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基于动态罚函数的铁路车流分配与径路优化模型

薛锋 刘泳博 户佐安 陈逸飞

薛锋, 刘泳博, 户佐安, 陈逸飞. 基于动态罚函数的铁路车流分配与径路优化模型[J]. 西南交通大学学报, 2022, 57(5): 941-948, 959. doi: 10.3969/j.issn.0258-2724.20210226
引用本文: 薛锋, 刘泳博, 户佐安, 陈逸飞. 基于动态罚函数的铁路车流分配与径路优化模型[J]. 西南交通大学学报, 2022, 57(5): 941-948, 959. doi: 10.3969/j.issn.0258-2724.20210226
XUE Feng, LIU Yongbo, HU Zuoan, CHEN Yifei. Railcar Traffic Distribution and Route Optimization Model Based on Dynamic Penalty Function[J]. Journal of Southwest Jiaotong University, 2022, 57(5): 941-948, 959. doi: 10.3969/j.issn.0258-2724.20210226
Citation: XUE Feng, LIU Yongbo, HU Zuoan, CHEN Yifei. Railcar Traffic Distribution and Route Optimization Model Based on Dynamic Penalty Function[J]. Journal of Southwest Jiaotong University, 2022, 57(5): 941-948, 959. doi: 10.3969/j.issn.0258-2724.20210226

基于动态罚函数的铁路车流分配与径路优化模型

doi: 10.3969/j.issn.0258-2724.20210226
基金项目: 国家自然科学基金(61203175);四川省自然科学基金(2022NSFSC0471);四川省科技计划(2021YJ0067,2021YJ0077)
详细信息
    作者简介:

    薛锋(1981— ),男,副教授,博士,研究方向为运输组织理论与系统优化,E-mail:xuefeng.7@163.com

    通讯作者:

    户佐安(1979— ),男,副教授,博士,研究方向为运输组织理论与系统优化,E-mail:huzuoan@swjtu.edu.cn

  • 中图分类号: U292.3

Railcar Traffic Distribution and Route Optimization Model Based on Dynamic Penalty Function

  • 摘要:

    为解决铁路车流分配与径路优化模型中的难约束问题,避免群智能算法在应对该问题时难以求解的不足,提出了一种基于惩罚函数的约束优化方法. 首先,在车流分配及径路优化基本模型的基础上设置虚拟弧,在目标函数中增加惩罚项的方式松弛掉模型中的弧段能力约束,同时对惩罚项中的惩罚力度和惩罚因子设计动态更新的策略;然后,将改进灰狼算法(improved grey wolf algorithm,IGWO)应用于车流分配与径路优化模型的求解;最后,结合某一地区的路网数据,对改进前、后的模型和算法进行对比分析. 算例结果表明:与改进前的模型相比,引入惩罚项之后,IGWO可以在限定的范围内找到满足弧段能力约束的可行解;与灰狼算法(gray wolf algorithm,GWO)相比,IGWO计算所得的配流方案使OD (origin-destination)货流的平均绕行率和货物总走行公里数分别下降了2.6%和5.2%.

     

  • 图 1  简化路网

    Figure 1.  Simplified railway network

    图 2  两种方式下初始种群的分布

    Figure 2.  Distribution of initial population in two modes

    图 3  编码操作

    Figure 3.  Encoding operation

    图 4  IGWO在求解模型Q的流程

    Figure 4.  Flowchart of IGWO solving model Q

    图 5  某区域简化路网

    Figure 5.  Simplified railway network of a certain area

    图 6  GWO和IGWO的求解示意

    Figure 6.  Solution illustration of GWO and IGWO

    表  1  路网相关参数

    Table  1.   Railway network parameters

    弧段里程/km线路容量/
    ( × 104 车)
    弧段里程/km线路容量/
    ( × 104 车)
    (1,2)210300(6,10)246300
    (1,4)265300(6,11)280300
    (2,3)232300(9,12)503300
    (2,6)123300(10,11)130300
    (3,9)480380(10,13)115300
    (4,5)109300(11,12)336300
    (4,7)190300(11,14)218300
    (5,6)172300(13,14)158300
    (5,8)149380(7,8)117380
    (6,9)368380(8,10)220400
    下载: 导出CSV

    表  2  年车流OD量

    Table  2.   Annual OD volume of cargo flow

    发站到站年 OD 量/
    (× 104 车)
    发站到站年 OD 量/
    ( × 104 车)
    375531152
    793510340
    7145021250
    127454945
    896411446
    8125251370
    186051268
    1144014562
    1215031350
    386510145
    下载: 导出CSV

    表  3  车流径路的优化方案

    Table  3.   Optimization scheme of cargo flow route

    发站到站优化后的车流径路
    3 7 3→2→1→4→5→8→7
    7 9 7→8→5→6→2→3→9
    7 14 7→8→10→13→14
    12 7 12→11→6→2→1→4→7
    8 9 8→5→4→1→2→6→9
    8 12 8→5→6→9→12
    1 8 1→4→7→8
    1 14 1→4→5→8→10→13→14
    12 1 12→9→3→2→1
    3 8 3→9→6→10→8
    3 11 3→9→6→10→11
    10 3 10→6→2→3
    2 12 2→6→11→12
    4 9 4→7→8→10→6→9
    11 4 11→14→13→10→8→7→4
    5 13 5→8→10→11→14→13
    5 12 5→8→10→13→14→11→12
    14 5 14→11→6→5
    3 13 3→9→6→11→10→13
    10 1 10→6→2→1
    下载: 导出CSV

    表  4  区间通过流量统计

    Table  4.   Interval traffic statistics

    弧段 区间车流量/( × 104 车)线路利用率/%
    (1,2)25686.33
    (1,4)26488.00
    (2,3)18060.00
    (2,6)27993.00
    (3,9)25266.32
    (4,5)11939.67
    (4,7)23678.67
    (5,6)14949.67
    (5,8)34490.53
    (6,9)32886.31
    (6,10)24782.33
    (6,11)20769.00
    (9,12)10234.00
    (10,11)17257.33
    (0,13)25484.67
    (11,12)16354.33
    (11,14)24682.00
    (13,14)27491.33
    (7,8)33187.11
    (8,10)38496.00
    下载: 导出CSV

    表  5  改进前后模型的车流总走行公里

    Table  5.   Cargo flow kilometers before and after improving model

    模型算法 车流总走行数/
    (车 • km)
    模型 PGWO无法在限定范围内找
    到可行解
    IGWO
    模型 QGWO1132405
    IGWO1073973
    下载: 导出CSV

    表  6  两种算法的质量指标

    Table  6.   Quality metrics for two algorithms

    算法平均绕
    行率
    选择最短路径的
    OD 数/个
    车流总走行数/
    (车 • km)
    GWO1.5531132405
    IGWO1.5161073973
    下载: 导出CSV
  • [1] 纪丽君,林柏梁,乔国会,等. 基于多商品流模型的铁路网车流分配和径路优化模型[J]. 中国铁道科学,2011,32(3): 107-110.

    JI Lijun, LIN Boliang, QIAO Guohui, et al. Car flow assignment and routing optimization model of railway network based on multi-commodity flow model[J]. China Railway Science, 2011, 32(3): 107-110.
    [2] 温旭红,林柏梁,王龙,等. 基于多商品网络流理论的铁路车流分配及径路优化模型[J]. 北京交通大学学报,2013,37(3): 117-121. doi: 10.3969/j.issn.1673-0291.2013.03.022

    WEN Xuhong, LIN Boliang, WANG Long, et al. Optimization model for railway car flow assignment and routing plan based on multi-commodity network flow theory[J]. Journal of Beijing Jiaotong University, 2013, 37(3): 117-121. doi: 10.3969/j.issn.1673-0291.2013.03.022
    [3] 温旭红,林柏梁,陈雷. 基于树形结构的铁路车流径路优化模型[J]. 铁道学报,2016,38(4): 1-6. doi: 10.3969/j.issn.1001-8360.2016.04.001

    WEN Xuhong, LIN Boliang, CHEN Lei. Optimization model of railway vehicle flow routing based on tree form[J]. Journal of the China Railway Society, 2016, 38(4): 1-6. doi: 10.3969/j.issn.1001-8360.2016.04.001
    [4] 严余松,户佐安,李宵寅. 基于车流量波动的列车编组计划与车流径路综合优化[J]. 交通运输系统工程与信息,2017,17(4): 124-131. doi: 10.16097/j.cnki.1009-6744.2017.04.019

    YAN Yusong, HU Zuoan, LI Xiaoyin. Comprehensive optimization of train formation plan and wagon-flow path based on fluctuating wagon-flow[J]. Journal of Transportation Systems Engineering and Information Technology, 2017, 17(4): 124-131. doi: 10.16097/j.cnki.1009-6744.2017.04.019
    [5] 王文宪,柏伟,邓鹏. 考虑换重条件的重载直达车流组织研究[J]. 交通运输工程与信息学报,2013,11(1): 68-73. doi: 10.3969/j.issn.1672-4747.2013.01.013

    WANG Wenxian, BAI Wei, DENG Peng. Study on optimized organization scheme for through heavy haul trains based on changing-for-weight[J]. Journal of Transportation Engineering and Information, 2013, 11(1): 68-73. doi: 10.3969/j.issn.1672-4747.2013.01.013
    [6] UPADHYAY A, BOLIA N. Combined empty and loaded train scheduling for dedicated freight railway corridors[J]. Computers & Industrial Engineering, 2014, 76: 23-31.
    [7] BORNDÖRFER R, KLUG T, SCHLECHTE T, et al. The freight train routing problem for congested railway networks with mixed traffic[J]. Transportation Science, 2016, 50(2): 408-423. doi: 10.1287/trsc.2015.0656
    [8] YAGHINI M, MOMENI M, SARMADI M. An improved local branching approach for train formation planning[J]. Applied Mathematical Modelling, 2013, 37(4): 2300-2307. doi: 10.1016/j.apm.2012.05.016
    [9] KHALED A A, JIN M Z, CLARKE D B, et al. Train design and routing optimization for evaluating criticality of freight railroad infrastructures[J]. Transportation Research Part B:Methodological, 2015, 71: 71-84. doi: 10.1016/j.trb.2014.10.002
    [10] 温旭红. 铁路车流分配优化模型与拉格朗日松弛算法求解研究[D]. 北京: 北京交通大学, 2016.
    [11] MIRJALILI S, MIRJALILI S M, LEWIS A. Grey wolf optimizer[J]. Advances in Engineering Software, 2014, 69: 46-61. doi: 10.1016/j.advengsoft.2013.12.007
    [12] FARIS H, ALJARAH I, AL-BETAR M A, et al. Grey wolf optimizer:a review of recent variants and applications[J]. Neural Computing and Applications, 2018, 30(2): 413-435. doi: 10.1007/s00521-017-3272-5
    [13] ZHU E D, CRAINIC T G, GENDREAU M. Scheduled service network design for freight rail transportation[J]. Operations Research, 2014, 62(2): 383-400. doi: 10.1287/opre.2013.1254
    [14] 黄戈文,蔡延光,戚远航,等. 自适应遗传灰狼优化算法求解带容量约束的车辆路径问题[J]. 电子学报,2019,47(12): 2602-2610.

    HUANG Gewen, CAI Yanguang, QI Yuanhang, et al. Adaptive genetic grey wolf optimizer algorithm for capacitated vehicle routing problem[J]. Acta Electronica Sinica, 2019, 47(12): 2602-2610.
    [15] WANG C Y, MA C, ZHOU J C. A new class of exact penalty functions and penalty algorithms[J]. Journal of Global Optimization, 2014, 58(1): 51-73. doi: 10.1007/s10898-013-0111-9
    [16] 甘敏,彭辉. 一种新的自适应惩罚函数算法求解约束优化问题[J]. 信息与控制,2009,38(1): 24-28. doi: 10.3969/j.issn.1002-0411.2009.01.004

    GAN Min, PENG Hui. A new adaptive penalty function based algorithm for solving constrained optimization problems[J]. Information and Control, 2009, 38(1): 24-28. doi: 10.3969/j.issn.1002-0411.2009.01.004
    [17] 吴亮红,王耀南,周少武,等. 采用非固定多段映射罚函数的非线性约束优化差分进化算法[J]. 系统工程理论与实践,2007,27(3): 128-133,160. doi: 10.3321/j.issn:1000-6788.2007.03.019

    WU Lianghong, WANG Yaonan, ZHOU Shaowu, et al. Differential evolution for nonlinear constrained optimization using non-stationary multi-stage assignment penalty function[J]. Systems Engineering—Theory & Practice, 2007, 27(3): 128-133,160. doi: 10.3321/j.issn:1000-6788.2007.03.019
    [18] 肖赤心,蔡自兴,王勇,等. 一种基于佳点集原理的约束优化进化算法[J]. 控制与决策,2009,24(2): 249-253,258. doi: 10.3321/j.issn:1001-0920.2009.02.018

    XIAO Chixin, CAI Zixing, WANG Yong, et al. Constrained optimization evolutionary algorithm based on good lattice points principle[J]. Control and Decision, 2009, 24(2): 249-253,258. doi: 10.3321/j.issn:1001-0920.2009.02.018
    [19] 张文胜,郝孜奇,朱冀军,等. 基于改进灰狼算法优化BP神经网络的短时交通流预测模型[J]. 交通运输系统工程与信息,2020,20(2): 196-203. doi: 10.16097/j.cnki.1009-6744.2020.02.029

    ZHANG Wensheng, HAO Ziqi, ZHU Jijun, et al. BP neural network model for short-time traffic flow forecasting based on transformed grey wolf optimizer algorithm[J]. Journal of Transportation Systems Engineering and Information Technology, 2020, 20(2): 196-203. doi: 10.16097/j.cnki.1009-6744.2020.02.029
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出版历程
  • 收稿日期:  2021-03-29
  • 修回日期:  2021-12-13
  • 网络出版日期:  2022-08-02
  • 刊出日期:  2021-12-16

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