rail transit with online flexible train composition and fulllength and shortturn routings is designed based on the NSGAII algorithm. Finally, a case study is conducted to verify the feasibility and effectiveness of the algorithm for a specific rail transit line. The results show that compared to single routing, fulllength and shortturn routings, and mixed operation modes with multiple compositions, the proposed operational mode reduces vehicle operating kilometers by 42.68%, 22.81%, and 15.98% respectively, reduces vehicle utilization by 35%, 23.53%, and 16.13% respectively, and reduces the maximum load factor from 161.71%, 123.54%, and 135.49% to 119.68%. This operational mode effectively reduces vehicle operating kilometers and utilization while ensuring service levels and improving the balance of line load factor, thereby bringing greater benefits and improvements to urban rail transit systems.

, correspAuthors=Jikang XU, 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=Jiale FU, Jing WEN, Jikang XU, Yating FU, Yanli ZHOU, Yuhao SHI), CN=ArticleExt(id=1149729570368172730, articleId=1149729550315204956, tenantId=1146029695717560320, journalId=1146123302524792850, language=CN, title=基于NSGA-II的灵活编组大小交路开行方案优化研究, columnId=1152669340680761737, journalTitle=都市快轨交通, columnName=快轨论坛, runingTitle=null, highlight=null, articleAbstract=

针对客流出行需求多样化和不均衡化的问题,以提升服务水平为目标,提出一种城市轨道交通在线灵活编组大小交路的运营模式,并结合NSGAII 算法对开行方案进行优化。首先,分析列车在灵活编组条件下的折返场景,并确定折返时间与发车间隔之间的关系;其次,以乘客出行成本和列车运行公里数为目标函数,基于NSGAII 算法,设计在线灵活编组大小交路运营模式的数学模型;最后,针对线路情况,进行实例计算验证算法的可行性和有效性。结果表明:在线灵活编组大小交路运营模式相较于单一交路、大小交路和多编组混跑模式,其车辆运行公里数分别减少42.68%, 22.81%和15.98%,车辆运用数分别减少35%,23.53%和16.13%,断面最大满载率分别从161.71%,123.54%和135.49%减少到119.68%。该运营模式能够在确保服务水平的同时减少车辆运行公里数、车辆运用数,提高线路满载率均衡程度,为城市轨道交通系统带来更大的效益和改善。

, correspAuthors=徐纪康, authorNote=null, correspAuthorsNote=
徐纪康，男，讲师，从事城市轨道交通信号系统设计与研究，
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傅佳乐，男，硕士研究生，研究方向为城市轨道交通在线灵活编组关键技术，

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傅佳乐，男，硕士研究生，研究方向为城市轨道交通在线灵活编组关键技术，

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傅佳乐，男，硕士研究生，研究方向为城市轨道交通在线灵活编组关键技术，

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articleId=1149729550315204956, language=EN, label=Table 1, caption=Table of time point meanings, figureFileSmall=null, figureFileBig=null, tableContent=
时间点 含义 注释
${T}_{1}$ 列车至接车干扰点 时间点 受线路情况、列车车型参数、编 组数影响
${T}_{2}$ 列车接车干扰点至 停站时间点 受线路情况、列车车型参数、编 组数影响
${T}_{3}$ 列车清客并办理进 折返线进路时刻 清客、办理进路时间由站点需求 决定
${T}_{4}$ 列车驶入折返线 时间点 受线路情况、列车车型参数、编 组数影响
${T}_{5}$ 列车折返线内等待 时间点 若为联挂折返此时间包含联挂操 作；若为解编折返此时间包含解 编操作
${T}_{6}$ 列车驶出折返线 时间点 受线路情况、列车车型参数、编 组数影响
${T}_{7}$ 列车停站上客时间点 上客时间由站点需求决定
${T}_{8}$ 列车站台发车至出清 防护点时间点 受线路情况、列车车型参数、编 组数影响
), ArticleFig(id=1154051025318171378, tenantId=1146029695717560320, journalId=1146123302524792850, articleId=1149729550315204956, language=CN, label=表 1, caption=时间点含义, figureFileSmall=null, figureFileBig=null, tableContent=
时间点 含义 注释
${T}_{1}$ 列车至接车干扰点 时间点 受线路情况、列车车型参数、编 组数影响
${T}_{2}$ 列车接车干扰点至 停站时间点 受线路情况、列车车型参数、编 组数影响
${T}_{3}$ 列车清客并办理进 折返线进路时刻 清客、办理进路时间由站点需求 决定
${T}_{4}$ 列车驶入折返线 时间点 受线路情况、列车车型参数、编 组数影响
${T}_{5}$ 列车折返线内等待 时间点 若为联挂折返此时间包含联挂操 作；若为解编折返此时间包含解 编操作
${T}_{6}$ 列车驶出折返线 时间点 受线路情况、列车车型参数、编 组数影响
${T}_{7}$ 列车停站上客时间点 上客时间由站点需求决定
${T}_{8}$ 列车站台发车至出清 防护点时间点 受线路情况、列车车型参数、编 组数影响
), ArticleFig(id=1154051025372697331, tenantId=1146029695717560320, journalId=1146123302524792850, articleId=1149729550315204956, language=EN, label=Table 2, caption=Simulation results of station turnaround with flexible train composition, figureFileSmall=null, figureFileBig=null, tableContent=
站点编号 折返类型 折返时间 /s
1 直进弯出 172
4 弯进直出 182
8 存车线折返 224
9 存车线折返 224
16 存车线折返 224
23 直进弯出 182
30 弯进直出 172
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站点编号 折返类型 折返时间 /s
1 直进弯出 172
4 弯进直出 182
8 存车线折返 224
9 存车线折返 224
16 存车线折返 224
23 直进弯出 182
30 弯进直出 172
), ArticleFig(id=1154051025490137845, tenantId=1146029695717560320, journalId=1146123302524792850, articleId=1149729550315204956, language=EN, label=Table 3, caption=Pareto front solutions, figureFileSmall=null, figureFileBig=null, tableContent=
编号 大小交路 折返站编号 大小交路 折返站编号 大交路发车 频率 小交路发车 频率 列车编组数 /辆 列车编组数 /车两 乘客出行 时间 /s 车辆运行 公里数/km 满载率 均衡程度1%
1 12 30 12 12 3 3 3 189 593.12 278 497.27 1.25
2 12 30 14 7 3 3 3 169 127.72 957 611.21 1.38
3 16 30 14 7 3 3 3 190 407.02 148 769.28 2.54
4 23 30 9 9 6 3 3 521 562.57 4 392.14 3.71
5 8 23 8 16 6 3 3 181 730.90 4 530.08 0.25
6 16 30 12 6 3 3 3 270 554.71 34 756.79 3.46
7 16 30 12 6 3 3 4 338 727.15 3 952.12 3.42
8 16 23 8 8 6 3 4 770 688.40 3 904.12 3.63
9 16 23 8 24 6 3 4 122 746.53 4 000.12 3.32
10 12 30 11 11 3 3 3 230 242.87 48 571.46 1.49
), ArticleFig(id=1154051025553052406, tenantId=1146029695717560320, journalId=1146123302524792850, articleId=1149729550315204956, language=CN, label=表 3, caption=Pareto 前沿解集, figureFileSmall=null, figureFileBig=null, tableContent=
编号 大小交路 折返站编号 大小交路 折返站编号 大交路发车 频率 小交路发车 频率 列车编组数 /辆 列车编组数 /车两 乘客出行 时间 /s 车辆运行 公里数/km 满载率 均衡程度1%
1 12 30 12 12 3 3 3 189 593.12 278 497.27 1.25
2 12 30 14 7 3 3 3 169 127.72 957 611.21 1.38
3 16 30 14 7 3 3 3 190 407.02 148 769.28 2.54
4 23 30 9 9 6 3 3 521 562.57 4 392.14 3.71
5 8 23 8 16 6 3 3 181 730.90 4 530.08 0.25
6 16 30 12 6 3 3 3 270 554.71 34 756.79 3.46
7 16 30 12 6 3 3 4 338 727.15 3 952.12 3.42
8 16 23 8 8 6 3 4 770 688.40 3 904.12 3.63
9 16 23 8 24 6 3 4 122 746.53 4 000.12 3.32
10 12 30 11 11 3 3 3 230 242.87 48 571.46 1.49
), ArticleFig(id=1154051025620161271, tenantId=1146029695717560320, journalId=1146123302524792850, articleId=1149729550315204956, language=EN, label=Table 4, caption=Comparison of various indicators under four operational modes, figureFileSmall=null, figureFileBig=null, tableContent=
运营模式 发车频率/(对/h) 编组数/辆 大小交路位置 乘客出行 车辆运行 车辆运 断面最大 满载率
大交路 小交路 大交路 小交路 站点 站点 时间 /s 公里数/km 用数/辆 满载率1% 均衡程度1%
固定编 单一交路 18 - 6 - - - 2970164.51 7904.13 240 161.71 3.42
组模式 大小交路(1:2) 8 16 6 6 8 23 3122 483.17 5 869.29 204 123.54 1.38
多编组混跑(3,6 辆编组) 8 16 6 3 8 23 3 580 401.72 5 392.14 186 135.49 1.49
灵活编组(3+3) 8 16 6 3 8 23 3 181 730.90 4 530.08 156 119.68 0.25
), ArticleFig(id=1154051025674687224, tenantId=1146029695717560320, journalId=1146123302524792850, articleId=1149729550315204956, language=CN, label=表 4, caption=四种运营模式下各指标对比, figureFileSmall=null, figureFileBig=null, tableContent=
运营模式 发车频率/(对/h) 编组数/辆 大小交路位置 乘客出行 车辆运行 车辆运 断面最大 满载率
大交路 小交路 大交路 小交路 站点 站点 时间 /s 公里数/km 用数/辆 满载率1% 均衡程度1%
固定编 单一交路 18 - 6 - - - 2970164.51 7904.13 240 161.71 3.42
组模式 大小交路(1:2) 8 16 6 6 8 23 3122 483.17 5 869.29 204 123.54 1.38
多编组混跑(3,6 辆编组) 8 16 6 3 8 23 3 580 401.72 5 392.14 186 135.49 1.49
灵活编组(3+3) 8 16 6 3 8 23 3 181 730.90 4 530.08 156 119.68 0.25
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基于NSGA-II的灵活编组大小交路开行方案优化研究
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傅佳乐 1 , 文静 1 , 徐纪康 1 , 付雅婷 2 , 周艳丽 2 , 施宇豪 3
都市快轨交通 | 快轨论坛 2025,38(1): 44-52
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都市快轨交通 | 快轨论坛 2025, 38(1): 44-52
基于NSGA-II的灵活编组大小交路开行方案优化研究
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傅佳乐1 , 文静1, 徐纪康1 , 付雅婷2, 周艳丽2, 施宇豪3
作者信息
  • 1 上海工程技术大学 城市轨道交通学院 上海 201620
  • 2 华东交通大学 电气与自动化工程学院 南昌 330013
  • 3 上海市隧道工程轨道交通设计研究院 上海 200070

    • 傅佳乐，男，硕士研究生，研究方向为城市轨道交通在线灵活编组关键技术，

通讯作者:

徐纪康，男，讲师，从事城市轨道交通信号系统设计与研究，
Optimization Study of Flexible Train Composition and Full-Length and Short-Turn Routings Based on NSGA-II
Jiale FU1 , Jing WEN1, Jikang XU1 , Yating FU2, Yanli ZHOU2, Yuhao SHI3
Affiliations
  • 1 School of Urban Railway Transportation Shanghai University of Engineering Science Shanghai 201620
  • 2 East China Jiaotong University Nanchang 330013
  • 3 Shanghai Tunnel Engineering & Rail Transit Design and Research Institute Shanghai 200070
doi: 10.3969/j.issn.1672-6073.2025.01.006
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摘要
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针对客流出行需求多样化和不均衡化的问题,以提升服务水平为目标,提出一种城市轨道交通在线灵活编组大小交路的运营模式,并结合NSGAII 算法对开行方案进行优化。首先,分析列车在灵活编组条件下的折返场景,并确定折返时间与发车间隔之间的关系;其次,以乘客出行成本和列车运行公里数为目标函数,基于NSGAII 算法,设计在线灵活编组大小交路运营模式的数学模型;最后,针对线路情况,进行实例计算验证算法的可行性和有效性。结果表明:在线灵活编组大小交路运营模式相较于单一交路、大小交路和多编组混跑模式,其车辆运行公里数分别减少42.68%, 22.81%和15.98%,车辆运用数分别减少35%,23.53%和16.13%,断面最大满载率分别从161.71%,123.54%和135.49%减少到119.68%。该运营模式能够在确保服务水平的同时减少车辆运行公里数、车辆运用数,提高线路满载率均衡程度,为城市轨道交通系统带来更大的效益和改善。

城市轨道交通  /  灵活编组  /  大小交路  /  开行方案  /  NSGA-II算法

In response to the diversified and uneven demand for passenger travel, with the goal of improving service levels, this study proposes an operational mode for urban rail transit, which involves online flexible train composition and fulllength and shortturn routings, and integrates NSGAII algorithm to optimize the operational scheme. Firstly, the study analyzes the turnaround scenarios of trains under flexible composition conditions and determines the relationship between turnaround time and departure intervals. Secondly, using passenger travel costs and train operating kilometers as objective functions, a mathematical model for the operational mode of urban rail transit with online flexible train composition and fulllength and shortturn routings is designed based on the NSGAII algorithm. Finally, a case study is conducted to verify the feasibility and effectiveness of the algorithm for a specific rail transit line. The results show that compared to single routing, fulllength and shortturn routings, and mixed operation modes with multiple compositions, the proposed operational mode reduces vehicle operating kilometers by 42.68%, 22.81%, and 15.98% respectively, reduces vehicle utilization by 35%, 23.53%, and 16.13% respectively, and reduces the maximum load factor from 161.71%, 123.54%, and 135.49% to 119.68%. This operational mode effectively reduces vehicle operating kilometers and utilization while ensuring service levels and improving the balance of line load factor, thereby bringing greater benefits and improvements to urban rail transit systems.

urban rail transit  /  flexible train composition  /  full-length and short-turn routing  /  train operation plan  /  NSGA- II
傅佳乐, 文静, 徐纪康, 付雅婷, 周艳丽, 施宇豪. 基于NSGA-II的灵活编组大小交路开行方案优化研究. 都市快轨交通, 2025 , 38 (1) : 44 -52 . DOI: 10.3969/j.issn.1672-6073.2025.01.006
Jiale FU, Jing WEN, Jikang XU, Yating FU, Yanli ZHOU, Yuhao SHI. Optimization Study of Flexible Train Composition and Full-Length and Short-Turn Routings Based on NSGA-II[J]. Urban Rapid Rail Transit, 2025 , 38 (1) : 44 -52 . DOI: 10.3969/j.issn.1672-6073.2025.01.006
正文
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随着客流分布的不均衡性日益凸显, 城市轨道交通出现了同一线路部分断面运力紧张而其他部分运力过剩的问题。为了解决这一难题, 国内外学者从大小交路运营 [ 1 ] 、换乘组织 [ 2 ] 以及灵活编组运营 [ 3 ] 等方面展开研究。
国外关于灵活编组运营组织的研究开展较早, 文献[ 4 ]通过对桑德兰地铁的实际案例分析, 研究了多编组运营存在的技术难点, 以得到最优的发车频率。文献[ 5 ]则针对灵活编组列车的调度问题提出了基于车辆优先的 ADMM 算法, 以减少列车的使用总数。
国内广大学者基于多种不同的运营模式、编组方案、交路方案、客流控制方面开展了研究。在固定编组的研究方面, 文献[ 6 ]提出混合交路模式下交路计划及时刻表综合优化模型, 并设计分层优化算法求解; 文献[ 7 ]建立城轨非均匀发车间隔高峰时段的大小交路发车时刻表优化模型, 进行协同优化; 文献[ 8 ]以各区间列车运输能力与断面客流量差值的绝对值之和最小为优化目标, 建立整数规划模型求解; 文献[ 9 ]以乘客出行等待时间成本与开行列车运用成本最小为目标, 建立非线性规划模型进行优化; 文献[ 10 ]设计遗传算法求解直通运营条件下列车开行方案优化; 文献[ 11 ] 通过NSGA-II与熵权法结合求解大小交路和列车放空运行优化的问题。
在灵活编组的研究方面, 文献[ 12 ]构建虚拟编组列车的大小交路开行方案双层优化模型, 设计了基于多种群遗传算法的求解方法; 文献[ 13 ]通过整数规划求解列车运营里程最小为目标的列车配置优化模型; 文献[ 14 ]通过整数规划设计算法求解在线编解模式下列车灵活编组开行方案优化; 文献[ 15 ]基于三阶段模型求解灵活编组的时刻表优化模型。
本文提出在线灵活编组场景下列车站内各项作业占用时间以及折返能力的算法, 以最优化乘客出行成本和车辆运行公里数为目标, 将列车编组数、列车发车频率、交路方案作为决策变量, 以整线满载率均衡程度为评价指标, 建立在线灵活编组大小交路开行方案优化模型, 并设计使用 NSGA-II 算法进行求解。以某城市实际运行线路设置为算例, 验证模型及算法。
1 在线灵活编组条件下折返场景分析
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根据现有研究, 列车的折返路径主要可分为 4 个阶段, 如 图 1 所示, 第 1 个阶段为列车的进站过程, 列车由站外驶入至站台边停靠；第 2 个阶段为列车驶入折返线的过程, 列车完成下客作业后, 驶入折返线进行联挂解编操作并换端; 第 3 个阶段为列车驶出折返线的过程, 列车驶出折返线后开始制动停靠至站台; 第 4 个阶段为列车的出站过程, 列车完成上客后, 驶离车站。
通过对 4 个阶段的分析可以建立固定编组条件下的列车运行折返时空,如 图 2 所示。在实际折返路径中建立 5 个实际位置节点。点 1 代表由站外进站的出清点, 点 2 代表进站站台的下客位置; 点 3 代表折返线上的停车位置; 点 4 代表出站站台的上客位置; 点 5 代表由站内出站的出清点。时间点含义如 表 1 所示。
在线灵活编组条件下, 列车运行联挂折返时空如 图 3 所示。在联挂区域中,列车 ATO 模式运行, 3 编组列车 1 完成清客后驶入折返线内停车等待, 3 编组列车 2 在完成清客后驶入折返线进行停车低速碰撞联挂, 联挂成功后 6 编组联挂列车(1+2)进行系统配置并换端投入运营。列车运行解编折返时空如 图 4 所示。 在解编区域中, 6 编组联挂列车(1+2)清客后驶入折返线停车进行 ATO 解编操作, 依据行车计划, 3 编组列车 1 和 3 编组列车 2 依次驶出折返线投入运营。
由 4 个阶段、 5 个位置点的分析得出在线灵活编组折返间隔计算式为式(1), 联挂时间计算式为式(2), 解编时间计算式为式(3)。
${t}_{\text{折 }}= {T}_{8}- {T}_{1}$
${t}_{\text{联 }}= {T}_{5}- {T}_{4}= {t}_{2\text{ 进停 }}+ {t}_{\text{碰 }}+ {t}_{\text{系 }}$
${t}_{\text{解 }}= {T}_{5}- {T}_{4}= {t}_{\text{发 }}+ {t}_{\text{系 }}$
式中, ${t}_{\text{折}}$ 为列车折返间隔, $\mathrm{s};{t}_{\text{联}}$ 为联挂时间, $\mathrm{s};{t}_{2}$ 进停为列车 2 从进站行驶至折返线停车牌时间, $\mathrm{s}$ ； ${t}_{\text{碰 }}$ 为列车 2 低速碰撞列车 1 完成联挂时间, $\mathrm{s};{t}_{\text{系 }}$ 为系统配置时间, $\mathrm{s};{t}_{\mathrm{解}}$ 为解编时间, $\mathrm{s};{t}_{\mathrm{发}}$ 为发车间隔时间, s。
折返间隔的计算中, 对于没有设置折返线但可以在正线进行联挂/解编操作的符合灵活编组要求的车站依旧适用此算法。基于以上折返间隔的推算, 可以得出列车折返能力的计算式为
$ D =\frac{3600}{\max \left({{t}_{\text{折 }},{t}_{\text{发 }}}\right)} $
式中, $D$ 为列车折返能力,列。
2 灵活编组大小交路运营优化模型构建
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2.1 问题描述
本节研究的问题为: 基于在线灵活编组技术, 结合大小交路设计方案,列车驶入大小交路折返站的折返线进行联挂解编的操作, 以实现乘客需求与车辆运能相匹配。根据线路客流 OD 表、车站间距、运行时间、折返时间等参数, 以乘客出行成本最小和车辆运行公里数最小为目标函数, 同时以满载率均衡程度为指标, 计算大小交路的列车发车频率, 大小交路的折返站位置以及大小交路的列车编组辆数等的取值。列车运行上行方向灵活编组大小交路客流如 图 5 所示, 线路共有 $N + 1$ 个车站, $N$ 个区间,其中 $a, b$ 站分别为小交路起、终点车站编号,车站 1 至车站 $a$ 记为区间 ${\mathrm{M}}_{1}$ ,车站 $a$ 至车站 $b$ 记为区间 ${\mathrm{M}}_{2}$ ,车站 $b$ 至 $N + 1$ 记为区间 ${\mathrm{M}}_{3}$ 。大小交路列车发车频率分别为 ${f}_{1},{f}_{2}$ , 大小交路列车分别采用 ${n}_{1},{n}_{2}$ 编组数,计算周期 ${\Delta T}$ 为 ${3600}\mathrm{\;s}$ 。
2.2 模型构建
根据建模及算法求解要求以及城市轨道交通线路实际运营情况, 对本文模型做如下合理性假定: ①到达车站的乘客人数服从泊松分布; ②乘客在列车中的分配由交路方案、编组数决定, 不考虑乘客主观意愿; ③考虑换乘情况；④所有列车采用站站停模式；⑤部分车站具备折返条件, 不同站点同一折返方案采用相同的折返时间。
1) 乘客出行时间成本。以乘客出行最短时间作为本研究的目标函数之一, 包含乘客等待时间、乘客换乘时间、乘客乘车时间。由于乘客出行起点和终点不同,可乘坐的列车类型也不同,因此将乘客按照乘坐区间进行分类, 分别计算乘客的各项时间。第 1 类乘客包含: ①乘客起点和终点都在区间 ${\mathrm{M}}_{1}$ ; ②乘客起点和终点都在区间 ${\mathrm{M}}_{3}$ ；③乘客起点在区间 ${\mathrm{M}}_{1}$ ,终点在区间 ${\mathrm{M}}_{3}$ 。第 2 类乘客包含:④乘客起点终点都在区间 ${\mathrm{M}}_{2}$ 。第 3 类乘客包含:⑤乘客起点在区间 ${\mathrm{M}}_{1}$ ,终点在区间 ${\mathrm{M}}_{2}$ ; ⑥乘客起点在区间 ${\mathrm{M}}_{2}$ ,终点在区间 ${\mathrm{M}}_{3}$ 。 由此构建乘客出行成本最小的目标函数, 即
${T}_{\min }= \min \left\{{\frac{{\Delta T}{Q}_{1}}{2{f}_{1}}+ \frac{\Delta T}{{f}_{1}+ {f}_{2}}\left\lbrack {{Q}_{2}+ \left({1 +\beta }\right){Q}_{3}}\right\rbrack +}\right.\\\left.{\mathop{\sum }\limits_{{i = 1}}^{{N + 1}}\mathop{\sum }\limits_{{j = 1}}^{{N + 1}}\left({{q}_{ij}\mathop{\sum }\limits_{i}^{j}{t}_{ij}}\right)}\right\}$
其中, ${Q}_{1}= \mathop{\sum }\limits_{{i = 1}}^{{a - 1}}\mathop{\sum }\limits_{{j = i + 1}}^{a}{q}_{ij}+ \mathop{\sum }\limits_{{i = 1}}^{{a - 1}}\mathop{\sum }\limits_{{j = b + 1}}^{{N + 1}}{q}_{ij}+ \mathop{\sum }\limits_{{i = b}}^{N}\mathop{\sum }\limits_{{j = i + 1}}^{{N + 1}}{q}_{ij}+$
$\mathop{\sum }\limits_{{j = 1}}^{a}\mathop{\sum }\limits_{{i = j}}^{{a - 1}}{q}_{ij}+ \mathop{\sum }\limits_{{j = b + 1}}^{{N + 1}}\mathop{\sum }\limits_{{i = 1}}^{{a - 1}}{q}_{ij}+ \mathop{\sum }\limits_{{j = b}}^{{N + 1}}\mathop{\sum }\limits_{{i = j - 1}}^{N}{q}_{ij}\\{Q}_{2}= \mathop{\sum }\limits_{{i = a}}^{{b - 1}}\mathop{\sum }\limits_{{j = i + 1}}^{b}{q}_{ij}+ \mathop{\sum }\limits_{{j = a}}^{b}\mathop{\sum }\limits_{{i = j}}^{{b - 1}}{q}_{ij}\\{Q}_{3}= \mathop{\sum }\limits_{{i = a}}^{{b - 1}}\mathop{\sum }\limits_{{j = b + 1}}^{{N + 1}}{q}_{ij}+ \mathop{\sum }\limits_{{j = 1}}^{{b - 1}}\mathop{\sum }\limits_{{i = j + 1}}^{b}{q}_{ij}$
式中, ${T}_{\min }$ 为最小乘客出行时间, $\mathrm{s};{\Delta T}$ 为计算周期, s; ${q}_{ij}$ 为起点为 $i$ 站终点为 $j$ 站的客流量,人; ${Q}_{1}$ 为第 1 类乘客客流总量,人; ${Q}_{2}$ 为第 2 类乘客客流量,人; ${Q}_{3}$ 为第 3 类乘客客流量,人; $\beta$ 为换乘时间, $\mathrm{s};{t}_{ij}$ 为列车从 $i$ 站至 $j$ 站所需时间, $\mathrm{s}$ 。
2) 车辆运行公里数。运能是否浪费的直接影响因素是车辆运行公里数, 车辆运行公里数由交路方案、 发车频率和列车编组数决定。由此构建车辆运行公里数最小的目标函数, 即
${S}_{\min }= \min \left({2{L}_{N}{f}_{1}{n}_{1}+ 2{L}_{ab}{f}_{2}{n}_{2}}\right)$
式中, ${S}_{\min }$ 为最小车辆运行公里数, $\mathrm{{km}};{L}_{N}$ 为大交路整线的长度, $\mathrm{{km}};{L}_{ab}$ 为小交路 $a$ 站至 $b$ 站的长度, $\mathrm{{km}}$ ; ${n}_{1}$ 为大交路列车编组数; ${n}_{2}$ 为小交路列车编组数。
3) 满载率均衡程度。对于通过 NSGA-Ⅱ算法求得 Pareto 前沿解集后, 如何在 Pareto 前沿解集中选出最合适的解, 采用满载率均衡程度作为指标。对于第 3 类乘客需要在折返站 $a$ 或 $b$ 进行换乘,因此引入乘客换乘等待系数 $\varphi$ 。由此满载率均衡程度最小的目标函数为
${\gamma }_{\min }= \min \left\{\begin{array}{l}\frac{1}{{2C}{f}_{1}\left({{n}_{1}+ {n}_{2}}\right)}\left({{Q}_{1}+ \frac{{f}_{1}{Q}_{2}}{{f}_{1}+ {f}_{2}}+ \frac{\varphi {f}_{1}{Q}_{3}}{{f}_{1}+ {f}_{2}}}\right)- \\\frac{{f}_{2}\left\lbrack {{Q}_{2}+ {Q}_{3}\left({1 -\varphi }\right)}\right\rbrack }{{2C}{f}_{1}{n}_{2}\left({{f}_{1}+ {f}_{2}}\right)} \end{array}\right\}$
式中, ${\gamma }_{\min }$ 为最小满载率均衡程度; $C$ 为一辆车辆编组的定员, 人。
2.3 约束条件
式(8)和式(9)为车辆编组数约束；式(10)为大小交路发车频率约束,大小交路的发车频率呈整数倍关系； 式(11)为大小交路折返站位置约束；式(12)和式(13)为最小、最大发车频率约束。
$\left\{\begin{array}{l}{n}_{1}\geq 3 \\{n}_{2}\geq 3 \end{array}\right.$
$ 6 \leq {n}_{1}+ {n}_{2}\leq {n}_{0}$
${f}_{1}= m{f}_{2}$
$ 1 \leq a \leq b \leq N + 1 $
$\left\{\begin{array}{l}{f}_{1}\geq {f}_{\min }\\{f}_{2}\geq {f}_{\min }\end{array}\right.$
${f}_{1}+ {f}_{2}\leq {f}_{\max }$
式中, ${n}_{0}$ 为最大编组数; $m$ 为正整数。
运用车辆数受周转时间、发车频率、列车编组辆数、线路最大同行能力的影响, 计算大小交路列车的周转时间,计算出运用车辆数。具体计算式如下。
${Z}_{y}= 2{f}_{1}\left({{n}_{1}+ {n}_{2}}\right)\left({\mathop{\sum }\limits_{{i = 1}}^{N}{t}_{i}+ \mathop{\sum }\limits_{{j = 1}}^{{N + 1}}{t}_{j}+ {T}_{\text{折 }}}\right)+ $
$ 2{f}_{2}{n}_{2}\left({\mathop{\sum }\limits_{{i = a}}^{{b - 1}}{t}_{i}+ \mathop{\sum }\limits_{{j = a + 1}}^{b}{s}_{j}+ {T}_{\text{折 }}}\right)\leq {Z}_{0}$
式中, ${Z}_{y}$ 为运用车辆数,辆; ${Z}_{0}$ 为最大运用车辆数,辆; ${t}_{i}$ 为第 $i$ 区间的运行时间, $\mathrm{s};{t}_{j}$ 为第 $j$ 站的停站时间, $\mathrm{s}$ 。
2.4 模型求解
本文所建立的灵活编组大小交路运营优化模型为非线性整数规划模型, 本模型的目标函数存在矛盾关系, 故本文设计 NSGA-Ⅱ算法对所构建的多目标优化模型进行求解, 其求解算法流程如 图 6 所示, 步骤如下。
Step1: 编码。本模型将折返站位置 $a, b$ 和发车频率 ${f}_{1},{f}_{2}$ 采用二进制方法进行编码,同时由于列车编组数 ${n}_{1},{n}_{2}$ 的可行解是离散的,因此采用实数方法进行编码。一组可行解的编码示意如 图 7 所示。
Step2: 生成初始种群。随机生成符合约束的灵活编组折返站 $a, b$ ,列车的发车频率 ${f}_{1},{f}_{2}$ ,列车的编组数 ${n}_{1},{n}_{2}$ 的可行解,并形成 Step 1 中的编码,生成初始种群。
Step3: 针对染色体种群的选择, 利用快速非支配排序策略, 根据每条染色体的层级序号和拥挤距离, 保留优越性高的个体进行后续的交叉和变异。
Step4: 交叉和变异。在交叉过程中, 随机取种群中的 2 个个体,以交叉概率 ${P}_{\mathrm{c}}$ 交换随机交叉点的染色体, 将交叉后的个体加入下一代; 在变异过程中, 随机取种群中的 1 个个体并随机选择染色体的变异位置, 如果变异位置在前 20 位,则按变异概率 ${P}_{\mathrm{m}}$ 互换 0 和 1 值,如果变异位置在后 2 位,则按变异概率 ${P}_{\mathrm{m}}$ 将可行值变为其他可行值。
Step5: 根据排序结果, 保留优越性较高的个体作为当前种群, 进行迭代, 精英策略种群产生示意如 图 8 所示。
Step6: 停止。重复步骤 3~5,直到迭代次数达到最大值 $\mathrm{G}$ ,输出结果。
3 实例分析
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3.1 线路情况
以某城市轨道交通市域线为算例, 该线路上共有 30 座车站, 列车以 ATO 模式根据运行图自动运行至大小交路折返站, 通过全自动车钩进行联挂解编操作。 7:00-8:00 时段,对应客流 OD 热力和上下行断面客流量分别如 图 9 和 图 10 所示, 该线路的客流断面中间大、 两端小, 为典型的凸起型客流。考虑线路折返站现实改造条件,满足灵活编组条件的车站为1,4,8,9, 16,23,24,30号车站。
参考第 1 部分在线灵活编组条件下折返场景分析以及折返间隔算法, 根据线路情况采用自行开发 “城市轨道交通在线灵活编组仿真系统” 进行仿真, 在线灵活编组仿真系统运行如 图 11 所示。得出灵活编组车站折返仿真结果如 表 2 所示。为方便计算, 相同折返类型的灵活编组折返站采用相同的折返时间。
3.2 参数选取
结合地铁线路的实际情况和相关文献研究, 本文设置最大编组数取 9,最小发车频率取 6 对 $/\mathrm{h}$ ,最大发车频率取 30 对 $/\mathrm{h}$ ,一辆车辆编组的定员为240人,折返时间根据折返站位置按照 表 2 进行选择, 换乘时间为 $2\mathrm{\;{min}}$ ,等待系数取 0.1,最小满载率为 ${60}\%$ ,最大满载率为 120%。非支配排序遗传算法(NSGA-Ⅱ)的参数设置为: 迭代次数 $G ={120}$ ,种群大小 ${P}_{s}= {50}$ ,交叉概率 ${P}_{c}= {0.3}$ ,变异概率 ${P}_{m}= {0.2}$ 。在同等线路运营数据和客流条件下, 求得单一交路固定编组模式下的乘客总平均等待时间为 ${2970164.51}\mathrm{\;{min}}$ ,车辆运行公里数为 ${7904.13}\mathrm{\;{km}}$ ,车辆运用数为 240 辆。
3.3 计算结果及分析
利用 MATLAB 数学建模工具建模, 进行求解。 Pareto front 结果示意如 图 12 所示。在迭代 103 次时计算出 Pareto 前沿解集。乘客出行时间迭代变化如 图 13 所示, 车辆运行公里数成本迭代变化如 图 14 所示, 乘客出行成本和车辆运行公里数 2 个目标函数值随着迭代过程的进行逐渐接近于 Pareto 最优前沿, 迭代至 103 次时, 得到了 Pareto 前沿解集如 表 3 所示。
图 15 给出了满载率均衡程度随着迭代次数增加的变化过程。由图可知: 满载率均衡程度变化幅度很大, 且不呈现线性关系, 满载率均衡程度在迭代结束时不一定取得最小值。通过对 表 4 中的 Pareto 最优前沿解集求其满载率均衡程度, 得出解集中的满载率均衡程度的最小值为 0.25%,最优解为编号 5 。即当大小交路的起终点站 $a, b$ 分别选取为 8 号和 23 号,大小交路的发车频率 ${f}_{1},{f}_{2}$ 分别为8对 $/\mathrm{h}$ 和 16 对 $/\mathrm{h}$ ,大小交路列车编组数 ${n}_{1},{n}_{2}$ 分别为 6 辆编组和 3 辆编组,列车可在 8 号站解编、23 号站联挂发车。在基于满载率均衡程度最小的情况下得到的上行、下行方向各车站满载率如 图 16 所示。
为了证明相较于单一交路固定编组、大小交路固定编组、多编组混跑而言, 在线灵活编组大小交路的开行方案在乘客出行时间、车辆运行公里数、满载率均衡性上的优越性, 将 4 种运营模式进行对比分析。 其中: 单一交路只开行大交路, 列车设置为 6 辆编组; 固定编组大小交路模式设置列车开行比例为 $1 : 2$ ,由于早高峰时期的客流量较大, 列车设置为 6 辆编组; 多编组混跑采用结合大小交路的运行模式, 编组数、 折返车站与灵活编组运营方案相同, 根据线路情况最小编组设置为 3 辆编组, 最大编组设置为 6 辆编组; 灵活编组模式即本文提出的大小交路在线灵活编组组合模式, 运营方案按照通过多目标优化算法得出的最优解。
由 4 种运营模式下各指标对比 表 4 可知: 在线灵活编组大小交路运营模式与其他 3 种运营模式相比, 其车辆运行公里数分别减少 42.68%, 22.81%和 15.98%, 车辆运用数分别减少 ${35}\%,{23.53}\%$ 和 ${16.13}\%$ ,断面最大满载率则分别从 161.71%、123.54%和 135.49%减少至 119.68%。在线灵活编组大小交路运营模式虽然可以保证车辆运行公里数较低, 但是相较于其他运营模式, 在节约乘客出行成本方面没有显著区别; 在减少车辆运用数和降低线路各个区间满载率的效果以及提升满载率均衡程度方面效果显著。
4 结论
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1) 本文以城市轨道交通为研究对象, 提出一种在线灵活编组大小交路的运营模式。分析列车的折返场景, 得出基于灵活编组条件下折返间隔算法, 通过灵活编组仿真系统对案例进行仿真, 得出列车所需折返时间, 并通过设计非支配排序遗传算法(NSGA-II)进行案例分析。
2) 在线灵活编组大小交路运营模式与其他 3 种运营模式相比,其车辆运行公里数分别减少 42.68%, 22.81%和 15.98%,车辆运用数分别减少 35%,23.53% 和 16.13%,断面最大满载率则分别从 161.71%,123.54% 和 135.49%减少到 119.68%。乘客出行成本方面,在线灵活编组大小交路运营模式相比于单一交路仅增加了 7.12%,与固定编组大小交路相比仅增加了 1.8%, 与多编组混跑相比减少了 11.13%。
3) 在线灵活编组大小交路运营模式可以丰富传统的运输组织模式, 在乘客出行成本、车辆运行公里数、车辆运用数、断面最大满载率、整线满载率均衡程度等方面具有显著的效益。
基金
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  • 国家自然科学基金地区项目(62363011)
  • 上海市隧道工程轨道交通设计研究院科研项目((23)JJ-002)
文献
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2025年第38卷第1期
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doi: 10.3969/j.issn.1672-6073.2025.01.006
  • 接收时间：2024-04-13
  • 首发时间：2025-07-09
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  • 收稿日期：2024-04-13
  • 修回日期：2024-09-26
基金
国家自然科学基金地区项目(62363011)
上海市隧道工程轨道交通设计研究院科研项目((23)JJ-002)
作者信息
    1 上海工程技术大学 城市轨道交通学院 上海 201620
    2 华东交通大学 电气与自动化工程学院 南昌 330013
    3 上海市隧道工程轨道交通设计研究院 上海 200070

通讯作者:

徐纪康，男，讲师，从事城市轨道交通信号系统设计与研究，
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2种不同金属材料的力学参数
科
Family		 属数
Number of
genus		 种数
Number of
species		 占总种数比例
Percentage of
total species (%)		 属
Genus		 种数
Number of
species		 占总种数比例
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鹅膏菌科Amanitaceae 2 11 5.26 鹅膏菌属 Amanita 10 4.78
小菇科 Mycenaceae 2 12 5.74 丝盖伞属 Inocybe 5 2.39
多孔菌科 Polyporaceae 8 14 6.70 蜡蘑属 Laccaria 5 2.39
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
栓菌属 Trametes 5 2.39
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