Journal of Xidian University ›› 2022, Vol. 49 ›› Issue (4): 134-143.doi: 10.19665/j.issn1001-2400.2022.04.016
• Computer Science and Technology • Previous Articles Next Articles
Received:
2021-04-12
Online:
2022-08-20
Published:
2022-08-15
CLC Number:
LIU Tianyu,CAO Lei. Many-objective evolutionary algorithm based on the multitasking mechanism[J].Journal of Xidian University, 2022, 49(4): 134-143.
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算法 | 参数设置 |
---|---|
NSGA-Ⅲ | M=5时N=212,M=10时N=276,M=15时N=136,pc=1,pm=1/N,ηc=20,ηm=20 |
MaOEA-IGD | N=240,pc=0.9,pm=1/N,ηc=20,ηm=20 |
NSGA-Ⅱ-LPCA | N=100,pc=0.9,pm=1/N,ηc=20,ηm=20 |
NSGA-Ⅱ-k-EMOSS | N=100,pc=0.9,pm=1/N,ηc=20,ηm=20,k=3 |
MT-MaOEA-LPCA | N=100,n=50,G=60 |
MT-MaOEA-k-EMOSS | N=100,n=50,G=60,k=3 |
MT-MaOEA | N=100,n=50,G=60,k=3 |
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问题 | 平均IGD值 | ||||||||
---|---|---|---|---|---|---|---|---|---|
G=10 | G=20 | G=30 | G=40 | G=50 | G=60 | G=70 | G=80 | G=90 | |
DTLZ5(3,5) | 0.110 1 | 0.115 1 | 0.109 1 | 0.115 9 | 0.112 8 | 0.108 3 | 0.110 0 | 0.120 2 | 0.109 3 |
DTLZ5(5,10) | 0.382 0 | 0.538 3 | 0.331 7 | 0.379 3 | 0.333 9 | 0.265 8 | 0.287 1 | 0.360 3 | 0.329 9 |
DTLZ5(6,15) | 1.145 9 | 1.243 4 | 1.099 0 | 1.680 5 | 0.549 4 | 0.357 6 | 0.753 4 | 1.827 7 | 1.280 4 |
DTLZ2(5) | 0.617 2 | 0.572 8 | 0.487 4 | 0.249 7 | 0.222 7 | 0.594 5 | 0.608 1 | 0.629 6 | 0.648 3 |
DTLZ2(10) | 0.742 3 | 0.701 8 | 0.708 6 | 0.744 1 | 0.710 3 | 0.705 2 | 0.781 0 | 0.790 5 | 0.794 6 |
WFG3(15) | 2.759 5 | 2.511 8 | 2.742 8 | 2.725 2 | 2.662 8 | 2.664 3 | 2.612 5 | 2.633 0 | 2.714 8 |
"
问题 | 平均IGD值 | ||||
---|---|---|---|---|---|
NSGA-Ⅱ-LPCA | NSGA-Ⅱ-k-EMOSS | MT-MaOEA-LPCA | MT-MaOEA-k-EMOSS | MT-MaOEA | |
DTLZ5(3,5) | 0.263 4 | 0.386 7 | 0.109 9 | 0.120 0 | 0.108 3 |
DTLZ5(5,10) | 0.945 7 | 1.429 0 | 0.470 2 | 0.547 3 | 0.265 8 |
DTLZ5(6,15) | 1.148 6 | 7.588 5 | 0.576 8 | 1.832 9 | 0.357 6 |
DTLZ2(5) | 0.706 9 | 1.186 8 | 0.612 0 | 0.678 9 | 0.594 5 |
DTLZ2(10) | 1.691 1 | 1.978 9 | 1.186 2 | 1.141 3 | 0.705 2 |
WFG3(15) | 3.617 0 | 1.763 9 | 2.732 3 | 2.710 3 | 2.664 3 |
"
问题 | 算法 | ||||||
---|---|---|---|---|---|---|---|
NSGA-Ⅲ | MaOEA-IGD | NSGA-Ⅱ-LPCA | MT-MaOEA-LPCA | MT-MaOEA | |||
DTLZ5(I,M) | DTLZ5(3,5) | 1.17e-01 (3) | 3.74e-01 (5) | 2.63e-01 (4) | 1.10e-01 (2) | 1.08e-01 (1) | |
DTLZ5(3,10) | 2.11e-01 (3) | 4.38e-01 (5) | 2.23e-01 (4) | 1.91e-01 (2) | 1.09e-01 (1) | ||
DTLZ5(5,10) | 3.54e-01 (2) | 4.15e-01 (3) | 9.45e-01 (5) | 4.70e-01 (4) | 2.66e-01 (1) | ||
DTLZ5(7,10) | 5.51e-01 (3) | 5.48e-01 (2) | 1.02e+00 (5) | 6.23e-01 (4) | 4.97e-01 (1) | ||
DTLZ5(3,15) | 3.54e-01 (2) | 5.19e-01 (4) | 5.61e-01 (5) | 5.04e-01 (3) | 1.10e-01 (1) | ||
DTLZ5(6,15) | 5.39e-01 (2) | 6.30e-01 (4) | 1.15e+00 (5) | 5.77e-01 (3) | 3.58e-01 (1) | ||
DTLZ5(9,15) | 7.13e-01 (2) | 7.22e-01 (3) | 1.24e+00 (5) | 7.96e-01 (4) | 7.08e-01 (1) | ||
DTLZ2(M) | DTLZ2(3) | 5.96e-02 (1) | 4.80e-01 (5) | 1.18e-01 (4) | 9.59e-02 (3) | 6.02e-02 (2) | |
DTLZ2(5) | 5.99e-01 (2) | 6.16e-01 (4) | 7.07e-01 (5) | 6.12e-01 (3) | 5.94e-01 (1) | ||
DTLZ2(10) | 6.47e-01 (1) | 7.26e-01 (3) | 1.69e+00 (5) | 1.19e+00 (4) | 7.05e-01 (2) | ||
DTLZ2(15) | 1.49e+00 (4) | 7.94e-01 (1) | 1.76e+00 (5) | 1.25e+00 (3) | 9.32e-01 (2) | ||
DTLZ3(M) | DTLZ3(3) | 1.67e+01 (2) | 5.81e+01 (4) | 6.22e+01 (5) | 3.56e+01 (3) | 1.05e+01 (1) | |
DTLZ3(5) | 1.87e+01 (1) | 6.46e+01 (4) | 2.16e+02 (5) | 5.71e+01 (3) | 1.97e+01 (2) | ||
DTLZ3(10) | 7.67e+01 (3) | 6.61e+01 (1) | 3.09e+02 (5) | 7.27e+01 (3) | 6.94e+01 (2) | ||
DTLZ3(15) | 8.64e+01 (3) | 7.08e+01 (1) | 2.14e+02 (5) | 9.56e+01 (4) | 7.88e+01 (2) | ||
WFG3(M) | WFG3 (3) | 7.12e-01 (2) | 3.19e+00 (5) | 4.43e-01 (3) | 1.91e+00 (4) | 6.29e-01 (1) | |
WFG3 (5) | 8.51e-01 (2) | 4.44e+00 (5) | 1.06e+00 (3) | 2.14e+00 (4) | 6.68e-01 (1) | ||
WFG3 (10) | 1.70e+00 (2) | 6.20e+00 (5) | 3.54e+00 (4) | 2.59e+00 (3) | 1.52e+00 (1) | ||
WFG3 (15) | 2.14e+00 (2) | 1.29e+01 (1) | 3.62e+00 (5) | 2.73e+00 (4) | 2.66e+00 (3) | ||
WFG7(M) | WFG7 (3) | 2.58e-01 (2) | 1.25e+00 (3) | 1.94e+00 (5) | 1.46e+00 (4) | 2.32e-01 (1) | |
WFG7 (5) | 2.99e+00 (4) | 2.81e+00 (3) | 3.76e+00 (5) | 1.57e+00 (2) | 1.25e+00 (1) | ||
WFG7 (10) | 6.19e+00 (2) | 9.94e+00 (5) | 8.47e+00 (4) | 7.14e+00 (3) | 5.85e+00 (1) | ||
WFG7 (15) | 1.02e+01 (1) | 1.50e+01 (4) | 1.39e+01 (3) | 1.56e+01 (5) | 1.16e+01 (2) |
"
问题 | 算法 | |||||
---|---|---|---|---|---|---|
NSGA-Ⅲ | MaOEA-IGD | NSGA-Ⅱ-LPCA | MT-MaOEA-LPCA | MT-MaOEA | ||
DTLZ5(I,M) | DTLZ5(3,5) | 7.72e-02 (4) | 8.58e-02 (5) | 7.06e-02 (3) | 4.72e-02 (2) | 4.23e-02 (1) |
DTLZ5(3,10) | 9.97e-01 (5) | 8.86e-02 (3) | 8.95e-02 (4) | 5.61e-02 (2) | 5.14e-02 (1) | |
DTLZ5(5,10) | 3.25e-01 (5) | 2.96e-01 (4) | 1.53e-01 (2) | 2.09e-01 (3) | 1.36e-01 (1) | |
DTLZ5(7,10) | 4.07e-01 (1) | 5.67e-01 (3) | 4.13e-01 (2) | 6.04e-01 (5) | 4.60e-01 (4) | |
DTLZ5(3,15) | 7.89e-00 (5) | 7.71e-01 (4) | 6.61e-01 (3) | 6.36e-01 (2) | 1.03e-01 (1) | |
DTLZ5(6,15) | 2.89e-02 (1) | 1.42e-01 (2) | 2.48e-01 (5) | 1.99e-01 (4) | 1.48e-01 (3) | |
DTLZ5(9,15) | 6.36e-01 (3) | 3.60e-01 (2) | 7.34e-01 (5) | 6.70e-01 (4) | 2.03e-01 (1) | |
DTLZ2(M) | DTLZ2(3) | 4.39e-02 (3) | 6.40e-01 (5) | 6.32e-02 (4) | 4.24e-02 (2) | 3.58e-02 (1) |
DTLZ2(5) | 1.39e-01 (1) | 1.82e-01 (5) | 1.76e-01 (4) | 1.72e-01 (3) | 1.53e-01 (2) | |
DTLZ2(10) | 3.32e-01 (2) | 5.11e-01 (3) | 8.12e-01 (5) | 5.23e-01 (4) | 2.32e-01 (1) | |
DTLZ2(15) | 4.26e-01 (2) | 1.92e-02 (1) | 8.03e-01 (5) | 5.07e-01 (3) | 6.44e-01 (4) | |
DTLZ3(M) | DTLZ3(3) | 7.04e+00 (4) | 1.46e+01 (5) | 2.29e+00 (3) | 1.85e+00 (2) | 7.29e-01 (1) |
DTLZ3(5) | 7.41e+00 (2) | 1.18e+01 (3) | 2.88e+01 (5) | 1.93e+01 (4) | 9.31e-01 (1) | |
DTLZ3(10) | 8.36e+00 (1) | 1.16e+01 (3) | 4.91e+01 (5) | 2.38e+01 (4) | 9.11e+00 (2) | |
DTLZ3(15) | 1.17e+01 (1) | 3.55e+01 (4) | 3.93e+01 (5) | 2.97e+01 (3) | 2.37e+01 (2) | |
WFG3(M) | WFG3 (3) | 1.37e-01 (4) | 6.98e-03 (2) | 4.65e-02 (5) | 1.09e-02 (3) | 4.06e-03 (1) |
WFG3 (5) | 1.36e-01 (1) | 6.18e-01 (5) | 2.51e-01 (3) | 6.03e-01 (4) | 1.82e-01 (2) | |
WFG3 (10) | 5.35e-01 (2) | 3.11e+00 (5) | 1.89e+00 (4) | 6.85e-01 (3) | 4.38e-01 (1) | |
WFG3 (15) | 5.31e-01 (1) | 7.59e+00 (5) | 5.01e+00 (4) | 8.76e-01 (3) | 6.09e-01 (2) | |
WFG7(M) | WFG7 (3) | 6.16e-02 (3) | 2.03e-01 (4) | 1.33e+00 (5) | 2.18e-03 (2) | 1.16e-03 (1) |
WFG7 (5) | 4.97e-01 (1) | 8.82e-01 (4) | 3.99e+00 (5) | 8.62e-01 (3) | 3.69e-01 (1) | |
WFG7 (10) | 5.69e-01 (1) | 4.26e+00 (4) | 6.79e+00 (5) | 3.07e+00 (3) | 2.64e+00 (2) | |
WFG7 (15) | 6.68e+00 (3) | 5.15e+01 (1) | 1.21e+01 (5) | 9.85e+00 (4) | 5.68e+00 (2) |
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