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受约束的过道布置问题建模及优化方法

刘俊琦 张则强 龚举华 张裕

刘俊琦, 张则强, 龚举华, 张裕. 受约束的过道布置问题建模及优化方法[J]. 西南交通大学学报, 2022, 57(6): 1376-1385. doi: 10.3969/j.issn.0258-2724.20200803
引用本文: 刘俊琦, 张则强, 龚举华, 张裕. 受约束的过道布置问题建模及优化方法[J]. 西南交通大学学报, 2022, 57(6): 1376-1385. doi: 10.3969/j.issn.0258-2724.20200803
LIU Junqi, ZHANG Zeqiang, GONG Juhua, ZHANG Yu. Modeling and Optimization Method of Constrained Corridor Allocation Problem[J]. Journal of Southwest Jiaotong University, 2022, 57(6): 1376-1385. doi: 10.3969/j.issn.0258-2724.20200803
Citation: LIU Junqi, ZHANG Zeqiang, GONG Juhua, ZHANG Yu. Modeling and Optimization Method of Constrained Corridor Allocation Problem[J]. Journal of Southwest Jiaotong University, 2022, 57(6): 1376-1385. doi: 10.3969/j.issn.0258-2724.20200803

受约束的过道布置问题建模及优化方法

doi: 10.3969/j.issn.0258-2724.20200803
基金项目: 国家自然科学基金(51205328,51675450);教育部人文社会科学研究青年基金(18YJC630255);四川省科技计划(2022YFG0245)
详细信息
    作者简介:

    刘俊琦(1995—),男,博士研究生,研究方向为设施布局与智能优化,E-mail:junqi5497@163.com

    通讯作者:

    张则强(1978—),男,教授,研究方向为制造系统与智能优化,E-mail:zzq_22@163.com

  • 中图分类号: TH165;TP301.6

Modeling and Optimization Method of Constrained Corridor Allocation Problem

  • 摘要:

    为了研究过道布置问题中设施关系对布局的影响,首先,考虑定位约束与排序约束,构建过道布置问题混合整数规划模型,并提出一种求解该问题的自适应混合克隆选择算法,在克隆操作之前新增符合受约束过道布置问题特性的2-opt操作,随后对所产生种群中最优个体进行禁忌搜索操作,对其他个体进行变异操作并设置自适应变异概率;然后,对模型进行精确求解以验证模型的正确性且求解结果为算法提供了理论依据;最后,应用所提算法分别对受约束过道布置问题与基本过道布置问题的42 ~ 49规模实例进行测试,并将求解结果与克隆选择算法、遗传算法、分散搜索算法、花授粉算法以及烟花算法进行对比,结果表明:混合克隆选择算法可以达到当前先进算法的求解效果且在算例sko-42-04与算例sko49-03上表现更优.

     

  • 图 1  过道布置问题距离计算方式

    Figure 1.  Distance calculation method of CAP

    图 2  基于两种约束的2-opt操作示意

    Figure 2.  Improved 2-opt operation diagram based on two kinds of constraints

    图 3  ACSATS 流程

    Figure 3.  Flow chart of ACSATS

    图 4  CSA与ACSATS在9~15规模下问题求解结果箱线图

    Figure 4.  Box-plot of the solution results of CSA and ACATS in the scale of 9−15

    表  1  参数名称与定义

    Table  1.   Parameter names and definition

    变量意义
    n  问题规模,即布置的设施数目
    I  所有设施的集合,I={1, 2, 3, …, n}
    i, j, h, k  设施编号,i, j, hI
    cij  设施 i 与设施 j 之间的物流成本,$\forall $i∈{1,2,…, n−1},$\forall $j∈ {1,2,…,n−1}
    dij  设施 i, j 之间物流交互点在 X 轴方向的距离
    li  设施 i 沿 X 轴边线的长度
    w  通道宽度
    αij  二进制变量,i, j 分配在同一行,且设施 i 被放置在设施 j 的左侧 αij= 1,否则 αij= 0
    qij  二进制决策变量,若设施 i 与设施 j 被布置于同一行,则 qij= 1,否则 qij= 0
    βhi  二进制决策变量,若设施 h 的物料搬运点在设施 i 的左侧,则 βhi= 1,否则 βhi= 0
    f  设施间的总物流成本
    下载: 导出CSV

    表  2  CSA与ACSATS算法求解CCAP与CAP的参数

    Table  2.   Algorithm parameters of CSA and ACSATS in solving CCAP and CAP

    问题算法nNItermax_1GαS/搜索次数/次
    CCAPACSATS9~152002000.01120200
    254006000.011.240400
    306008000.021.680800
    3680010000.021.680800
    CSA42~49100010000.021.6100800
    9~152002000.011
    9~152002000.010.820200
    CAPACSATS306008000.021.680600
    3680010000.021.680600
    42100010000.021.6100800
    49100012000.021.8110800
    下载: 导出CSV

    表  3  LINGO精确解与ACSATS算法的计算结果

    Table  3.   LINGO exact solution and solving results of ACSATS

    问题nLINGOACSATS
    F0t/sFmint/sgap1
    S991372.59001372.51.340
    S9H92946.59002946.51.420
    S10101642.59001642.51.770
    S11114812.59004268.52.06−11.30
    Am12 a122269.09001919.02.38−15.43
    Am12 b122400.59002101.52.45−12.46
    Am13 a133401.59002968.52.61−12.73
    Am13 b134291.09003439.03.11−19.86
    Am15155146.09003989.03.05−22.48
    N-25-05259008408.044.78
    ste-36-053690050210.5798.67
    sko-42-0542900125647.51355.99
    注:下划线表示LINGO与算法ACSATS的求解结果较优的一方.
    下载: 导出CSV

    表  4  CSA算法与ACSATS算法对CCAP的求解结果

    Table  4.   Solving results of CSA and ACSATS for CCAP

    问题CSAACSATS
    FCSA标准偏差FACSATS标准偏差
    S9 1372.5 6.49 1372.5 0
    S9H 2946.5 2.63 2946.5 0
    S10 1642.5 11.60 1642.5 0
    S11 4268.5 22.97 4268.5 0
    Am12 a 1919.0 9.51 1919.0 0
    Am12 b 2101.5 13.11 2101.5 0
    Am13 a 2968.5 15.40 2968.5 0
    Am13 b 3457.0 20.29 3439.0 10.68
    Am15 3989.0 37.57 3989.0 3.81
    下载: 导出CSV

    表  5  SS、GA、IDFPA、IFWA与ACSATS在42与49规模问题下测试CAP的求解结果

    Table  5.   Results of solving CAP with SS, GA, IDFPA, IFWA and ACSATS in 42 and 49 scale instances

    算例SS[4]GA[4]IDFPA[11]IFWA[9]ACSATS
    ft/sft/sft/sft/sft/s
    42-1 12731.0 1249.04 12731.0 7174.64 12731.0 279.37 12731.0 321.29 12731.0 322.38
    42-2 108020.5 1249.04 108049.5 6815.77 108006.5 681.43 108020.5 604.61 108006.5 489.94
    42-3 86667.5 956.28 86667.5 6854.25 86644.5 427.61 86655.5 621.45 86644.5 497.01
    42-4 68733.0 1141.34 68769.0 6509.35 68708.0 493.77 68722.0 867.15 68701.0 517.67
    42-5 124058.5 1236.47 124099.5 7052.59 124017.5 546.72 124017.5 554.07 124017.5 519.47
    49-1 20479.0 2683.93 20472.0 14934.38 20470.0 515.02 20470.0 542.13 20470.0 598.67
    49-2 208081.0 2733.87 208270.0 14338.86 208068.0 760.20 208078.0 1009.45 208068.0 1007.99
    49-3 162196.0 2877.19 162267.0 14351.91 162187.0 822.33 162187.0 1173.59 162183.0 1006.58
    49-4 118264.5 3716.16 118311.5 14290.03 118260.5 1809.86 118260.5 1193.88 118260.5 843.93
    49-5 332855.0 2596.39 332990.0 14913.18 332836.0 821.67 332811.0 989.91 332836.0 799.05
    下载: 导出CSV
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  • 收稿日期:  2020-12-01
  • 修回日期:  2021-03-22
  • 网络出版日期:  2022-08-13
  • 刊出日期:  2021-03-26

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