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基于问题性质的分布式低碳并行机调度算法研究

潘子肖 雷德明

潘子肖, 雷德明. 基于问题性质的分布式低碳并行机调度算法研究. 自动化学报, 2020, 46(11): 2427-2438 doi: 10.16383/j.aas.c180581
引用本文: 潘子肖, 雷德明. 基于问题性质的分布式低碳并行机调度算法研究. 自动化学报, 2020, 46(11): 2427-2438 doi: 10.16383/j.aas.c180581
Pan Zi-Xiao, Lei De-Ming. Research on property-based distributed low carbon parallel machines scheduling algorithm. Acta Automatica Sinica, 2020, 46(11): 2427-2438 doi: 10.16383/j.aas.c180581
Citation: Pan Zi-Xiao, Lei De-Ming. Research on property-based distributed low carbon parallel machines scheduling algorithm. Acta Automatica Sinica, 2020, 46(11): 2427-2438 doi: 10.16383/j.aas.c180581

基于问题性质的分布式低碳并行机调度算法研究

doi: 10.16383/j.aas.c180581
基金项目: 

国家自然科学基金 61573264

详细信息
    作者简介:

    潘子肖  清华大学控制科学与工程博士研究生.主要研究方向为智能系统优化与调度. E-mail: pzxwhut@126.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 Property-based Distributed Low Carbon Parallel Machines Scheduling Algorithm

Funds: 

National Natural Science Foundation of China 61573264

More Information
    Author Bio:

    PAN Zi-Xiao  Ph. D. candidate in control theory and control engineering at Tsinghua University. His research interest covers manufacturing 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: 针对分布式低碳并行机调度问题(Distributed low carbon parallel machine scheduling problem, DLCPMSP), 由于该问题子问题众多, 为此, 首先将问题转换为扩展的低碳不相关并行机调度问题以降低子问题的数量; 然后提出了一种基于问题性质的非劣排序遗传算法-Ⅱ(Property-based non-dominated sorting genetic algorithm-Ⅱ, PNSGA-Ⅱ)以同时最优化总延迟时间和总能耗, 该算法运用针对问题特征的两种启发式算法初始化种群, 给出了问题的四种性质及证明, 提出了两种基于问题性质的局部搜索方法.运用大量实例进行了算法策略分析和对比实验, 结果分析表明, PNSGA-Ⅱ在求解DLCPMSP方面具有较强优势.
    Recommended by Associate Editor WU Zhou
    1)  本文责任编委  伍洲
  • 图  1  PNSGA-Ⅱ算法流程图

    Fig.  1  The flowchart of PNSGA-Ⅱ

    图  2  均值主效应图

    Fig.  2  Principal effect plot of mean

    图  3  6种算法关于四个实例的非劣解分布

    Fig.  3  Distribution of non-dominated solutions of six algorithms on four instances

    表  1  参数各水平取值

    Table  1  Factor levels of parameters

    参数水平
    1234
    $p_c$0.800.850.9095
    $p_m$0.000.050.100.15
    $N$6090120150
    下载: 导出CSV

    表  2  参数正交表及$DI_R$值

    Table  2  Orthogonal array and $DI_R$ value

    No.Factor$DI_R$
    $p_c$$p_m$$N$
    111120.94
    212213.42
    31336.012
    41446.519
    521219.85
    622113.82
    72346.721
    82436.000
    931311.89
    103248.126
    1133110.68
    123426.536
    1341411.13
    144238.531
    154328.199
    1644114.84
    下载: 导出CSV

    表  3  各参数平均$DI_R$

    Table  3  Average $DI_R$ of factors

    水平$p_c$$p_m$$N$
    111.7215.9515.07
    211.6010.9712.00
    39.3087.9038.108
    410.688.4748.124
    Delta2.4158.0506.962
    排秩312
    下载: 导出CSV

    表  4  种算法关于指标$DI_R$的对比

    Table  4  Comparisons of six algorithms on metric $DI_R$

    实例PNSGA-ⅡA1A2NSGA-ⅡSPEA2TIPG
    $2\times 10$1.0095.9893.75313.501.14729.95
    $2\times 20$0.2816.3763.3887.7964.38853.21
    $2\times 30$0.2976.2723.3619.4655.24047.96
    $2\times 40$0.7305.5591.7146.0744.89468.06
    $3\times 40$0.0746.5830.6767.4326.26963.24
    $4\times 40$0.1389.1223.64011.819.68275.89
    $2\times 50$0.9339.6062.0458.02412.7372.65
    $3\times 50$0.5754.5342.1599.2299.56782.67
    $4\times 50$0.0457.0532.2438.3497.63983.56
    $2\times 60$1.3529.8570.8979.0369.90573.18
    $3\times 60$0.8665.1661.6086.8617.68573.38
    $4\times 60$0.2578.6100.9449.48510.0977.30
    $2\times 80$1.8518.6160.8719.53914.0483.09
    $3\times 80$0.9328.2990.97910.0811.3084.17
    $4\times 80$1.01714.530.59416.1818.0698.23
    $5\times 80$0.59112.020.51211.7714.9191.74
    $2\times 100$1.6115.9171.9966.71410.7376.21
    $3\times 100$0.2346.3281.2957.72911.8483.59
    $4\times 100$0.0837.4401.07911.5315.1388.09
    $5\times 100$1.29913.470.56513.4617.3488.42
    $2\times 200$1.66421.422.19828.4836.18$-$
    $3\times 200$2.80839.371.55945.6956.06$-$
    $4\times 200$0.64033.891.88638.9648.04$-$
    $5\times 200$0.29134.633.11836.6554.36$-$
    均值0.81612.111.79514.3316.5574.73
    下载: 导出CSV

    表  5  6种算法关于指标$\rho $的结果对比

    Table  5  Comparisons of six algorithms on metric $\rho $

    实例PNSGA-ⅡA1A2NSGA-ⅡSPEA2TIPG
    $2\times 10$0.4440.1110.0000.0000.5560.000
    $2\times 20$0.5830.0210.3330.0210.0830.000
    $2\times 30$0.9750.0250.0000.0000.0120.000
    $2\times 40$0.8470.0200.0530.0670.0200.000
    $3\times 40$0.9100.0100.0800.0000.0100.000
    $4\times 40$0.7100.0110.2900.0000.0000.000
    $2\times 50$0.7180.1370.0760.0460.0310.000
    $3\times 50$0.8720.0320.1060.0000.0000.000
    $4\times 50$0.8960.0150.1040.0000.0000.000
    $2\times 60$0.8400.0240.0800.0320.0320.000
    $3\times 60$0.8220.0590.1290.0000.0000.000
    $4\times 60$0.7930.0090.1980.0000.0090.000
    $2\times 80$0.5510.0590.3240.0740.0000.000
    $3\times 80$0.6320.0080.3610.0000.0080.000
    $4\times 80$0.6460.0150.3540.0000.0000.000
    $5\times 80$0.6480.0140.3520.0000.0000.000
    $2\times 100$0.7590.0360.0150.1970.0000.000
    $3\times 100$0.9120.0540.0390.0000.0000.000
    $4\times 100$0.8970.0150.0880.0040.0000.000
    $5\times 100$0.4800.0100.5200.0000.0000.000
    $2\times 200$0.8530.0410.0860.0240.000$-$
    $3\times 200$0.7650.0080.2120.0190.000$-$
    $4\times 200$0.8520.0040.1480.0000.000$-$
    $5\times 200$0.9260.0050.0740.0000.000$-$
    均值0.7640.0310.1680.0200.0320.000
    下载: 导出CSV

    表  6  6种算法关于指标$SP$的结果对比

    Table  6  Comparisons of six algorithms on metric $SP$

    实例PNSGA-ⅡA1A2NSGA-ⅡSPEA2TIPG
    $2\times 10$1.1273.2074.55414.682.7847.470
    $2\times 20$5.0677.4658.55411.716.24210.89
    $2\times 30$5.03613.7710.958.81614.2218.55
    $2\times 40$5.99111.068.5338.8438.17332.89
    $3\times 40$6.4778.19910.129.6246.82313.56
    $4\times 40$11.626.9397.77828.527.42313.82
    $2\times 50$10.946.34514.2613.6016.3221.35
    $3\times 50$7.4556.91713.6611.198.6419.448
    $4\times 50$8.0899.01427.5210.738.11424.12
    $2\times 60$6.58715.739.2648.06410.1714.75
    $3\times 60$9.44712.2717.7413.228.95713.86
    $4\times 60$20.6017.8110.1314.207.3109.080
    $2\times 80$13.9813.508.97710.196.92336.90
    $3\times 80$17.0216.838.46414.6710.7713.87
    $4\times 80$4.88117.2610.3417.977.76012.32
    $5\times 80$6.40112.1911.5417.1811.8419.29
    $2\times 100$11.7812.9217.6537.6838.74101.1
    $3\times 100$22.3819.9015.5014.3214.0015.60
    $4\times 100$10.3116.2712.0910.9320.6026.28
    $5\times 100$4.99710.2046.7512.727.56420.12
    $2\times 200$20.3722.1053.7216.0841.22$-$
    $3\times 200$8.38834.4018.1419.9825.37$-$
    $4\times 200$23.6836.7818.3723.0032.56$-$
    $5\times 200$24.1228.5920.1933.7411.76$-$
    均值11.1114.9916.0315.9013.9321.77
    下载: 导出CSV

    表  7  配对样本$t$-test

    Table  7  Paired-sample $t$-test

    $t$-test experiment$p-$值$\left(DI_R\right)$ $p-$值$\left(\rho \right)$$p-$值$\left(SP\right)$
    $t$-test (PNSGA-Ⅱ, A1)0.0000.0000.007
    $t$-test (PNSGA-Ⅱ, A2)0.0010.0000.048
    $t$-test (PNSGA-Ⅱ, NSGA-Ⅱ)0.0000.0000.005
    $t$-test (PNSGA-Ⅱ, SPEA2)0.0000.0000.148
    $t$-test (PNSGA-Ⅱ, TIPG)0.0000.0000.014
    下载: 导出CSV
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出版历程
  • 收稿日期:  2018-08-31
  • 录用日期:  2018-11-09
  • 刊出日期:  2020-11-24

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