都市快轨交通

城市轨道交通列车开行方案编制优化研究综述

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陶思宇 ¹^,²^,³ , 李治德 ¹^,²^,³ , 张永祥 ¹^,²^,³

都市快轨交通 | 快轨论坛 2025,38(5): 23-34

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都市快轨交通 |快轨论坛 2025 , 38 (5) : 23 -34

城市轨道交通列车开行方案编制优化研究综述

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陶思宇¹^,²^,³, 李治德¹^,²^,³, 张永祥¹^,²^,³

作者信息

^1.西南交通大学交通运输与物流学院，成都　611756

^2.西南交通大学综合交通运输智能化国家地方联合工程实验室，成都　611756

^3.西南交通大学综合交通大数据应用技术国家工程实验室，成都　611756

作者简介:

陶思宇，男，博士，副教授，从事轨道交通运输组织优化研究，taosiyu@swjtu.edu.cn

A Review of Research on the Optimization of Train Operation Planning in Urban Rail Transit

Siyu TAO¹^,²^,³, Zhide LI¹^,²^,³, Yongxiang ZHANG¹^,²^,³

Affiliations

^1.School of Transportation and Logistics, Southwest Jiaotong University, Chengdu 611756

^2.National United Engineering Laboratory of Integrated and Intelligent Transportation, Southwest Jiaotong University, Chengdu 611756

^3.National Engineering Laboratory of Integrated Transportation Big Data Application Technology, Southwest Jiaotong University, Chengdu 611756

出版时间: 2025-10-10 doi: 10.3969/j.issn.1672-6073.2025.05.004

文章导航

摘要

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列车开行方案优化作为城市轨道交通运输组织中的核心研究问题，是提升轨道交通运营效率和服务质量的关键。为全面梳理该领域的研究进展，并促进其进一步发展，本文对国内外相关文献进行系统论述。首先，从数学建模角度出发，分别从线路层面和网络层面总结列车开行方案优化的目标函数和约束条件等核心内容；在此基础上总结求解算法的研究，详细回顾启发式算法和精确算法的最新进展。最后，指出现有研究中的不足，并提出未来研究的方向，包括加强动态客流和乘客行为特征的建模，深化网络互联互通情境下的运营优化，探索多策略组合的运营组织模式，以及结合智能化优化算法进行综合分析，以推动城市轨道交通列车开行方案优化研究的创新与发展。

关键词

城市轨道交通 / 列车开行方案 / 研究综述 / 数学模型 / 优化算法

Abstract

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Train scheduling optimization, as a core issue in urban rail transit transportation organization, is crucial for enhancing the operational efficiency and service quality of rail transit systems. To systematically review the research progress in this field and promote its further development, this study conducts a comprehensive survey of relevant literature from both domestic and international sources. From the perspective of mathematical modeling, the paper summarizes the core elements of train scheduling optimization, including objective functions and constraints, from both the line-level and network-level perspectives. Furthermore, a detailed review of solution methods is presented, categorizing the approaches into heuristic algorithms and exact algorithms. Finally, the paper identifies existing research gaps and proposes future directions, including the need for improved modeling of dynamic passenger flow and behavior patterns, optimization of operations under network interconnection scenarios, exploration of multi-strategy operational models, and the integration of intelligent optimization algorithms, to further advance research on train scheduling optimization in urban rail transit.

Key words

urban rail transit / train scheduling plan / literature review / mathematical model / optimization algorithm

引用本文

陶思宇, 李治德, 张永祥. 城市轨道交通列车开行方案编制优化研究综述. 都市快轨交通, 2025 , 38 (5) : 23 -34 . DOI: 10.3969/j.issn.1672-6073.2025.05.004

Siyu TAO, Zhide LI, Yongxiang ZHANG. A Review of Research on the Optimization of Train Operation Planning in Urban Rail Transit[J]. Urban Rapid Rail Transit, 2025 , 38 (5) : 23 -34 . DOI: 10.3969/j.issn.1672-6073.2025.05.004

基金

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国家重点研发计划项目(2022YFB4300500)
国家自然科学基金青年基金项目(72201218)
四川省科技计划资助(2023NSFSC0901)

参考文献

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参考文献引证文献

排序方式：

[1]

GOOSSENS J W, VAN HOESEL S, KROON L. A branch-and-cut approach for solving railway line-planning problems[J]. Transportation science, 2004, 38(3): 379-393.

[2]

FENG Tao, LUSBY R M, ZHANG Yongxiang, et al. An ADMM-based dual decomposition mechanism for integrating crew scheduling and rostering in an urban rail transit line[J]. Transportation research part C: emerging technologies, 2023, 149: 104081.

[3]

PARK B H, SEO Y I, HONG S P, et al. Column generation approach to line planning with various halting patterns: application to the Korean high-speed railway[J]. Asia-Pacific journal of operational research, 2013, 30(4): 1350006.

[4]

ELLEGOOD W A, CAMPBELL J F, NORTH J. Continuous approximation models for mixed load school bus routing[J]. Transportation research part B: methodological, 2015, 77: 182-198.

[5]

NOLD M, CORMAN F. Dynamic train unit coupling and decoupling at cruising speed: Systematic classification, operational potentials, and research agenda[J]. Journal of rail transport planning & management, 2021, 18: 100241.

[6]

毛保华, 刘明君, 黄荣, 等. 轨道交通网络化运营组织理论与关键技术[M]. 北京: 科学出版社, 2011.

[7]

田媛媛, 彭磊. 双碳背景下城市轨道交通列车灵活编组技术研究[J]. 城市轨道交通研究, 2024, 27(9): 288-292. TIAN Yuanyuan, PENG Lei. Research on flexible train marshalling technology for urban rail transit under the dualcarbon background[J]. Urban mass transit, 2024, 27(9): 288-292.

[8]

李伟, 陈思倩, 周珺, 等. 在线编解模式下城市轨道交通列车灵活编组开行方案优化方法[J]. 中国铁道科学, 2024, 45(1): 203-214. LI Wei, CHEN Siqian, ZHOU Jun, et al. Optimization method of flexible train composition scheduling in urban rail transit under online coupling/decoupling mode[J]. China railway science, 2024, 45(1): 203-214.

[9]

ZHOU Xu, LU Fang, WANG Liyu. Optimization of train operation planning with full-length and short-turn routes of virtual coupling trains[J]. Applied sciences, 2022, 12(15): 7935.

[10]

LI Sijie, XU Ruihua, HAN Ke. Demand-oriented train services optimization for a congested urban rail line: integrating short turning and heterogeneous headways[J]. Transportmetrica A: transport science, 2019, 15(2): 1459-1486.

[11]

LI Zhengyang, ZHAO Jun, PENG Qiyuan. Train service design in an urban rail transit line incorporating multiple service routes and multiple train compositions[J]. Transportation research part C: emerging technologies, 2021, 123: 102959.

[12]

ZHOU Housheng, QI Jianguo, YANG Lixing, et al. Joint optimization of train timetabling and rolling stock circulation planning: a novel flexible train composition mode[J]. Transportation research part B: methodological, 2022, 162: 352-385.

[13]

曾庆文, 彭其渊. 考虑多编组的城轨列车跨线运营开行方案研究[J]. 铁道科学与工程学报, 2023, 20(3): 878-889. ZENG Qingwen, PENG Qiyuan. Cross-line train plan in urban rail transit considering the multi-group train[J]. Journal of railway science and engineering, 2023, 20(3): 878-889.

[14]

蒋伟, 叶茂, 郭孝洁, 等. 面向运力精准投放的城轨列车多编组开行方案优化研究[J]. 江苏科技信息, 2024, 41(5): 125-131. JIANG Wei, YE Mao, GUO Xiaojie, et al. Research on the optimization of multi-formation operation of urban rail trains for precise transport capacity[J]. Jiangsu science and technology information, 2024, 41(5): 125-131.

[15]

付兵, 马新源, 田婉琪, 等. 面向虚拟编组的城市轨道交通运行优化调度方法[J]. 铁道运输与经济, 2024, 46(1): 124-132. FU Bing, MA Xinyuan, TIAN Wanqi, et al. Urban rail transit scheduling optimization method for virtual coupling trains[J]. Railway transport and economy, 2024, 46(1): 124-132.

[16]

YANG Xiyu, JI Yuxiong, DU Yuchuan, et al. Bi-level model for design of transit short-turning service considering bus crowding[J]. Transportation research record: journal of the transportation research board, 2017, 2649(1): 52-60.

[17]

谭彬彬, 金华, 刘爽, 等. 考虑城市轨道交通折返进路占用的大小交路列车运行组织优化[J]. 铁道科学与工程学报, 2022, 19(8): 2161-2168. TAN Binbin, JIN Hua, LIU Shuang, et al. Optimization on train operation organization of full-length and short-turn routing mode considering the occupation of turn-back route[J]. Journal of railway science and engineering, 2022, 19(8): 2161-2168.

[18]

李思杰, 王磊, 潘寒川, 等. 大小交路条件下的城市轨道交通线路多站协同限流优化[J]. 铁道科学与工程学报, 2022, 19(12): 3536-3545. LI Sijie, WANG Lei, PAN Hanchuan, et al. Optimization of multi-station collaborative passenger flow control for an urban rail transit line with full-length and short-turn routings[J]. Journal of railway science and engineering, 2022, 19(12): 3536-3545.

[19]

戴延泽, 占曙光. 考虑碳排放的城轨开行大小交路方案分析[J]. 铁道科学与工程学报, 2022, 19(12): 3546-3556. DAI Yanze, ZHAN Shuguang. Analysis of full-length and short-turn routing of urban rail transit considering carbon emission[J]. Journal of railway science and engineering, 2022, 19(12): 3546-3556.

[20]

杨雯雯, 孟学雷, 高如虎, 等. 考虑运能利用和碳排放的绿色城轨开行方案研究[J]. 交通运输系统工程与信息, 2025, 25(1): 122-132. YANG Wenwen, MENG Xuelei, GAO Ruhu, et al. Train operation plan of green urban rail transit considering transportation capacity utilization and carbon emissions[J]. Journal of transportation systems engineering and information technology, 2025, 25(1): 122-132.

[21]

CANCA D, BARRENA E, LAPORTE G, et al. A shortturning policy for the management of demand disruptions in rapid transit systems[J]. Annals of operations research, 2016, 246(1): 145-166.

[22]

李正洋, 赵军, 彭其渊. 考虑多交路多编组的城市轨道线路列车交路计划优化[J]. 铁道学报, 2020, 42(6): 1-11. LI Zhengyang, ZHAO Jun, PENG Qiyuan. Optimizing the train service route plan in an urban rail transit line with multiple service routes and multiple train sizes[J]. Journal of the China railway society, 2020, 42(6): 1-11.

[23]

姚恩建, 张金萌, 郇宁. 效率与公平导向下城轨大小交路开行方案优化[J]. 华南理工大学学报(自然科学版), 2020, 48(5): 41-48. YAO Enjian, ZHANG Jinmeng, HUAN Ning. Equality-efficiency balance-oriented optimization of long-short route strategy in urban rail transit[J]. Journal of South China University of Technology (Natural Science Edition), 2020, 48(5): 41-48.

[24]

FENG Tao, LUSBY R M, ZHANG Yongxiang, et al. Integrating train service route design with passenger flow allocation for an urban rail transit line[J]. European journal of operational research, 2024, 313(1): 146-170.

[25]

陈垚, 柏赟, 毛保华, 等. 跨线条件下城市轨道交通列车交路计划优化方法[J]. 铁道学报, 2024, 46(8): 21-29. CHEN Yao, BAI Yun, MAO Baohua, et al. Optimization of train routing plan for interconnected lines in urban rail transit[J]. Journal of the China railway society, 2024, 46(8): 21-29.

[26]

NIU Huimin, ZHOU Xuesong, GAO Ruhu. Train scheduling for minimizing passenger waiting time with time-dependent demand and skip-stop patterns: Nonlinear integer programming models with linear constraints[J]. Transportation research part B: methodological, 2015, 76: 117-135.

[27]

ZHANG Tong, LI Dawei, SONG Yuchen. Urban rail transit congestion management: coordinated optimization of passenger guidance and train scheduling with skip-stop patterns[J]. Journal of transportation engineering, part A: systems, 2025, 151(2): 04024101.

[28]

JIANG Zhibin, GU Jinjing, FAN Wei, et al. Q-learning approach to coordinated optimization of passenger inflow control with train skip-stopping on a urban rail transit line[J]. Computers & industrial engineering, 2019, 127: 1131-1142.

[29]

杨安安, 汪波, 陈绍宽, 等. 基于客流直达的城市轨道交通跨站停开行方案优化研究[J]. 都市快轨交通, 2022, 35(2): 91-98. YANG An'an, WANG Bo, CHEN Shaokuan, et al. Train planning optimization for skip stop operation without transfers in urban rail transit[J]. Urban rapid rail transit, 2022, 35(2): 91-98.

[30]

游婷, 马法运, 苗峰, 等. 城市轨道交通虚拟编组列车优化运行方案研究[J]. 都市快轨交通, 2023, 36(1): 36-42. YOU Ting, MA Fayun, MIAO Feng, et al. Optimal operation plan design for virtually coupled trains in urban rail transit[J]. Urban rapid rail transit, 2023, 36(1): 36-42.

[31]

黄静仪, 张琦. 基于虚拟编组技术的城市轨道交通列车延误跳停调整研究[J]. 铁道运输与经济, 2024, 46(2): 151-158. HUANG Jingyi, ZHANG Qi. Research on train delay skip-stop adjustment in urban rail transit based on virtual coupling technology[J]. Railway transport and economy, 2024, 46(2): 151-158.

[32]

YUAN Fuya, SUN Huijun, KANG Liujiang, et al. An integrated optimization approach for passenger flow control strategy and metro train scheduling considering skip-stop patterns in special situations[J]. Applied mathematical modelling, 2023, 118: 412-436.

[33]

YIN Jiateng, YANG Lixing, TANG Tao, et al. Dynamic passenger demand oriented metro train scheduling with energy-efficiency and waiting time minimization: Mixed-integer linear programming approaches[J]. Transportation research part B: methodological, 2017, 97: 182-213.

[34]

Gong C, Shi J, Wang, Y, et al. Train timetabling with dynamic and random passenger demand: A stochastic optimization method[J]. Transportation research part C: emerging technologies, 123.

[35]

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 transit considering dynamic passenger demand and full-length & short-turn routing modes[J]. China railway science, 2018, 39(2): 128-136.

[36]

WANG Yihui, ZHU Songwei, D'ARIANO A, et al. Energy-efficient timetabling and rolling stock circulation planning based on automatic train operation levels for metro lines[J]. Transportation research part C: emerging technologies, 2021, 129: 103209.

[37]

李宪, 王伟鹏, 王巍, 等. 城市轨道交通夜间正线停车运营组织方案研究[J]. 现代城市轨道交通, 2025(1): 110-113. LI Xian, WANG Weipeng, WANG Wei, et al. Research on the operation organization scheme for main line parking at night of urban rail transit[J]. Modern urban transit, 2025(1): 110-113.

[38]

田佩宁, 毛保华, 周琪, 等. 城市轨道交通不成对开行方案研究[J]. 深圳大学学报(理工版), 2023, 40(5): 521-528. TIAN Peining, MAO Baohua, ZHOU Qi, et al. The unpaired operation of urban rail transit[J]. Journal of Shenzhen University (Science and Engineering), 2023, 40(5): 521-528.

[39]

ZHU Yuting, MAO Baohua, BAI Yun, et al. A bi-level model for single-line rail timetable design with consideration of demand and capacity[J]. Transportation research part C: emerging technologies, 2017, 85: 211-233.

[40]

YIN Jiateng, D'ARIANO A, WANG Yihui, et al. Timetable coordination in a rail transit network with time-dependent passenger demand[J]. European journal of operational research, 2021, 295(1): 183-202.

[41]

WANG Miao, CHEN Xing, YIN Jiateng, et al. A bi-objective optimization model for coordinated train timetabling in rail transit networks[C]//2021 IEEE International Intelligent Transportation Systems Conference (ITSC). Indianapolis, IN, USA. IEEE, 2021: 2350-2355.

[42]

陈磊, 段晓宇, 柏赟. 城市轨道交通跨线列车开行方案优化研究[J]. 都市快轨交通, 2023, 36(3): 59-64. CHEN Lei, DUAN Xiaoyu, BAI Yun. Optimizing crossline train service planning in urban rail transit network[J]. Urban rapid rail transit, 2023, 36(3): 59-64.

[43]

杨冀琴, 田秦, 徐占东, 等. 城市轨道交通网络首班车时段时刻表优化研究[J]. 重庆交通大学学报(自然科学版), 2021, 40(8): 50-56. YANG Jiqin, TIAN Qin, XU Zhandong, et al. Optimizing timetable for urban rail transit network during the first train time period[J]. Journal of Chongqing Jiaotong University (Natural Science), 2021, 40(8): 50-56.

[44]

YANG Lixing, DI Zhen, DESSOUKY M M, et al. Collaborative optimization of last-train timetables with accessibility: a space-time network design based approach[J]. Transportation research part C: emerging technologies, 2020, 114: 572-597.

[45]

李思杰, 徐瑞华, 杨儒冬. 基于运力协调的城市轨道交通网络列车运行计划优化[J]. 东南大学学报(自然科学版), 2017, 47(5): 1048-1054. LI Sijie, XU Ruihua, YANG Rudong. Optimizing urban rail transit network operation plans based on transport capacity coordination[J]. Journal of Southeast University (Natural Science Edition), 2017, 47(5): 1048-1054.

[46]

ZHOU Yu, WANG Yun, YANG Hai, et al. Last train scheduling for maximizing passenger destination reachability in urban rail transit networks[J]. Transportation research part B: methodological, 2019, 129: 79-95.

[47]

WANG Yizhen, LI Dewei, CAO Zhichao. Integrated timetable synchronization optimization with capacity constraint under time-dependent demand for a rail transit network[J]. Computers & industrial engineering, 2020, 142: 106374.

[48]

黄俊生, 陈垚, 张安英, 等. 考虑互联互通的城市轨道交通网络列车开行方案优化[J]. 铁道科学与工程学报, 2023, 20(5): 1587-1597. HUANG Junsheng, CHEN Yao, ZHANG Anying, et al. Optimization of urban rail network operation scheme considering interconnection[J]. Journal of railway science and engineering, 2023, 20(5): 1587-1597.

[49]

袁也, 徐皓, 王悉, 等. 基于量子计算的城市轨道交通网络末班车衔接优化[J]. 都市快轨交通, 2024, 37(2): 139-145. YUAN Ye, XU Hao, WANG Xi, et al. Quantum computing-based optimization for the last-train connection planning problem in urban rail transit networks[J]. Urban rapid rail transit, 2024, 37(2): 139-145.

[50]

GAO Yuan, KROON L, SCHMIDT M, et al. Rescheduling a metro line in an over-crowded situation after disruptions[J]. Transportation research part B: methodological, 2016, 93: 425-449.

[51]

黄柒光, 李建全. 基于实时客流的城市轨道交通列车自动调整方法[J]. 铁道运输与经济, 2021, 43(5): 130-134. HUANG Qiguang, LI Jianquan. Design and implementation of automatic train adjustment based on real-time passenger flow in urban rail transit[J]. Railway transport and economy, 2021, 43(5): 130-134.

[52]

BEŠINOVIĆ N, WANG Yihui, ZHU Songwei, et al. A matheuristic for the integrated disruption management of traffic, passengers and stations in urban railway lines[J]. IEEE transactions on intelligent transportation systems, 2022, 23(8): 10380-10394.

[53]

彭其渊, 江山, 刘思源, 等. 多干扰下地铁列车运行与车底周转一体化调整优化[J]. 交通运输系统工程与信息, 2024, 24(6): 113-125. PENG Qiyuan, JIANG Shan, LIU Siyuan, et al. Integrated metro train timetabling and rolling stock rescheduling under multi-disturbances[J]. Journal of transportation systems engineering and information technology, 2024, 24(6): 113-125.

[54]

WEN Longhui, HU Liyang, ZHOU Wei, et al. Soft actor-critic deep reinforcement learning for train timetable collaborative optimization of large-scale urban rail transit network under dynamic demand[J]. IEEE transactions on intelligent transportation systems, 2025, 26(5): 7021-7035.

[55]

茧敏, 陈绍宽, 王卓, 等. 城市轨道交通网络跨线列车开行方案优化模型研究[J]. 交通运输系统工程与信息, 2024, 24(5): 116-127. JIAN Min, CHEN Shaokuan, WANG Zhuo, et al. Cross-line train service plan optimization in urban rail transit network[J]. Journal of transportation systems engineering and information technology, 2024, 24(5): 116-127.

[56]

邓连波, 谢子若, 甘书怀, 等. 城市轨道交通乘务交路方案编制的禁忌搜索优化方法[J]. 北京交通大学学报, 2024, 48(4): 164-171. DENG Lianbo, XIE Ziruo, GAN Shuhuai, et al. Optimization method of Tabu Search algorithm for urban rail transit crew scheduling scheme[J]. Journal of Beijing Jiaotong University, 2024, 48(4): 164-171.

[57]

谭丽, 韦子文. 基于CCLPSO算法的Y型交路列车开行方案优化研究[J]. 铁道科学与工程学报, 2019, 16(8): 2122-2129. TAN Li, WEI Ziwen. Optimization research of train schedule of Y-type train routing mode based on CCLPSO algorithm[J]. Journal of railway science and engineering, 2019, 16(8): 2122-2129.

[58]

陈维亚, 章雍, 陈鑫, 等. 城市轨道交通大小交路开行方案与多站联合限流协同优化研究[J]. 交通运输系统工程与信息, 2019, 19(5): 177-184. CHEN Weiya, ZHANG Yong, CHEN Xin, et al. Collaborative full-length and short-turning plan and joint multistation control of passenger flow in urban rail transit[J]. Journal of transportation systems engineering and information technology, 2019, 19(5): 177-184.

[59]

DI Zhen, YANG Lixing, SHI Jungang, et al. Joint optimization of carriage arrangement and flow control in a metro-based underground logistics system[J]. Transportation research part B: methodological, 2022, 159: 1-23.

[60]

SHI Jungang, YANG Jing, YANG Lixing, et al. Safety-oriented train timetabling and stop planning with timevarying and elastic demand on overcrowded commuter metro lines[J]. Transportation research part E: logistics and transportation review, 2023, 175: 103136.

[61]

彭其渊, 刘思源, 江山, 等. 贯通运营下市域铁路与地铁列车开行方案协同优化[J]. 交通运输系统工程与信息, 2025, 25(2): 36-47. PENG Qiyuan, LIU Siyuan, JIANG Shan, et al. Collaborative optimization of suburban railway and metro train operation plans under interconnection operational mode[J]. Journal of transportation systems engineering and information technology, 2025, 25(2): 36-47.

2025年第38卷第5期

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文章信息

doi: 10.3969/j.issn.1672-6073.2025.05.004

接收时间：2025-02-24
首发时间：2026-10-19
出版时间：2025-10-10

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出版历史

收稿日期：2025-02-24
修回日期：2025-07-15

基金

国家重点研发计划项目(2022YFB4300500)

国家自然科学基金青年基金项目(72201218)

四川省科技计划资助(2023NSFSC0901)

作者信息

^1.西南交通大学交通运输与物流学院，成都　611756

^2.西南交通大学综合交通运输智能化国家地方联合工程实验室，成都　611756

^3.西南交通大学综合交通大数据应用技术国家工程实验室，成都　611756

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https://castjournals.cast.org.cn/joweb/dskgjt/CN/10.3969/j.issn.1672-6073.2025.05.004

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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 Percentage of total species (%)
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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