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考虑有限理性和公平性的危险品运输网络优化

张宏刚 王伟 潘敏荣 刘志远

张宏刚, 王伟, 潘敏荣, 刘志远. 考虑有限理性和公平性的危险品运输网络优化[J]. 交通信息与安全, 2022, 40(4): 38-45. doi: 10.3963/j.jssn.1674-4861.2022.04.004
引用本文: 张宏刚, 王伟, 潘敏荣, 刘志远. 考虑有限理性和公平性的危险品运输网络优化[J]. 交通信息与安全, 2022, 40(4): 38-45. doi: 10.3963/j.jssn.1674-4861.2022.04.004
ZHANG Honggang, WANG Wei, PAN Minrong, LIU Zhiyuan. Optimization of the Transportation Network of Hazardous Materials Considering Bounded Rationality and Equity[J]. Journal of Transport Information and Safety, 2022, 40(4): 38-45. doi: 10.3963/j.jssn.1674-4861.2022.04.004
Citation: ZHANG Honggang, WANG Wei, PAN Minrong, LIU Zhiyuan. Optimization of the Transportation Network of Hazardous Materials Considering Bounded Rationality and Equity[J]. Journal of Transport Information and Safety, 2022, 40(4): 38-45. doi: 10.3963/j.jssn.1674-4861.2022.04.004

考虑有限理性和公平性的危险品运输网络优化

doi: 10.3963/j.jssn.1674-4861.2022.04.004
基金项目: 

国家自然科学基金重点项目 52131203

国家优秀青年科学基金项目 71922007

详细信息
    作者简介:

    张宏刚(1994—),博士研究生. 研究方向:危险品运输管理、多模式物流网络优化. E-mail:zhang_honggang@seu.edu.cn

    通讯作者:

    刘志远(1984—),博士,教授. 研究方向:多模式物流网络优化等. E-mail:leakeliu@163.com

  • 中图分类号: U492

Optimization of the Transportation Network of Hazardous Materials Considering Bounded Rationality and Equity

  • 摘要: 针对含有风险控制的危险品运输网络优化问题,讨论了运输商的有限理性路径选择行为对运输风险的影响。基于鲁棒优化的方法构建了双层规划模型,通过增加各路段最大风险值的上界约束来实现不同路段之间运输风险分布的公平性,上层规划表示政府部门通过关闭部分路段来最小化最大运输网络总风险、路段最大风险的上界值以及路段关闭总数;下层规划表示有限理性的运输商在考虑感知偏差的情形下选择总成本最小的运输路径。考虑到传统启发式算法容易陷入局部最优解,通过重新定义上下层问题,设计了割平面算法求解该模型,并给出了算例分析。结果表明:虽然有限理性运输商的总成本增加了3.5%,但危险品运输网络的最大总风险下降了约8.4%;通过改变政府部门对各目标的关注度,可以影响有限理性运输商的路径选择行为,使得方差系数和基尼系数分别下降了约36.1%和26.2%,实现了不同路段之间风险分布的公平性目标;在实施车辆限行策略的情形下,针对有限理性运输商的感知偏差进行灵敏度分析,发现运输网络最大总风险的最小值不会改变,但会对路段关闭总数产生影响。在考虑运输商为有限理性决策者的情形下,可为政府部门设计更加符合实际情况的危险品运输网络,从而有效降低运输风险。

     

  • 图  1  危险品运输网络优化模型

    Figure  1.  The model of hazmat transportation network optimization

    图  2  危险品运输网络

    Figure  2.  Hazmat transportation network

    图  3  优化前各流向的可行路径

    Figure  3.  The feasible paths for each shipment before optimization

    图  4  公平性约束有无情况下不同λ取值时的方差系数和基尼系数

    Figure  4.  The coefficient of variance and Gini coefficient at different values of λ with and without fairness constraint

    图  5  不同权重取值时,k取值对优化前后最大总风险的最小值和路段关闭数量的影响

    Figure  5.  Effect of k on the minimum value of the maximum total risk and the number of link closures before and after optimization at different weights

    表  1  符号说明

    Table  1.   Thesymbol table

    符号 说明
    i, j, p, q 运输网络G中的节点,i, j, p, qN
    (i, j), (p, q) 运输网络G中的路段,(i, j)∈ A, (p, q)∈ A
    n 运输网络的总路段数
    S 危险品的所有流向
    s s种流向,由运输的起点和终点决定,且sS
    Os s种流向的起点
    Ds s种流向的终点
    Rij, Rpq 各路段的运输风险值
    R 运输网络的总风险值
    R 路段最大总风险的均值,即R = maxR/n
    γ 方差系数
    ω 基尼系数
    θ 各路段上最大风险的上界值
    ρij 路段(ij)沿线的人口密度
    ds s种流向所需车辆数,辆
    α 关闭的总路段数量对于运输风险的转换系数
    ζs 运输商对于第s种流向上产生的运输成本的感知偏差集合
    λ 最大总风险在上层规划中的权重λ ∈ [0, 1]
    yij 0-1决策变量,当政府决定开放路段(ij)时取值为1,否则,取值为0
    aijs 对于第s种流向,当运输商选择路段(ij)时取值为1,否则,取值为0
    εs 运输商对于第s种流向上产生的运输成本的感知偏差
    下载: 导出CSV

    表  2  路段运输成本和沿线人口密度

    Table  2.   Travel costof each link and population density along the line

    路段 运输成本(cij) 人口密度ρij /(人/km2
    1-5 50 100
    4-5 70 150
    5-9 35 112
    4-9 85 238
    1-12 38 115
    5-6 40 198
    12-6 55 130
    6-7 36 110
    7-11 40 129
    8-2 32 115
    6-10 56 137
    9-10 58 148
    10-11 45 123
    9-13 60 232
    13-3 86 211
    11-3 42 156
    12-8 38 178
    7-8 46 108
    11-2 30 103
    下载: 导出CSV

    表  3  危险品运输网络的优化结果(λ = 0, 0.2, 0.4, 0.6)

    Table  3.   Optimization results of hazmat transportation network (λ = 0, 0.2, 0.4, 0.6)

    路段(i, j) 决策变量yij 路段(i, j) 决策变量yij
    1-12 1 12-8 1
    1-5 1 12-6 1
    4-5 1 6-7 1
    4-9 1 6-10 1
    5-9 1 10-11 1
    5-6 0 7-8 1
    9-10 1 7-11 1
    9-13 1 8-2 1
    13-3 0 11-2 1
    11-3 1
    下载: 导出CSV

    表  4  危险品运输网络的优化结果(λ = 0.8)

    Table  4.   Optimization results of hazmat transportation network (λ = 0.8)

    路段(i, j) 决策变量yij 路段(i, j) 决策变量 yij
    1-12 1 12-8 1
    1-5 1 12-6 1
    4-5 1 6-7 1
    4-9 1 6-10 1
    5-9 0 10-11 1
    5-6 0 7-8 1
    9-10 1 7-11 1
    9-13 1 8-2 1
    13-3 1 11-2 1
    11-3 1
    下载: 导出CSV

    表  5  危险品运输网络的优化结果(λ = 1.0)

    Table  5.   Optimization results of hazmat transportation network (λ = 1.0)

    路段(i, j) 决策变量yij 路段(i, j) 决策变量yij
    1-12 1 12-8 1
    1-5 1 12-6 0
    4-5 0 6-7 1
    4-9 1 6-10 1
    5-9 1 10-11 1
    5-6 0 7-8 1
    9-10 1 7-11 1
    9-13 0 8-2 1
    13-3 1 11-2 1
    11-3 1
    下载: 导出CSV

    表  6  不同权重取值时,优化后各流向的可行路径

    Table  6.   The feasible paths for each shipment after optimization at different weights

    权重 ds 可行路径 总风险 总成本
    λ = 0, 0.2, 0.4, 0.6 d1 = 2 1-12-6-7-11-3 1 280 422
    1-5-9-10-11-3 1 278 460
    d2 = 3 4-9-10-11-2 1 836 654
    4-5-9-10-11-2 1 908 714
    λ = 0.8 d1=2 1-12-6-7-11-3 1 280 422
    d2 = 3 4-9-10-11-2 1 836 654
    λ = 1.0 d1=2 1-5-9-10-11-3 1 278 460
    d2 =3 4-9-10-11-2 1 836 654
    下载: 导出CSV
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  • 收稿日期:  2022-03-29
  • 网络出版日期:  2022-09-17

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