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具有总能耗约束的柔性作业车间调度问题研究

雷德明 杨冬婧

雷德明, 杨冬婧. 具有总能耗约束的柔性作业车间调度问题研究. 自动化学报, 2018, 44(11): 2083-2091. doi: 10.16383/j.aas.2018.c170345
引用本文: 雷德明, 杨冬婧. 具有总能耗约束的柔性作业车间调度问题研究. 自动化学报, 2018, 44(11): 2083-2091. doi: 10.16383/j.aas.2018.c170345
LEI De-Ming, YANG Dong-Jing. Research on Flexible Job Shop Scheduling Problem With Total Energy Consumption Constraint. ACTA AUTOMATICA SINICA, 2018, 44(11): 2083-2091. doi: 10.16383/j.aas.2018.c170345
Citation: LEI De-Ming, YANG Dong-Jing. Research on Flexible Job Shop Scheduling Problem With Total Energy Consumption Constraint. ACTA AUTOMATICA SINICA, 2018, 44(11): 2083-2091. doi: 10.16383/j.aas.2018.c170345

具有总能耗约束的柔性作业车间调度问题研究

doi: 10.16383/j.aas.2018.c170345
基金项目: 

国家自然科学基金 71471151

国家自然科学基金 61573264

数字制造装备与技术国家重点实验室开放课题 DMETKF2017015

详细信息
    作者简介:

    杨冬婧  武汉理工大学自动化学院硕士研究生.主要研究方向为制造系统智能优化与调度.E-mail:niceydj@163.com

    通讯作者:

    雷德明  武汉理工大学自动化学院教授.主要研究方向为智能系统优化与控制.本文通信作者.E-mail:deminglei11@163.com

Research on Flexible Job Shop Scheduling Problem With Total Energy Consumption Constraint

Funds: 

National Natural Science Foundation of China 71471151

National Natural Science Foundation of China 61573264

Open project of State Key Laboratory of Digital Manufacturing Equipment and Technology DMETKF2017015

More Information
    Author Bio:

     Master student at the School of Automation, Wuhan University of Technology. Her research interest covers maufacturing systems intelligent optimization and scheduling

    Corresponding author: LEI De-Ming  Professor at the School of Automation, Wuhan University of Technology. His research interest covers intelligent system optimization and control. Corresponding author of this paper
  • 摘要: 针对具有总能耗约束的柔性作业车间调度问题(Flexible job shop scheduling problem,FJSP),提出一种基于帝国竞争算法(Imperialist competitive algorithm,ICA)和变邻域搜索(Variable neighborhood search,VNS)的双阶段算法,该算法在总能耗不超过给定阈值的条件下最小化Makespan和总延迟时间.由于能耗约束不是总能满足且阈值往往难以事先给定,为此,第一阶段,首先,将原问题转化为具有Makespan、总延迟时间和总能耗的三目标FJSP,然后,利用初始帝国构建和帝国竞争的新策略设计一种ICA对问题求解,并根据ICA的结果确定总能耗阈值;第二阶段,应用解的比较新策略、非劣解集更新方法和当前解周期性更新,构建VNS对原问题求解.计算实验和结果分析表明,两阶段算法对于所研究的问题搜索能力强.
    1)  本文责任编委  鲁仁全
  • 表  1  $\delta $的设置

    Table  1  The setting on $\delta $

    $\delta $Instances$\delta $Instances
    $[0.5, 0.7]$MK01, MK03-05$[1.0, 1.5]$DP1-12
    $[0.3, 0.5]$MK02, 06, 08-10$[1.2, 1.6]$MK11-15
    $[0, 1, 0.3]$Ka4$\times $5, 10$\times $7, 15$\times $10$[0.7, 0.9]$MK07
    $[1.2, 1.7]$DP13-18$[0.05, 0.2]$Ka10$\times $10
    下载: 导出CSV

    表  2  阈值的确定

    Table  2  Decision on threshold

    所有$Q_i $大于$\bar {Q}$的$Q_i $剩余的$Q_i $
    216.7, 198.9, 227.3, 218.0230.2, 231.6231.6, 245.9
    230.2, 224.6, 231.6, 244.4244.4, 237.7237.7
    218.9, 208.2, 237.7, 221.4253.4, 245.9253.4
    223.1, 253.4, 245.9, 232.4232.4, 254.1232.4
    207.6, 254.1, 284.1, 216.4284.1284.1
    下载: 导出CSV

    表  3  总能耗阈值和三种算法的ATEC和MTEC

    Table  3  Total energy consumption threshold and ATEC and MTEC of three algorithms

    Instance$Q_{EC} $两阶段算法NSGA-ⅡVNS
    ATECMTECATEC MTECATEC MTEC
    Ka4$\times $5152.396.15495.25996.08095.25995.25995.259
    Ka10$\times $7245.9196.27185.41194.39193.26200.52193.50
    Ka10$\times $10159.5124.81121.26130.29128.24132.17124.26
    Ka15$\times $10443.3313.85302.87325.01321.45365.49354.56
    MK01682.4653.38650.79666.54664.84655.55654.41
    MK02550.7509.51496.17525.17519.14508.72506.36
    MK033 597314 8.63 128.23 311.53 291.13 278.43 235.5
    MK041 1911 083.41 064.41 097.51 078.41 086.41 074.9
    MK052 7482 628.12 619.82 588.02 578.72 648.42 631.6
    MK062 3492 162.82 145.92 189.42 168.52 127.02 106.3
    MK071 7281 504.21 486.01 567.61 561.11 524.61 517.7
    MK0810 1569 786.49 713.110 0049 976.49 747.89 747.8
    MK099 0828 627.08 604.98 996.08 961.38 622.38 572.3
    MK109 7288 537.18 536.28 991.68 955.69 022.78 972.6
    MK1112 89012 41512 27612 64012 57712 41712 353
    MK1214 93314 29114 22014 31414 14814 21414 109
    MK1314 20213 13113 10413 84513 76313 38213 310
    MK1416 98514 91614 85615 30715 23915 02014 981
    MK1517 00013 79313 65613 87713 78613 64313 612
    DP134 53433 82933 74534 11734 02633 90233 758
    DP240 33238 57438 39438 87438 81338 65438 512
    DP336 42835 27135 08635 70135 50435 36735 215
    DP436 88036 17135 65636 07735 74236 22536 089
    DP540 08538 81538 76639 42839 25238 88238 619
    DP637 09135 88235 72936 44536 16236 18535 897
    DP726 37360 66760 54261 03360 98960 70760 673
    DP852 42249 94849 87050 63850 62750 72250 527
    DP964 53962 39562 23263 45863 20263 28262 966
    DP1060 35058 58058 13359 24259 14559 27759 070
    DP1157 61355 54855 37356 33256 26056 11855 612
    DP1260 71158 02257 98159 28858 94758 26058 220
    DP1386 14284 38284 33585 04685 02785 20085 062
    DP1483 00080 94080 80382 33282 13581 88981 787
    DP1573 00070 97770 63172 03371 85471 80071 702
    DP1680 46878 79078 58479 97679 87879 41779 266
    DP1786 67784 88684 79885 96385 67585 39485 324
    DP1886 33084 11483 68584 95184 78585 04584 679
    下载: 导出CSV

    表  4  三种算法的计算结果

    Table  4  Computational results of three algorithms

    InstanceDIR$\rho _l $
    两阶段算法NSGA-ⅡVNS两阶段算法NSGA-ⅡVNS
    Ka4$\times $51.2350.8901.1250.3070.2220.370
    Ka10$\times $715.100.00020.650.0001.0000.000
    Ka10$\times $100.0040.340.0860.9690.0000.031
    Ka15$\times $100.2569.45635.880.8890.1110.000
    MK010.4466 1217.3050.6940.0000.306
    MK020.003 7319.326 1.0000.000.00
    MK030.00051.9030.71 1.0000.000.00
    MK042 7632 9301 6520.6000.1500.250
    MK053.11959.047.0240.6670.0000.333
    MK0618.1545.790.000.000.001.000
    MK070.00031.499.899 1.0000.000.00
    MK080.00025.0410.86 1.0000.000.00
    MK090.00049.7610.23 1.0000.000.00
    MK100.00038.2418.00 1.0000.000.00
    MK1113.423 2651 3250.5880.0000.412
    MK120.003 7011 542 1.0000.000.00
    MK130.00064.4032.30 1.0000.000.00
    MK140.00060.0423.99 1.0000.000.00
    MK150.29739.9919.860.9440.0000.056
    DP10.002 5281 324 1.0000.000.00
    DP27.50739.164.6630.5500.0000.45
    DP31.42437.625.6380.9150.0000.085
    DP41 4272 9117 3020.7500.0000.250
    DP55.86150.894.4520.5830.0000.417
    DP60.00052.1612.64 1.0000.000.00
    DP70.00033.5319.41 1.0000.000.00
    DP80.65242.320.470.9880.0000.012
    DP90.00066.4334.33 1.0000.000.00
    DP100.5434 83611.200.9500.0000.050
    DP110.00034.2114.03 1.0000.000.00
    DP122.59767.654.8140.6670.0000.333
    DP130.003 32620.31 1.0000.000.00
    DP140.25846.0812640.9810.0000.019
    DP150.00046.2019.04 1.0000.000.00
    DP160.00067.3444.41 1.0000.000.00
    DP170.00034.6916.09 1.0000.000.00
    DP180.00039.6421.59 1.0000.000.00
    下载: 导出CSV

    表  5  三种算法的计算时间

    Table  5  Comparisons on the computational times of three algorithms

    InstanceRunning time (s)InstanceRunning time (s)
    两阶段算法NSGA-ⅡVNS两阶段算法NSGA-ⅡVNS
    Ka4$\times $50.6880.6660.272DP110.7410.8513.03
    Ka10$\times $71.9013.3411.795DP212.9111.3514.52
    Ka10$\times $101.8793.3231.984DP311.5910.9614.67
    Ka15$\times $103.3394.3373.417DP411.8311.4911.76
    MK012.7914.0683.136DP511.2110.9411.73
    MK022.7994.0373.358DP610.8411.1811.47
    MK037.3517.5958.498DP718.3318.0919.68
    MK044.1105.1414.895DP818.2617.4619.84
    MK056.7405.3356.600DP917.0217.8018.79
    MK067.6546.0377.419DP1018.7317.8420.16
    MK075.2386.0725.325DP1117.5818.0219.78
    MK0814.1813.9815.31DP1217.7517.9219.82
    MK0912.5414.8414.87DP1331.5431.9428.87
    MK1012.5113.1614.82DP1430.2432.1427.82
    MK1112.2912.2712.39DP1529.4131.7028.97
    MK1212.8413.4414.93DP1631.7433.5627.42
    MK1313.2013.6215.08DP1731.1341.8428.07
    MK1416.6316.7718.95DP1829.3832.9628.71
    MK1516.1416.6018.65
    下载: 导出CSV
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出版历程
  • 收稿日期:  2017-06-22
  • 录用日期:  2017-09-07
  • 刊出日期:  2018-11-20

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