Article(id=1308454718460679122, tenantId=1146029695717560320, journalId=1146123302524792850, issueId=1308454712513156008, articleNumber=null, orderNo=null, doi=10.3969/j.issn.1672-6073.2026.04.006, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1779033600000, receivedDateStr=2026-05-18, revisedDate=1783008000000, revisedDateStr=2026-07-03, acceptedDate=null, acceptedDateStr=null, onlineDate=1789889514794, onlineDateStr=2026-09-20, pubDate=null, pubDateStr=null, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1789889514794, onlineIssueDateStr=2026-09-20, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1789889514794, creator=13701087609, updateTime=1789889514794, updator=13701087609, issue=Issue{id=1308454712513156008, tenantId=1146029695717560320, journalId=1146123302524792850, year='2026', volume='39', issue='4', pageStart='1', pageEnd='197', issueExtLink='null', onlineDate='null', pubDate='1786291200000', pubDateStr='2026-08-10', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=1, specialIssue=null, createTime=1789889513376, creator='13701087609', updateTime=1789889839088, updator='13701087609', preIssue=null, nextIssue=null, articleTotal=null, ext={EN=IssueExt(id=1308456079029986178, tenantId=1146029695717560320, journalId=1146123302524792850, issueId=1308454712513156008, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1308456079029986179, tenantId=1146029695717560320, journalId=1146123302524792850, issueId=1308454712513156008, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null, downloadFileDto=null}, startPage=53, endPage=58, ext={EN=ArticleExt(id=1308454718687171539, articleId=1308454718460679122, tenantId=1146029695717560320, journalId=1146123302524792850, language=EN, title=Review of Research Progress in Urban Rail Transit Network Optimization Models and Methods, columnId=1308454713645618089, journalTitle=Urban Rapid Rail Transit, columnName=Special Feature: 200th Issue, runingTitle=null, highlight=null, articleAbstract=

With the transition of urban rail transit toward networked operations, the scientific planning of transit networks is critical for ensuring operational efficiency and service quality. This systematically the research progress on optimization models and methodologies for urban rail transit networks, based on relevant studies published from 2015 to 2025. Current rail transit network optimization models suffer from idealized assumptions and insufficient characterization of practical constraints. Moreover, the three mainstream solution approaches—exact algorithms, intelligent heuristic algorithms, and deep reinforcement learning—each have respective drawbacks in computation efficiency, stability, generalization capacity and other aspects. The paper begins by establishing a taxonomy of transit network planning problems from three perspectives: planning scenarios, modeling formulations, and solution method. Then, in terms of optimization models, the evolution from single-objective to multi-objective formulations is reviewed, highlighting the development of multi-dimensional objective systems involving efficiency, cost, equity, and resilience. This paper further summarizes the main advances in initial network generation models and existing network expansion optimization models. On the algorithmic side, the paper covers exact methods, metaheuristic algorithms, surrogate-assisted optimization, and the emerging deep reinforcement learning (DRL) paradigm, with particular attention to studies that formulate network design as a Markov Decision Process (MDP). It is concluded that the existing optimization models generally have structural defects and deviate from engineering practice. They fail to fully characterize practical constraints such as transfer layouts, capacity limits and time-varying passenger flows, which greatly reduces their practical application value. Five research directions are therefore proposed to improve relevant research: constructing a hybrid optimization framework for large-scale networks, establishing an integrated supply-demand coordination model, developing collaborative optimization theories for multi-mode rail transit systems, forming a low-carbon sustainable optimization system, and building a digital twin-driven dynamic decision-making model.

, authors=Ya Liu¹, Zijia Wang², Ruoyu Hou¹, authorsList=Ya Liu, Zijia Wang, Ruoyu Hou, authorCompany=null, correspAuthors=null, 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, fund=null), CN=ArticleExt(id=1308454718917858260, articleId=1308454718460679122, tenantId=1146029695717560320, journalId=1146123302524792850, language=CN, title=城市轨道交通线网优化模型与方法研究进展综述, columnId=1308454713796613035, journalTitle=都市快轨交通, columnName=200期专辑, runingTitle=null, highlight=null, articleAbstract=

针对目前轨道交通线网优化模型存在理想化假设、现实约束刻画不足的问题，且精确算法、智能启发算法、深度强化学习3类主流求解方法各有计算、稳定性、泛化等短板，基于2015年至2025年相关文献数据，系统论述城市轨道交通线网优化模型与方法的研究进展。首先构建线网规划问题的分类框架，从规划场景、建模形式与求解方法3个维度对问题进行归纳。然后在优化模型方面，梳理单目标向多目标优化的发展路径，归纳效率、成本、公平性及韧性等多维目标体系的演化特征，并进一步总结初始线网生成模型与既有网络扩展优化模型的主要研究进展与建模思路。在求解方法方面，对比分析精确算法、元启发式算法以及深度强化学习方法的发展特点，重点阐述基于马尔可夫决策过程（MDP）的线网序贯决策建模思路。结果表明：当前各类优化模型普遍存在结构性缺陷，落地应用价值受限，脱离工程实际，难以完整刻画换乘、运力、时变客流等现实约束，并提出可通过构建大规模网络混合优化框架、供需协同统一模型、多制式协同优化理论、低碳可持续优化体系及数字孪生驱动的动态决策模型五大方向完善相关研究。

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刘亚，男，硕士，工程师，从事轨道交通政策研究、线网规划、工程咨询等，18201130515@163.com

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刘亚，男，硕士，工程师，从事轨道交通政策研究、线网规划、工程咨询等，18201130515@163.com

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