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Article(id=1268884544628355851, tenantId=1146029695717560320, journalId=1268266580820377661, issueId=1268884383122494171, articleNumber=null, orderNo=null, doi=10.3969/j.issn.1001-4632.2026.02.19, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1753286400000, receivedDateStr=2025-07-24, revisedDate=1772121600000, revisedDateStr=2026-02-27, acceptedDate=null, acceptedDateStr=null, onlineDate=1780455250173, onlineDateStr=2026-06-03, pubDate=1772294400000, pubDateStr=2026-03-01, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1780455250173, onlineIssueDateStr=2026-06-03, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1780455250173, creator=13701087609, updateTime=1780455250173, updator=13701087609, issue=Issue{id=1268884383122494171, tenantId=1146029695717560320, journalId=1268266580820377661, year='2026', volume='47', issue='2', pageStart='1', pageEnd='255', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=1, specialIssue=null, createTime=1780455211667, creator=13701087609, updateTime=1780455310713, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1268884798719300557, tenantId=1146029695717560320, journalId=1268266580820377661, issueId=1268884383122494171, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1268884798723494862, tenantId=1146029695717560320, journalId=1268266580820377661, issueId=1268884383122494171, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=221, endPage=231, ext={EN=ArticleExt(id=1268884546297688845, articleId=1268884544628355851, tenantId=1146029695717560320, journalId=1268266580820377661, language=EN, title=Research on Layout Optimization and Hybrid Algorithm Improvement of Railway Rescue Trains Based on Arc Risk Quantification, columnId=null, journalTitle=China Railway Science, columnName=null, runingTitle=null, highlight=null, articleAbstract=

To optimize the layout of railway rescue trains and enhance railway emergency rescue efficiency in China,the genetic-simulated annealing hybrid algorithm is improved based on the arc risk quantification. First, a multi-dimensional risk quantification evaluation index system for the railway network is constructed. Through the Entropy Weight-TOPSIS method, risk quantification evaluation is conducted on each arc segment of the network. Then, combined with coverage theory, an optimal layout model for railway rescue trains is established with objectives including network rescue coverage rate, rescue time satisfaction, and rescue train layout cost. Secondly, the Multi-Phase Adaptive Simulated Annealing Genetic Algorithm (MP-ASAGA) is designed to solve the model. The solution process is divided into the exploration phase focusing on searching for the global optimum and the development phase focusing on accelerating convergence, with different evolutionary strategies applied in each phase to improve the algorithm's solving performance. Finally, a case study using actual railway network data from a railway bureau in China is conducted for calculation and validation. The results show that compared with the original layout scheme of the railway bureau in the case study, the optimal railway rescue train layout scheme obtained by the proposed method achieves an improvement of 8.99% in network rescue coverage rate, and an improvement of 11.62% in rescue time satisfaction. This method can provide corresponding theoretical support for the layout optimization of railway rescue trains and the enhancement of rescue efficiency.

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为优化我国铁路救援列车布局以提高铁路应急救援效能，在弧段风险量化的基础上，对遗传-模拟退火混合算法进行改进。首先，构建多维度路网风险量化评价指标体系，运用熵权-TOPSIS法对路网各弧段进行风险量化评价，并结合覆盖理论，构建以路网救援覆盖率、救援时间满意度和救援列车布局成本为目标的铁路救援列车最优布局模型；其次，设计多阶段自适应模拟退火遗传算法（MP-ASAGA）对模型进行求解，将求解过程分为重点搜索全局最优解的探索阶段和重点加速收敛的开发阶段，在各阶段采取不同进化策略提升算法的求解性能；最后，以我国某铁路局的实际路网数据为案例进行计算验证。结果表明：与案例中路局的原布局方案相比，运用所提方法求解得到的铁路救援列车最优布局方案的路网救援覆盖率提升8.99%，救援时间满意度提升11.62%。该方法可为铁路救援列车的布局优化及救援效能提升提供相应的理论支持。

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韩佳英（1994—），男，内蒙古乌兰察布人，助理研究员。E-mail：

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韩佳英（1994—），男，内蒙古乌兰察布人，助理研究员。E-mail：

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韩佳英（1994—），男，内蒙古乌兰察布人，助理研究员。E-mail：

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Journal of Xi’an Jiaotong University， 2002， 36 （3）： 226-229. in Chinese, articleTitle=Improved Genetic Algorithm of Adaptive Real Range Search, refAbstract=null), Reference(id=1268884578405086105, tenantId=1146029695717560320, journalId=1268266580820377661, articleId=1268884544628355851, doi=null, pmid=null, pmcid=null, year=2004, volume=32, issue=6, pageStart=802, pageEnd=805, url=null, language=null, rfNumber=[15], rfOrder=25, authorNames=陈华根, 吴健生, 王家林, journalName=同济大学学报（自然科学版）, refType=null, unstructuredReference=陈华根，吴健生，王家林，等.模拟退火算法机理研究［J］.同济大学学报（自然科学版），2004，32（6）：802-805., articleTitle=模拟退火算法机理研究, refAbstract=null), Reference(id=1268884578463806362, tenantId=1146029695717560320, journalId=1268266580820377661, articleId=1268884544628355851, doi=null, pmid=null, pmcid=null, year=2004, volume=32, issue=6, pageStart=802, pageEnd=805, url=null, language=null, rfNumber=[15], rfOrder=26, authorNames=CHEN Huagen, WU Jiansheng, WANG Jialin, journalName=Journal of Tongji University （Natural Science）, refType=null, unstructuredReference=CHEN Huagen， WU Jiansheng， WANG Jialin， et al. 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序号类别名称建设标准备注
1停留线250 m应设在两端接通，便于救援列车出动的段（站）管线上，具备轨道起重机回转条件。
2练功线80 m救援人员演练及体能训练场地。
3配套房屋≥600 m2设备、健身、钳工、办公、学习、值班、浴室、锅炉、危险品、油脂、配件备品。
), ArticleFig(id=1268884573795545972, tenantId=1146029695717560320, journalId=1268266580820377661, articleId=1268884544628355851, language=CN, label=表1, caption=

成本类别的建设标准

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序号类别名称建设标准备注
1停留线250 m应设在两端接通，便于救援列车出动的段（站）管线上，具备轨道起重机回转条件。
2练功线80 m救援人员演练及体能训练场地。
3配套房屋≥600 m2设备、健身、钳工、办公、学习、值班、浴室、锅炉、危险品、油脂、配件备品。
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弧段序号首端站点j尾端站点k近五年事故数量/件事故直接损失/万元线路速度/(km ∙ h-1)隧道数量/个桥梁数量/个年均降雨量/mm年均风力/级年均降雪量/mm
151008011404.8410.1
2142108011267.5410.5
3424311.5512011512.2410.5
443440012011399.0410.3
544450016012679.159.2
462144380035021337.049.8
4634384390035021393.358.5
464439811.1235021421.858.7
46514440213.5125001609.758.5
4664404410025001673.458.5
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弧段基本数据（部分）

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弧段序号首端站点j尾端站点k近五年事故数量/件事故直接损失/万元线路速度/(km ∙ h-1)隧道数量/个桥梁数量/个年均降雨量/mm年均风力/级年均降雪量/mm
151008011404.8410.1
2142108011267.5410.5
3424311.5512011512.2410.5
443440012011399.0410.3
544450016012679.159.2
462144380035021337.049.8
4634384390035021393.358.5
464439811.1235021421.858.7
46514440213.5125001609.758.5
4664404410025001673.458.5
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弧段序号Cjk值弧段序号Cjk值
10.002 14620.005 8
20.001 54630.005 7
30.001 84640.005 8
40.001 84650.004 2
50.002 54660.004 1
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各弧段风险值Cjk（部分）

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弧段序号Cjk值弧段序号Cjk值
10.002 14620.005 8
20.001 54630.005 7
30.001 84640.005 8
40.001 84650.004 2
50.002 54660.004 1
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弧段序号首端站点尾端站点站点间线路距离/km
1515.03
21424.35
342436.70
443443.96
46343843918.10
464439813.54
4651444019.26
46644044133.29
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弧段距离信息（部分）

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弧段序号首端站点尾端站点站点间线路距离/km
1515.03
21424.35
342436.70
443443.96
46343843918.10
464439813.54
4651444019.26
46644044133.29
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始发站编号不同编号终到站对应区间的最短线路距离
1234438439440441
10274.1070.2328.23155.90174.00128.60161.89
2274.100344.32302.32429.99448.09402.70435.99
370.23344.32042.00169.67187.77142.37175.66
428.23302.3242.000127.67145.77100.37133.66
438155.90429.99169.67127.67018.1065.8299.11
439174.00448.09187.77145.7718.10083.92117.21
440128.60402.70142.37100.3765.8283.92033.29
441161.89435.99175.66133.6699.11117.2133.290
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D（i，j）取值信息（部分）

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始发站编号不同编号终到站对应区间的最短线路距离
1234438439440441
10274.1070.2328.23155.90174.00128.60161.89
2274.100344.32302.32429.99448.09402.70435.99
370.23344.32042.00169.67187.77142.37175.66
428.23302.3242.000127.67145.77100.37133.66
438155.90429.99169.67127.67018.1065.8299.11
439174.00448.09187.77145.7718.10083.92117.21
440128.60402.70142.37100.3765.8283.92033.29
441161.89435.99175.66133.6699.11117.2133.290
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方案名称救援列车布局点Z1Z2Z3/万元
原布局方案1,2,7,23,26,41,145,166,217,3060.890.860
最优布局方案2,7,9,17,23,26,41,56,217,3980.970.961 590
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2种方案对比结果

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方案名称救援列车布局点Z1Z2Z3/万元
原布局方案1,2,7,23,26,41,145,166,217,3060.890.860
最优布局方案2,7,9,17,23,26,41,56,217,3980.970.961 590
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基于弧段风险量化的铁路救援列车布局优化及混合算法改进研究
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韩佳英 1, 2 , 刘敬辉 2 , 李秋芬 2 , 刘鑫贵 2 , 张俊伟 2 , 张济洲 2 , 张雨晨 2
中国铁道科学 | 2026,47(2): 221-231
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中国铁道科学 | 2026, 47(2): 221-231
基于弧段风险量化的铁路救援列车布局优化及混合算法改进研究
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韩佳英1, 2 , 刘敬辉2, 李秋芬2, 刘鑫贵2, 张俊伟2, 张济洲2, 张雨晨2
作者信息
  • 1．中国铁道科学研究院集团有限公司 研究生部，北京100081
  • 2．中国国家铁路集团有限公司 铁路安全研究中心，北京100081

    • 韩佳英（1994—），男，内蒙古乌兰察布人，助理研究员。E-mail：

Research on Layout Optimization and Hybrid Algorithm Improvement of Railway Rescue Trains Based on Arc Risk Quantification
Jiaying HAN1, 2 , Jinghui LIU2, Qiufen LI2, Xingui LIU2, Junwei ZHANG2, Jizhou ZHANG2, Yuchen ZHANG2
Affiliations
  • 1.Graduate Department, China Academy of Railway Sciences, Beijing100081, China
  • 2.China Railway Safety Research and Development Center, China State Railway Group Co., Ltd., Beijing100081, China
出版时间: 2026-03-01 doi: 10.3969/j.issn.1001-4632.2026.02.19
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摘要
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为优化我国铁路救援列车布局以提高铁路应急救援效能，在弧段风险量化的基础上，对遗传-模拟退火混合算法进行改进。首先，构建多维度路网风险量化评价指标体系，运用熵权-TOPSIS法对路网各弧段进行风险量化评价，并结合覆盖理论，构建以路网救援覆盖率、救援时间满意度和救援列车布局成本为目标的铁路救援列车最优布局模型；其次，设计多阶段自适应模拟退火遗传算法（MP-ASAGA）对模型进行求解，将求解过程分为重点搜索全局最优解的探索阶段和重点加速收敛的开发阶段，在各阶段采取不同进化策略提升算法的求解性能；最后，以我国某铁路局的实际路网数据为案例进行计算验证。结果表明：与案例中路局的原布局方案相比，运用所提方法求解得到的铁路救援列车最优布局方案的路网救援覆盖率提升8.99%，救援时间满意度提升11.62%。该方法可为铁路救援列车的布局优化及救援效能提升提供相应的理论支持。

铁路救援列车  /  熵权-TOPSIS法  /  覆盖理论  /  最大覆盖选址问题  /  启发式算法

To optimize the layout of railway rescue trains and enhance railway emergency rescue efficiency in China,the genetic-simulated annealing hybrid algorithm is improved based on the arc risk quantification. First, a multi-dimensional risk quantification evaluation index system for the railway network is constructed. Through the Entropy Weight-TOPSIS method, risk quantification evaluation is conducted on each arc segment of the network. Then, combined with coverage theory, an optimal layout model for railway rescue trains is established with objectives including network rescue coverage rate, rescue time satisfaction, and rescue train layout cost. Secondly, the Multi-Phase Adaptive Simulated Annealing Genetic Algorithm (MP-ASAGA) is designed to solve the model. The solution process is divided into the exploration phase focusing on searching for the global optimum and the development phase focusing on accelerating convergence, with different evolutionary strategies applied in each phase to improve the algorithm's solving performance. Finally, a case study using actual railway network data from a railway bureau in China is conducted for calculation and validation. The results show that compared with the original layout scheme of the railway bureau in the case study, the optimal railway rescue train layout scheme obtained by the proposed method achieves an improvement of 8.99% in network rescue coverage rate, and an improvement of 11.62% in rescue time satisfaction. This method can provide corresponding theoretical support for the layout optimization of railway rescue trains and the enhancement of rescue efficiency.

Railway rescue trains  /  Entropy Weight-TOPSIS method  /  Coverage theory  /  Maximum Covering Location Problem (MCLP)  /  Heuristic algorithm
韩佳英, 刘敬辉, 李秋芬, 刘鑫贵, 张俊伟, 张济洲, 张雨晨. 基于弧段风险量化的铁路救援列车布局优化及混合算法改进研究. 中国铁道科学, 2026 , 47 (2) : 221 -231 . DOI: 10.3969/j.issn.1001-4632.2026.02.19
Jiaying HAN, Jinghui LIU, Qiufen LI, Xingui LIU, Junwei ZHANG, Jizhou ZHANG, Yuchen ZHANG. Research on Layout Optimization and Hybrid Algorithm Improvement of Railway Rescue Trains Based on Arc Risk Quantification[J]. China Railway Science, 2026 , 47 (2) : 221 -231 . DOI: 10.3969/j.issn.1001-4632.2026.02.19
正文
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随着我国铁路路网规模快速扩张和运营环境日益复杂，铁路应急救援能力面临严峻挑战。救援列车作为铁路应急救援体系的核心装备，其科学布局对缩短应急响应时间、降低事故损失具有关键作用。复杂路网结构及风险条件下，构建兼顾救援覆盖能力、救援时效性与救援经济性的铁路救援列车最优布局模型，有利于最大程度提高应急救援效能。
铁路救援列车作为救援设施的1种，其优化布局属于典型的救援设施布局问题，考虑到我国各路局目前配属的救援列车数量确定，在不考虑新增或废止救援列车的情况下，铁路救援列车最优布局可归类为最大覆盖选址问题（Maximum Covering Location Problem，MCLP）。国内外学者对于救援设施布局问题已开展了较为丰富的研究。Zhao［1］等基于风险绘图，通过多目标优化平衡救援设施布局的救援能力、服务能力和公平性，并采用NAGA-Ⅱ进行求解，但忽视了救援设施布局的成本约束。Ren［2］等以救援需求满足度和救援时间最小化为目标构建救援设施布局模型，采用植物生长模拟算法进行求解，但没有反映救援设施布局的成本因素，且其离散需求点建模难以模拟区域突发事件发生场所的随机性。国内学者中，王富章［3］、吴艳华［4］利用AHP进行风险分析并构建了铁路救援基地布局点覆盖模型，通过蚁群算法进行求解，但同样将救援覆盖简化为对离散救援点的覆盖，难以表征突发事件发生地点的随机性，且蚁群算法易收敛于局部极值，不适用于大规模算例问题。汤霖［5］等将救援列车对路网的覆盖细化为对弧段的覆盖，建立了最大覆盖率和最大时间满意度为目标的救援列车布局模型，但其运用网络拓扑特征确定弧段风险权重的方法，缺少线路及事故数据的支撑，无法反映线路实际的风险程度，且未考虑既有设施改址的成本约束。雷斌［6］等构建了基于站点脆弱性分析的应急救援点选址方法，但该研究限制于应急设施和需求点的单对单救援，对于覆盖水平函数采用的线性假设缺少验证。
综合上述研究发现，当前研究的局限性主要体现在以下3个层面：一是模型假设层面，将救援设施对路网的救援覆盖简化为对路网中各离散救援点的覆盖，无法反映突发事件在路网分布的随机性和连续性；二是模型构建层面，既有研究对救援设施布局的影响因素考虑不全面，如忽略救援列车布局成本目标等，且在路网风险分析中多偏重定性分析，缺乏数据支持；三是求解算法方面，传统启发式算法如蚁群算法等在处理大规模路网数据时，普遍存在收敛速度慢、易陷入局部最优解等问题。针对上述问题，本文做出以下改进：首先，基于实际路网数据，运用熵权-TOPSIS方法对路网中各弧段的风险进行量化评估，从而克服以往风险分析主观性强、数据支撑弱的问题；其次，结合风险分析构建了以路网救援覆盖率最大化、救援时间满意度最高和布局成本最低为目标的多目标优化模型，特别加入了救援列车布局成本的量化分析，弥补了以往研究中经济性目标缺失的不足；最后，设计多阶段自适应模拟退火遗传算法（Multi-Phase Adaptive Simulated Annealing Genetic Algorithm，MP-ASAGA），通过应用分级进化策略将算法划分为探索期和开发期2个阶段，前者重在扩大解集多样性，后者重在加速收敛，从而改进传统算法在解空间探索与收敛速度间的矛盾，有效提升求解效率。
1　路网风险量化评价
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1.1　路网风险量化评价指标体系
铁路救援列车最优布局应充分考虑因路网风险程度区域差异所产生的不同程度的救援需求。对于路网风险量化评价，刘敬辉［7］提出评价应包括设施设备故障、人员操作、外部环境因素、历史事故故障信息等关键因素。为避免定性指标对风险判识带来的人为误差，基于路局日常风险管控过的关键项点及实际可获取数据，从线路条件、自然环境和事故数据3个维度选取8项指标，构建了路网风险量化评价指标体系，如图1所示。
1.2　基于熵权-TOPSIS法的路网风险量化评价
定义“弧段”为路网中各相邻站点之间的区段，基于构建的路网风险量化评价指标体系，运用熵权法-TOPSIS组合方法对路网中各弧段的风险进行量化评价，具体方法如下。
1）熵权法确定指标权重
熵权法可较好避免主观赋权带来的偏差，更适用于由全定量指标构成的指标体系［8］。其计算按以下步骤进行。
步骤1：确定初始评价矩阵。设路网中有共m个弧段，各弧段均包含路网风险量化评价指标体系中的n个指标值（n=8），全弧段初始评价矩阵S的计算式为
S=[spq]m×n
式中：spq为第p个弧段所对应的第q个评价指标的数值。
步骤2：数据标准化。为消除数据量纲不同带来的影响，将各评价指标值spq（均为正向指标）标准化为spq'，其表达式为
spq'=spq-minq(spq)maxq(spq)-minq(spq)
步骤3：计算各指标权重。权重值uq的计算式为
uq=(1-eq)/n-∑q=1neq      0≤uq≤1,∑q=1nuq=1
其中，
eq=-1lnm∑p=1mspq/∑q=1nspqlnspq/∑q=1nspq
步骤4：构建加权标准化评价矩阵。矩阵Y的计算式为
Y=[ypq]m×n
其中，
ypq=uqs'pq
2）基于加权标准化评价矩阵的TOPSIS法确定各弧段风险值
在熵权法确定指标权重并构建加权标准化评价矩阵Y的基础上，运用TOPSIS法通过确定各评价对象到正负理想解的欧式距离计算最终的评价结果［9］，其计算按以下步骤进行。
步骤1：计算正负理想解。基于加权标准化评价矩阵Y，计算全部指标的正理想解和负理想解。
vq+=max(ypq)       p=1,2,…,m
vq-=min(ypq)         p=1,2,…,m
式中：vq+和vq-为第q个评价指标的正理想解和负理想解。
步骤2：确定各弧段同理想解的加权欧式距离。第p个弧段到正、负理想解的欧氏距离Vp+和Vp-分别为
Vp+=∑q=1nuq(spq'-vq+)2
Vp-=∑q=1nuq(spq'-vq-)2
步骤3：计算各弧段风险值。风险值Cp的计算式为
Cp=cp/∑p=1mcp
其中，
cp=Vp-/(Vp++Vp-)
式中：cp为第p个弧段到正理想解的相对贴近度。
路网各弧段风险值将作为重要参数用于铁路救援列车最优布局模型的构建与求解。
2　铁路救援列车最优布局模型构建
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2.1　模型假设
根据铁路应急救援工作实际特点，铁路救援列车最优布局模型包含以下假设。
（1）路网中救援列车的布局数量保持不变。
（2）救援覆盖范围为对路网中各弧段的覆盖，而不仅是对各离散救援点的覆盖。
（3）考虑弧段两端的救援列车对其进行联合救援覆盖。
（4）不考虑救援列车的服务能力限制。
（5）救援列车优先布局在具备停放条件的站点。
（6）救援距离定义为布局站点到救援需求处所的最短线路长度，不考虑救援列车在站点内的走行距离。
（7）救援时间指救援列车出动到抵达救援需求处所的时间。
2.2　模型构建
2.2.1　目标函数
所构建的铁路救援列车最优布局模型以最大化路网救援覆盖率Z1、最大化救援时间满意度Z2以及最小化救援列车布局成本Z3为优化目标。为避免各优化目标间量纲差异对求解结果的影响，运用min-max方法对Z1，Z2和Z3进行归一化处理，并通过加权方式将其整合为目标函数Z，其表达式为
Z=maxw1Z1-Z1maxZ1max-Z1min+w2Z2-Z2maxZ2max-Z2min-w3Z3-Z3maxZ3max-Z3min
其中，
Z1=∑(j,k)∈ACjkminmaxβ,γ∈I,β≠γ(aβjkxβ+aγkjxγ),1
Z2=∑β,γ∈I,(j,k)∈ACjke-Kdjk+minD(β,j)xβ,D(γ,k)xγ-R
Z3=∑i∈NMixi
式中：Z1max，Z1min，Z2max，Z2min，Z3max，Z3min分别为Z1，Z2和Z3在算法各次迭代中的最大值与最小值；w1，w2和w3分别为Z1，Z2和Z3对应的权重，权重值依据路局的调研结果确定，且满足w1+w2+w3=1；i为救援列车布局站点编号；N为路网中全站点集合；I为救援列车布局站点集合；A为线路各相邻站点间的弧段集合；j和k为A中各弧段对应的首、末站点编号；ljk为相邻站点j和k间的弧段；Cjk为弧段ljk的风险值；aβjk为救援列车从站点β出发对弧段ljk从j到k端方向的单侧覆盖率；aγkj为救援列车从站点γ出发对弧段ljk从k到j端方向的单侧覆盖率；xi为0-1决策变量，表示站点i是否布局救援列车；K为服务满意度衰减系数；Mi为站点i的救援列车布局成本；D（i，j）为站点i和j间的最短线路距离。
2.2.2　约束条件
模型约束条件主要包括决策变量约束、救援列车数量约束、救援列车单侧覆盖率约束、救援列车联合覆盖率约束、救援时间满意度约束以及救援列车布局成本约束。
1）决策变量约束
若站点i布局有救援列车则xi取值为1，否则取值为0，其约束为
xi∈0,1       ∀i∈N
2）救援列车数量约束
模型不改变路局保有的救援列车数量，即路网中待布局的救援列车固定为P辆，其约束为
∑i∈Nxi=P
3）救援列车单侧覆盖率约束
该约束表示仅出动1辆救援列车进行救援时，能够覆盖被救援弧段ljk的范围占其总长度的比例。其表达式为
aβjkβ∈I,(j,k)∈A=1                             D(β,j)+djk≤RR-D(β,j)djk       D(β,j)<R<D(β,j)+djk0                            R≤D(β,j)
式中：R为救援列车最大救援距离；djk为弧段ljk的长度。
aβjk计算原理示意图如图2所示。救援列车从站点β出动对弧段ljk进行救援，可分为3种情况。情况1：当R≥D（β,j）+djk时，救援列车在最大救援距离内可完全覆盖ljk，则aβjk=1。情况2：当D（β,j）<R<D（β,j）+djk时，救援列车在最大救援距离内只能覆盖部分ljk，此时aβjk为可覆盖部分占总长度的比例。情况3：当R<D（β,j）时，救援列车无法覆盖ljk，此时aβjk=0。
同理，单侧覆盖率aγkj的约束为
aγkjγ∈I,(j,k)∈A=1                           D(γ,k)+djk≤RR-D(γ,k)djk       D(γ,k)<R<D(γ,k)+djk0                           R≤D(γ,k)
4）救援列车联合覆盖率约束
为保证最大救援效率，考虑不同的救援列车从待救援弧段两端的不同站点同时出动救援。设救援列车对弧段ljk的联合覆盖率为Ujk，其约束为
Ujk=minmaxβ,γ∈I,β≠γ(aβjkxβ+aγkjxγ),1
联合覆盖率示意图如图3所示。救援列车自站点β和γ（距被救援弧段ljk两端最近的不同救援列车布局站点）同时出动救援，可分为2种情况。情况Ⅰ：当aβjk+aγjk<1时，联合救援无法覆盖ljk全长，则Ujk=aβjk+aγkj。情况Ⅱ：当aβjk+aγkj ≥1时，Ujk=1。
5）救援时间满意度约束
对于超过规定救援范围的待救援点，不能弃之不顾仍应施以救援，但超出规定范围之外的救援距离将导致救援时间满意度的衰减。弧段ljk的救援时间满意度Tjk的约束为
Tjkβ,γ∈I,(j,k)∈A=e-Kdjk+minD(β,j)xβ,D(γ,k)xγ-R
式中：K为服务满意度衰减系数［10］。
对于弧段ljk，救援时间简化认为由距离弧段任一端点最近的救援列车负责覆盖全弧段的救援，若超过规定的最大救援距离，Tjk将进行衰减。救援时间满意度衰减示意图如图4所示。站点β为距离ljk任一端点最近的救援列车布局站点，救援过程中Tjk在ljk超出R的救援范围部分（绿色部分）将产生衰减。
6）救援列车布局成本约束
站点i的救援列车布局成本Mi的约束为
Mii∈I=0              i∈B1ε1             i∈B\B1ε2             i∉B 
式中：ε1为救援列车新布局在具备救援列车停放条件站点的布局成本；ε2为救援列车新布局在不具备救援列车停放条件站点的布局成本；B1为救援列车原布局站点集合；B为具备救援列车停放能力的站点集合。
依据《铁路救援列车管理办法》，驻地建设需包含轨道起重机停放库、停留线及配套房屋设施等，涉及成本主要包括设施、特种物品及设备机具。所提模型不改变救援列车总数，故不涉及新增特种物品与设备机具的费用，布局成本聚焦于驻地主要设施。在设施成本中，可利旧设备（如台式电脑）及低造价部分（如遮阳雨棚）亦不予计入。因此，最终影响取值的核心成本项为新建停留线、练功线及配套房屋，其具体建设标准见表1。
由于成本造价受地形条件、施工条件以及用料等多种因素影响，为简化计算，各部分的成本单价参考路局调研得到的类似工程数据，其中：列车停留线和练功线的建造成本约为1 万元 ∙ m-1，配套房屋建造成本约为0.3 万元 ∙ m-2。因此，站点建设费用需分2种情况核算。①对于已设有整备场（点）的站点，认为具备救援列车的停放条件，无须额外设置列车停留线及配套练功线，成本仅涉及救援列车配套房屋的建设费用，因此按房屋面积600 m2、建造成本0.3万元 ∙ m-2算得成本ε1为180万元；②对于不具备救援列车停留条件的站点，需要额外设置列车停留线、练功线及配套房屋，因此，按房屋面积600 m2、建造成本0.3万元 ∙ m-2，新建停留线及练功线330 m、建造成本1.0万元 ∙ m-1算得成本ε2为510万元。
3　基于MP-ASAGA的模型求解
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3.1　算法流程设计
所提MP-ASAGA算法流程如图5所示。将遗传算法（Genetic Algorithm，GA）和模拟退火算法（Simulated Annealing，SA）相结合，通过搭配不同进化策略，将最优布局模型的求解过程分解为探索和开发2个阶段。在迭代初期，算法默认处于探索阶段，采用轮盘赌选择、高概率交叉变异、单一个体精英保留以及缓慢降温的进化组合，尽可能保持高种群多样性，提升全局搜索能力；当迭代次数或种群多样性触发阶段转换条件时，算法转为开发阶段，通过锦标赛选择、低概率交叉变异、扩大精英保留数量及快速降温的进化组合，尽可能快速收敛至全局最优解，从而有效改善传统优化算法在解空间探索与收敛速度间的矛盾。
3.2　算法流程实现
步骤1：种群初始化及染色体编码。设染色体（救援列车随机布局方案）种群数量（随机方案个数）为NA，每个染色体包括P个基因（救援列车），各基因编码为序列1~NS之间的随机整数，表示各随机布局方案中P个救援列车对应布局的站点编号。设置算法初始参数，按照所构建的铁路救援列车最优布局模型计算各染色体的适应度f（即目标函数值），随后开始迭代。
步骤2：判断算法进化阶段。算法在迭代初期默认处于探索阶段，通过设计种群多样性D与迭代次数it的双重判据，构建阶段转换机制，其中种群多样性D采用变异系数法［11-12］计算，当满足预设条件时，算法自动转化为开发阶段，阶段转换表达式为
J=1       若D<D1或it>iC 0       否则
其中，
D=1NA∑i=1NAf(i)-1NA∑i=1NAf(i)21NA∑i=1NAf(i)
式中：J为阶段转化布尔量，取值为1表示算法转换为开发阶段，取值为0表示保持当前探索阶段；iC为转阶段迭代次数；D1为转阶段种群多样性阈值。
根据J的计算结果，若J=1，算法进入步骤3，否则进入步骤4。
步骤3：探索阶段进化策略执行。通过选择不同进化策略组合以尽可能扩大解空间搜索范围，其具体策略包括遗传和模拟退火2部分。
遗传部分包括选择、交叉、变异和精英保留4个环节。选择环节采用基于排序的轮盘赌法［13］按适应度比例概率选择父代个体进行交叉变异，因低适应度个体存在参与进化概率，与锦标赛法［14］等其他选择方式相比，该方法允许低适应度个体参与进化，更有利于保留种群多样性。
交叉环节设计了1种自适应交叉概率的混合交叉策略，其中自适应交叉概率pexplore为
pexplore=pini(1-it/iM)+0.1
式中：pini为探索期交叉概率的初始值；iM为规定的算法迭代次数最大值。
迭代过程中交叉概率在［pini，0.1］区间内线性下降，探索前期交叉概率较大，可使更多个体参与交叉，从而增加种群多样性，后期交叉概率较小，可降低对种群优良基因的破坏。交叉方式采用轮盘赌策略，按照0.1，0.2和0.7的概率分别执行单点交叉、双点交叉和均匀交叉，形成混合交叉策略。该策略示意图如图6所示。
变异环节采用自适应高斯变异策略，在固定高斯变异策略［15-16］的基础上，将变异步长（扰动幅度）由固定值改为自适应步长σt，其表达式为
σt=0.21-itiM
η'=round(η+δ)
式中：η为当前解；δ为对原基因值施加随迭代衰减的正态分布变异扰动，δ~N(0,σt2)；η'为变异后的解。
自适应高斯变异策略示意图如图7所示，随着迭代次数增加，变异扰动逐步减小，变异由初期的施加大幅随机扰动逐步向后期减小扰动强度转变。
精英保留环节在交叉变异排序后的种群中，保留1个适应度最大的个体为当前种群精英，直接继承到下次迭代，其余个体进入模拟退火环节，避免完全随机破坏当前最优个体。
模拟退火部分［17-18］首先计算初始退火温度T0，其计算式为
T0=fmax-fmin
式中：fmax和fmin分别为当前种群染色体适应度的最大值与最小值。
然后设置探索期降温系数αexplore，采用较大值以延长对种群强扰动的过程。接着接受较劣解，采用Metropolis准则，计算种群对于较劣解的接受概率PS，其计算式为
PS=1           Δf>0 eΔf/T      Δf≤0
其中，
Δf=f(Snew)- f(Scurrent)
T=T0(aexplore)it
式中：Scurrent为当前种群中的非精英个体（单个解）；Snew为通过邻域扰动产生的新解；f（∙）为适应度函数；Δf为适应度差值；T为本次迭代的退火温度。
最后记录当前种群最优个体并进入步骤5。
步骤4：开发阶段进化策略执行。当满足阶段转换条件，算法转化为开发阶段。开发阶段重在尽可能提升收敛速度，其具体策略也包含遗传和模拟退火2个部分。
遗传部分包括选择、交叉、变异和精英保留4个环节。选择环节采用锦标赛选择法选择父代个体进行后续进化，同探索期轮盘赌方式相比，增强选择压力，推动种群向精英解区域收敛。交叉环节同探索期采用相同交叉策略，但降低交叉概率，加速种群收敛。变异环节采用固定σt值高斯变异，但降低变异概率，减小变异扰动。精英保留环节对比探索期仅保留1个精英，开发期选取种群前10%作为精英个体，增加精英比例加速收敛。
模拟退火部分采用加速降温策略，降温系数αexpoit<αexplore，相比探索期以更快的降温速度降低扰动加速种群收敛。记录当前种群最优个体并进入步骤5。
步骤5：迭代终止判断。判断当前迭代次数是否小于最大迭代次数iM，若满足it<iM，则返回步骤2；否则输出种群最优个体，流程结束。
4　实例验证
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通过调研获取了我国某铁路局的实际运营数据，主要包括自然环境、事故故障、路网参数和救援资源布局4个方面。其中：路网数据涵盖该局所辖主要线路的441个站点和466个弧段的站点里程、线路速度及线路隧道桥梁分布等信息；事故数据包括各线路历史事故数、事故直接损失等信息；自然环境数据包括各线路年均降雨量、降雪量及风力等级信息；救援资源配置则包括该局现有救援列车配属数量及配置位置信息。
考虑到铁路数据的安全性要求，采用数字及字母编码代替实际的线路及站点名称。该路局目前保有救援列车10辆，分别部署于站点编号1，2，7，23，26，41，145，166，217和306处。救援列车的平均速度为100 km ∙ h-1，在实际工作中，该局在救援作业中设定的最大有效救援距离为200 km。此外，该局已具备救援列车配置条件的布局待选点共41个。
4.1　路网各弧段风险量化评价
路网中各弧段ljk的基本数据见表2（仅列出部分代表性数据）。基于各弧段基本数据，运用熵权-TOPSIS对各弧段的风险值Cjk进行量化评价，计算结果见表3（仅列出部分代表性数据）。
4.2　路网站点间最短路径计算
实施救援时，为最大化救援效率，救援路径必须为路网站点间的最短路径，该案例路局各弧段的距离信息见表4（仅列出部分代表性数据）。
运用Warshall-Floyd算法［19-20］，计算站点i与站点j间的最短距离D（i，j），若站点间在路网中无连接关系，则距离为+∞，各站点间最短线路距离D（i，j）取值信息见表5（仅列出部分代表性数据）。
4.3　基于MP-ASAGA的铁路救援列车最优布局方案计算
将该案例中的参数Cjk和D（i，j）等输入铁路救援列车最优布局模型，并根据MP-ASAGA算法在模型求解过程中的表现，调试并设置各算法参数。算法基本参数设置：种群数量NA为200；染色体基因编码位数为10位（救援列车数量）；最大迭代次数iM为300。探索期参数设置：自适应交叉概率初始值pini为0.9；变异概率pexplore为0.2；降温系数αexplore为0.97。开发期参数设置：固定交叉概率pexploit为0.7；变异概率pexploit为0.03；降温系数αexpoit为0.8。阶段转换参数设置：转阶段种群多样性阈值D1为0.1；转阶段迭代次数iC为0.3iM。模型优化目标Z1，Z2和Z3权重分别设为0.4，0.4和0.2；服务满意度衰减系数K按照Li等［10］的原参数设为0.05。
在Matlab环境中，运用MP-ASAGA对最优布局模型进行求解，得到优化目标Z1，Z2和Z3的迭代进化情况如图8所示。由图8可知，各优化目标在迭代进化中均得到显著改善，Z1从初始值0.88提升至0.97，Z2从0.86提升至0.96，Z3从4 080万元大幅下降至1 590万元。表明经算法优化，救援覆盖率和救援时间满意度显著提升，救援列车布局成本大幅降低。
目标函数Z的收敛曲线如图9所示。由图9可知，算法在第161次迭代时获得全局最优解，最优目标函数值为0.84。
救援列车原布局方案同最优布局方案对比如图10所示（仅标识部分关键站点和线路）。由图10可知：原布局方案的救援列车布局站点分别为1，2，7，23，26，41，145，166，217和306；经计算最优布局方案的救援列车布局站点分别为2，7，9，17，23，26，41，56，217和398。
原布局方案与最优布局方案的对比结果见表6。由表6可知：与原布局方案相比，最优布局方案虽使救援列车布局成本增加了1 590万元，但在2项关键效能指标上实现了显著提升，其路网救援覆盖率提高8.99%，救援时间满意度提升11.62%。这表明基于MP-ASAGA的铁路救援列车优化布局方法，能够在可接受的成本增长范围内，对救援列车救援效能提升具有明显作用。
4.4　MP-ASAGA同GA、SA算法对比
在本案例中，将MP-ASAGA同常规遗传算法（GA）与模拟退火算法（SA）同时进行算法求解性能对比，目标函数Z的收敛性能对比如图11所示。由图11可知，MP-ASAGA在第161次迭代时已收敛至全局最优解，而GA与SA在300次迭代范围内均无法收敛至全局最优。这表明MP-ASAGA相比于GA和SA在收敛性能方面具有明显的提升，更适用于大规模数据条件下的优化求解。
5　结语
收起
本文针对铁路救援列车布局优化问题，运用熵权-TOPSIS法对路网风险全面量化分析，并在此基础上提出了1种以最大化救援列车覆盖率、最大化救援时间满意度以及最小化救援列车布局成本为目标的最优布局模型，更全面考虑救援列车布局的关键要素。为有效求解该模型，设计了1种多阶段自适应模拟退火遗传算法（MP-ASAGA）。与原方案相比，该算法路网救援覆盖率提升了8.99%，救援时间满意度提升了11.62%。同时，与GA和SA等传统优化算法相比，MP-ASAGA算法在大规模数据求解的情况下收敛性能提升效果明显。
为进一步完善研究成果，未来工作可在以下方面展开：一是继续拓展我国铁路实际数据的调研范围，深入分析线路运输量、沿线人口数量、危险品分布等因素对路网风险的影响；二是综合考虑路外救援力量协同参与等现实因素，进一步丰富与优化救援列车布局模型，增强其在复杂真实场景中的适用性与可靠性。
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2026年第47卷第2期
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doi: 10.3969/j.issn.1001-4632.2026.02.19
  • 接收时间：2025-07-24
  • 首发时间：2026-06-03
  • 出版时间：2026-03-01
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  • 收稿日期：2025-07-24
  • 修回日期：2026-02-27
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    1．中国铁道科学研究院集团有限公司 研究生部，北京100081
    2．中国国家铁路集团有限公司 铁路安全研究中心，北京100081
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多孔菌科 Polyporaceae 8 14 6.70 蜡蘑属 Laccaria 5 2.39
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小菇属 Mycena 11 5.26
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红菇属 Russula 17 8.13
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