Journal of System Simulation ›› 2024, Vol. 36 ›› Issue (11): 2578-2591.doi: 10.16182/j.issn1004731x.joss.23-0896
Ma Xunde1, Bi Li1, Wang Junjie2,3
Received:
2023-07-17
Revised:
2023-09-11
Online:
2024-11-13
Published:
2024-11-19
Contact:
Bi Li
CLC Number:
Ma Xunde, Bi Li, Wang Junjie. Research on Green Job Shop Scheduling Based on Herd Immunity Optimizer[J]. Journal of System Simulation, 2024, 36(11): 2578-2591.
Table 1
Model symbol definition
符号 | 定义 |
---|---|
m | 机器总数目 |
n | 工件总数目 |
i,g | 工件索引, |
ni | 工件i包含的工序总数目 |
j, h | 工件i和g的工序索引, |
k, p | 机器的索引, |
Oij | 工件i的第j道工序 |
Mij | |
Oijk | |
Tijk | |
JRti | |
STijk | |
FTijk | |
Sij | Oij |
Oij | |
SEEk | |
Ek | |
Table 2
Energy consumption parameters of machine
机器 | 档位1 | 档位2 | 档位3 | 开关机/(W/min) | 待机/W | |||
---|---|---|---|---|---|---|---|---|
UPE | UIE | UPE | UIE | UPE | UIE | |||
1 | 1 230 | 230 | 1 510 | 320 | 2 270 | 370 | 2 600 | 20 |
2 | 1 160 | 180 | 1 500 | 280 | 1 820 | 350 | 2 530 | 22 |
3 | 1 150 | 190 | 1 390 | 300 | 1 880 | 350 | 2 560 | 25 |
4 | 1 380 | 230 | 1 920 | 330 | 2 340 | 390 | 2 740 | 30 |
5 | 1 040 | 220 | 1 500 | 310 | 2 220 | 380 | 2 640 | 25 |
6 | 1 270 | 230 | 1 560 | 270 | 2 260 | 370 | 2 600 | 27 |
7 | 1 170 | 220 | 1 510 | 300 | 2 160 | 400 | 2 570 | 22 |
8 | 1 000 | 170 | 1 210 | 290 | 1 690 | 350 | 2 550 | 20 |
9 | 1 300 | 250 | 1 770 | 320 | 2 510 | 400 | 2 860 | 30 |
10 | 1 360 | 250 | 1 960 | 310 | 2 510 | 380 | 2 840 | 28 |
11 | 1 350 | 240 | 1 850 | 340 | 2 440 | 390 | 2 800 | 22 |
12 | 1 030 | 190 | 1 480 | 280 | 1 920 | 320 | 2 630 | 21 |
13 | 1 310 | 230 | 1 860 | 310 | 2 290 | 390 | 2 860 | 28 |
14 | 1 060 | 200 | 1 450 | 300 | 1 960 | 400 | 2 760 | 29 |
15 | 1 450 | 300 | 2 090 | 350 | 2 970 | 400 | 3 050 | 30 |
Table 3
HV results of all variant algorithms in all examples
算例 | CHIO1 | CHIO2 | CHIO3 | DCHIO | ||||
---|---|---|---|---|---|---|---|---|
mean | std | mean | std | mean | std | mean | std | |
-/=/+ | 10/0/0 | 6/3/1 | 2/7/1 | |||||
MK01 | 0.124 1- | 0.008 3 | 0.167 6- | 0.005 5 | 0.180 9= | 0.004 9 | 0.181 6 | 0.002 5 |
MK02 | 0.159 9- | 0.027 7 | 0.277 2- | 0.009 7 | 0.290 8= | 0.008 6 | 0.290 3 | 0.008 6 |
MK03 | 0.112 9- | 0.009 3 | 0.219 6= | 0.005 3 | 0.222 6- | 0.0045 | 0.227 2 | 0.002 3 |
MK04 | 0.173 4- | 0.009 9 | 0.247 9- | 0.007 8 | 0.256 7- | 0.008 8 | 0.263 1 | 0.006 6 |
MK05 | 0.103 6- | 0.004 7 | 0.138 7= | 0.002 8 | 0.140 3= | 0.003 4 | 0.143 3 | 0.003 7 |
MK06 | 0.115 8- | 0.023 7 | 0.315 0- | 0.014 5 | 0.336 1= | 0.014 5 | 0.342 1 | 0.012 2 |
MK07 | 0.115 0- | 0.012 8 | 0.214 1- | 0.004 2 | 0.220 4= | 0.003 7 | 0.222 6 | 0.003 0 |
MK08 | 0.114 4- | 0.003 6 | 0.156 5= | 0.003 5 | 0.160 1= | 0.001 9 | 0.162 8 | 0.001 4 |
MK09 | 0.135 2- | 0.008 6 | 0.241 9+ | 0.006 0 | 0.241 8+ | 0.008 1 | 0.232 1 | 0.006 8 |
MK10 | 0.123 4- | 0.013 2 | 0.252 5- | 0.011 2 | 0.268 9= | 0.007 9 | 0.271 4 | 0.005 6 |
Table 4
Comparison results with traditional algorithms
算例 | Pareto解个数 | min(Cmax) | min(E) | HV | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
A | B | C | A | B | C | A | B | C | A | B | C | |
mean | 6.9 | 7.4 | 21.4 | 286.8 | 283.8 | 187.0 | 44.56 | 42.89 | 35.00 | 0.438 0 | 0.442 2 | 0.777 0 |
MK01 | 5 | 6 | 11 | 59.2 | 67.2 | 42.0 | 6.67 | 6.66 | 5.26 | 0.654 6 | 0.559 6 | 0.869 7 |
MK02 | 5 | 7 | 16 | 56.0 | 57.9 | 29.2 | 6.76 | 7.03 | 4.76 | 0.579 0 | 0.552 1 | 0.964 6 |
MK03 | 5 | 8 | 5 | 312.5 | 315.1 | 204.0 | 49.51 | 43.54 | 30.94 | 0.450 4 | 0.450 2 | 0.773 0 |
MK04 | 10 | 9 | 30 | 99.7 | 97.6 | 68.2 | 14.05 | 13.34 | 11.13 | 0.423 9 | 0.445 3 | 0.717 0 |
MK05 | 7 | 6 | 32 | 248.0 | 244.0 | 179.0 | 24.14 | 23.50 | 21.97 | 0.393 0 | 0.409 0 | 0.658 3 |
MK06 | 6 | 7 | 14 | 158.2 | 145.5 | 70.8 | 26.28 | 23.48 | 14.57 | 0.318 4 | 0.399 2 | 0.888 3 |
MK07 | 7 | 7 | 41 | 251.3 | 254.3 | 154.0 | 30.79 | 29.56 | 21.99 | 0.486 1 | 0.478 5 | 0.829 6 |
MK08 | 7 | 11 | 34 | 689.7 | 675.9 | 523.0 | 101.30 | 98.97 | 89.92 | 0.296 4 | 0.316 9 | 0.540 6 |
MK09 | 8 | 7 | 20 | 540.2 | 549.1 | 337.7 | 96.47 | 95.02 | 79.32 | 0.440 1 | 0.428 1 | 0.792 7 |
MK10 | 9 | 6 | 11 | 453.6 | 431.1 | 261.7 | 89.73 | 87.79 | 70.08 | 0.337 9 | 0.383 2 | 0.735 7 |
Table 5
Comparison results with improved algorithm
算例 | Pareto解个数 | min(Cmax) | min(E) | HV | ||||
---|---|---|---|---|---|---|---|---|
LCSA | DCHIO | LCSA | DCHIO | LCSA | DCHIO | LCSA | DCHIO | |
mean | 8.8 | 18.7 | 182.5 | 187.0 | 42.09 | 35.00 | 0.088 9 | 0.135 0 |
MK01 | 6 | 11 | 42 | 42.0 | 6.20 | 5.26 | 0.109 2 | 0.166 9 |
MK02 | 7 | 13 | 28 | 29.2 | 5.56 | 4.76 | 0.125 3 | 0.178 4 |
MK03 | 7 | 4 | 204 | 204.0 | 37.65 | 30.94 | 0.057 6 | 0.103 5 |
MK04 | 7 | 24 | 68 | 68.2 | 13.88 | 11.13 | 0.098 4 | 0.167 1 |
MK05 | 12 | 31 | 181 | 179.0 | 27.57 | 21.97 | 0.079 6 | 0.151 4 |
MK06 | 11 | 8 | 67 | 70.8 | 14.83 | 14.57 | 0.101 3 | 0.099 2 |
MK07 | 5 | 48 | 146 | 154.0 | 27.78 | 21.99 | 0.078 9 | 0.129 4 |
MK08 | 3 | 30 | 523 | 523.0 | 109.93 | 89.92 | 0.059 1 | 0.110 4 |
MK09 | 21 | 11 | 326 | 337.7 | 93.11 | 79.32 | 0.103 0 | 0.147 3 |
MK10 | 9 | 7 | 240 | 261.7 | 84.37 | 70.08 | 0.076 3 | 0.096 8 |
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