金波;郭佑星;王青元;孙鹏飞;冯晓云;

• 1:西南交通大学电气工程学院

摘要(Abstract)：

为降低城市轨道交通大小交路开行方案对时刻表和车底运用计划编制的难度，更好地服务不均衡客流需求，提出一种考虑大小交路的城市轨道交通时刻表与车底运用计划协同优化方法。先针对大小交路开行方案，以提升时刻表服务质量和降低车底运用成本为双目标，通过优化发车间隔、车底接续关系和大小交路开行次序，设计能够统筹时刻表和车底运用计划关系的约束条件，构建两者协同优化模型；再结合模型特点引入辅助变量，将其重构为混合整数线性规划模型，从而实现对模型的有效求解；最后依托广州地铁2号线实际运营数据，验证方法的有效性。结果表明：与原方案相比，优化后的方案可降低车底出入库次数约4.65%，降低总发车间隔偏差约94.80%；在长时段复杂交路计划下，优化方法仍可在兼顾时刻表和车底运用效率的同时实现一体化编制，从而有效降低不均衡客流下的列车运行计划编制难度。

关键词(KeyWords)： 城市轨道交通;大小交路;列车运行计划;计划编制;协同优化;混合整数线性规划

Abstract:

Keywords:

基金项目(Foundation): 国家自然科学基金高铁联合基金资助项目（U1934221）

作者(Authors): 金波;郭佑星;王青元;孙鹏飞;冯晓云;

参考文献(References)：

• [1]许得杰，巩亮，曾俊伟.考虑客流时变需求的大小交路列车时刻表优化模型[J].交通运输系统工程与信息，2019,19(2):122-129.(XU Dejie,GONG Liang,ZENG Junwei.Modeling of Train Timetable with Full-Length and Short-Turn Routing Considering the Time-Varying Demand[J].Journal of Transportation Systems Engineering and Information Technology,2019,19(2):122-129.in Chinese）
• [2]何必胜，宋瑞，何世伟，等.城市轨道交通车底运用计划编制优化模型求解的混合列生成算法[J].中国铁道科学，2014,35(1):122-129.(HE Bisheng,SONG Rui,HE Shiwei,et al.A Hybrid Column Generation Approach for Solving Rolling Stock Assignment Optimization Model of Urban Rail Transit[J].China Railway Science,2014,35(1):122-129.in Chinese）
• [3]ZHANG M,WANG Y H,SU S,et al.A Short Turning Strategy for Train Scheduling Optimization in an Urban Rail Transit Line:the Case of Beijing Subway Line 4[J].Journal of Advanced Transportation,2018,2018:5367295.
• [4]许得杰，毛保华，陈绍宽，等.考虑开行比例的大小交路列车开行方案优化[J].交通运输工程学报，2021,21(2):173-186.(XU Dejie,MAO Baohua,CHEN Shaokuan,et al.Optimization of Operation Scheme for Full-Length and Short-Turn Routings Considering Operation Proportion[J].Journal of Traffic and Transportation Engineering,2021,21(2):173-186.in Chinese）
• [5]白广争，郭进，杨扬，等.大小交路嵌套方式下城市轨道交通列车最优车组数开行方案[J].城市轨道交通研究，2015,18(3):45-50.(BAI Guangzheng,GUO Jin,YANG Yang,et al.On Operation Scheme of Urban Rail Transit in Long/Short Routing Mode[J].Urban Mass Transit,2015,18(3):45-50.in Chinese）
• [6]CANCA D,BARRENA E,LAPORTE G,et al.A Short-Turning Policy for the Management of Demand Disruptions in Rapid Transit Systems[J].Annals of Operations Research,2016,246(1/2):145-166.
• [7]江志彬，徐瑞华，吴强，等.计算机编制城市轨道交通共线交路列车运行图[J].同济大学学报：自然科学版，2010,38(5):692-696.(JIANG Zhibin,XU Ruihua,WU Qiang,et al.Shared-Path Routing Timetable Computer Designing in Rail Transit System.Journal of Tongji University:Natural Science,2010,38(5):692-696.in Chinese）
• [8]张晓倩，崔炳谋.城市轨道交通共线交路运行图的优化与编制[J].计算机应用与软件，2016,33(3):248-251.(ZHANG Xiaoqian,CUI Bingmou.Shard-Path Routing Timetable Optimisation and Designing of Urban Rapid Transit[J].Computer Applications and Software,2016,33(3):248-251.in Chinese）
• [9]徐瑞华，陈菁菁，杜世敏.城轨交通多种列车交路模式下的通过能力和车底运用研究[J].铁道学报，2005,27(4):6-10.(XU Ruihua,CHEN Jingjing,DU Shimin.Study on Carrying Capacity and Use of Rolling Stock with Multi-Routing in Urban Rail Transit[J].Journal of the China Railway Society,2005,27(4):6-10.in Chinese）
• [10]姚宇，朱晓宁，康柳江，等.城市轨道交通列车时刻表与车底运用整合优化模型[J].交通运输系统工程与信息，2018,18(1):200-206.(YAO Yu,ZHU Xiaoning,KANG Liujiang,et al.An Integrated Optimization Model of Train Timetabling and Rolling Stock Scheduling for an Urban Railway Line[J].Journal of Transportation Systems Engineering and Information Technology,2018,18(1):200-206.in Chinese）
• [11]WANG Y H,D'ARIANO A,YIN J T,et al.Passenger Demand Oriented Train Scheduling and Rolling Stock Circulation Planning for an Urban Rail Transit Line[J].Transportation Research Part B:Methodological,2018,118:193-227.
• [12]GHOSEIRI K,SZIDAROVSZKY F,ASGHARPOUR M J.A Multi-Objective Train Scheduling Model and Solution[J].Transportation Research Part B:Methodological,2004,38(10):927-952.
• [13]代存杰，李引珍，展宗思，等.考虑动态客流需求和大小交路模式的城市轨道交通列车开行方案优化[J].中国铁道科学，2018,39(2):128-136.(DAI Cunjie,LI Yinzhen,ZHAN Zongsi,et al.Optimization of Train Operation Scheme for Urban Rail TransitConsidering Dynamic Passenger Demand and Full-Length&Short-Turn Routing Modes[J].China Railway Science,2018,39(2):128-136.in Chinese)
• [14]WANG Y H,TANG T,NING B,et al.Passenger-Demands-Oriented Train Scheduling for an Urban Rail Transit Network[J].Transportation Research Part C:Emerging Technologies,2015,60:1-23.
• [15]王媛媛，倪少权.城市轨道交通大小交路模式列车开行方案的优化[J].铁道学报，2013,35(7):1-8.(WANG Yuanyuan,NI Shaoquan.Optimization of Train Schedules of Full-Length&Short-Turn Operation Modes in Urban Rail Transit[J].Journal of the China Railway Society,2013,35(7):1-8.in Chinese）
• [16]BEMPORAD A,MORARI M.Control of Systems Integrating Logic,Dynamics,and Constraints[J].Automatica,1999,35(3):407-427.