电子学报 ›› 2021, Vol. 49 ›› Issue (11): 2208-2216.DOI: 10.12263/DZXB.20201044
所属专题: 多目标优化
刘冰洁1, 毕晓君2
收稿日期:
2020-09-22
修回日期:
2021-04-07
出版日期:
2021-11-25
发布日期:
2021-11-25
作者简介:
基金资助:
Bing-jie LIU1, Xiao-jun BI2
Received:
2020-09-22
Revised:
2021-04-07
Online:
2021-11-25
Published:
2021-11-25
摘要:
目前约束高维多目标进化算法大多注重提高收敛精度, 而收敛速度相对较慢. 为提高算法的收敛速度, 提出一种基于角度信息的约束高维多目标进化算法. 该算法提出基于角度违反度函数的选择操作, 依据动态的收敛性和分布性直接选择较优个体, 提高收敛速度; 此外, 提出了基于差分进化算法的交叉操作, 在不同的进化阶段选用不可行解参与交叉操作, 补偿收敛精度.在标准测试函数集C-DTLZ上进行仿真实验, 并与当前国内外性能优异的4种约束高维多目标进化算法进行对比, 证明了本文算法收敛精度保持良好, 而收敛速度得到了提升, 且目标维数越高提升效果越明显.
中图分类号:
刘冰洁, 毕晓君. 一种基于角度信息的约束高维多目标进化算法[J]. 电子学报, 2021, 49(11): 2208-2216.
Bing-jie LIU, Xiao-jun BI. A Constrained Many‑Objective Evolutionary Algorithm Based on Angle Information[J]. Acta Electronica Sinica, 2021, 49(11): 2208-2216.
M | 参考方向规模 | 种群大小(N) |
---|---|---|
3 | 91(H=12) | 92 |
5 | 210(H=6) | 212 |
8 | 156(H1=3, H2=2) | 156 |
10 | 275(H1=3, H2=2) | 276 |
15 | 135(H1=2, H2=1) | 136 |
表1 设置种群大小
M | 参考方向规模 | 种群大小(N) |
---|---|---|
3 | 91(H=12) | 92 |
5 | 210(H=6) | 212 |
8 | 156(H1=3, H2=2) | 156 |
10 | 275(H1=3, H2=2) | 276 |
15 | 135(H1=2, H2=1) | 136 |
测试问题 | M | Gmax | C-NSGA-III | C-MOEA/D | C-MOEA/DD | C-TAEA | CMaOEA-AI |
---|---|---|---|---|---|---|---|
C1-DTLZ1 | 3 | 5000 | 2.0376e-2 (2.08e-4) + | 2.1100e-2 (3.17e-3) ≈ | 2.0371e-2 (1.50e-4) + | 2.0726e-2 (1.23e-3) ≈ | 2.6617e-2 (1.13e-3) |
5 | 6000 | 5.1603e-2 (4.10e-4) + | 5.2940e-2 (7.79e-3) ≈ | 5.1352e-2 (2.90e-4) + | 5.9782e-2 (4.98e-4) - | 6.2075e-2 (1.24e-3) | |
8 | 8000 | 1.2470e-1 (1.15e-2) - | 1.0935e-1 (6.75e-3) + | 1.2066e-1 (2.98e-4) - | 1.0007e-1 (2.32e-3) + | 1.3925e-2 (2.62e-3) | |
10 | 10000 | 1.3617e-1 (7.93e-3) - | 1.8022e-1 (7.81e-3) - | 1.3179e-1 (8.07e-4) ≈ | 1.3010e-1 (1.85e-4) + | 1.5584e-1 (7.77e-4) | |
15 | 15000 | 1.9966e-1 (9.80e-4) + | 2.6049e-1 (7.74e-3) ≈ | 2.4220e-1 (1.03e-1) - | 1.9058e-1 (1.68e-4) + | 2.3030e-1 (4.21e-3) | |
C1-DTLZ3 | 3 | 10000 | 8.0133e+0 (6.31e-3) - | 8.007e+0 (1.72e-3) - | 8.6610e-2 (3.05e-2) - | 5.7687e-2 (8.17e-3) + | 9.7757e-2 (3.55e-2) |
5 | 15000 | 1.1571e+1 (1.02e-2) - | 1.1554e+0 (3.69e-3) - | 2.1601e-1 (1.60e-2) - | 1.7177e-1 (3.19e-1) - | 6.6539e-1 (2.29e-3) | |
8 | 25000 | 1.1668e+1 (7.83e-2) - | 1.1610e+1 (2.64e-3) - | 3.1596e-1 (6.90e-2) ≈ | 2.1762e-1 (1.45e-2) + | 8.1711e-1 (1.31e-2) | |
10 | 35000 | 1.4267e+1 (5.12e-2) - | 1.4140e+1 (4.30e-2) - | 2.4128e-1 (5.72e-3) - | 5.8109e-1 (1.09e-3) + | 8.4374e-1 (4.23e-3) | |
15 | 50000 | 1.4630e+1 (2.26e-1) - | 1.4463e+1 (8.22e-2) - | 7.4207e-1 (1.24e-3) + | 8.6244e-1 (4.52e-2) - | 9.4453e-1 (3.09e-2) | |
+/≈/- | 3/0/7 | 1/3/6 | 3/2/5 | 6/1/3 |
表2 5种算法在第一类约束问题上实验结果的IGD平均值与标准差
测试问题 | M | Gmax | C-NSGA-III | C-MOEA/D | C-MOEA/DD | C-TAEA | CMaOEA-AI |
---|---|---|---|---|---|---|---|
C1-DTLZ1 | 3 | 5000 | 2.0376e-2 (2.08e-4) + | 2.1100e-2 (3.17e-3) ≈ | 2.0371e-2 (1.50e-4) + | 2.0726e-2 (1.23e-3) ≈ | 2.6617e-2 (1.13e-3) |
5 | 6000 | 5.1603e-2 (4.10e-4) + | 5.2940e-2 (7.79e-3) ≈ | 5.1352e-2 (2.90e-4) + | 5.9782e-2 (4.98e-4) - | 6.2075e-2 (1.24e-3) | |
8 | 8000 | 1.2470e-1 (1.15e-2) - | 1.0935e-1 (6.75e-3) + | 1.2066e-1 (2.98e-4) - | 1.0007e-1 (2.32e-3) + | 1.3925e-2 (2.62e-3) | |
10 | 10000 | 1.3617e-1 (7.93e-3) - | 1.8022e-1 (7.81e-3) - | 1.3179e-1 (8.07e-4) ≈ | 1.3010e-1 (1.85e-4) + | 1.5584e-1 (7.77e-4) | |
15 | 15000 | 1.9966e-1 (9.80e-4) + | 2.6049e-1 (7.74e-3) ≈ | 2.4220e-1 (1.03e-1) - | 1.9058e-1 (1.68e-4) + | 2.3030e-1 (4.21e-3) | |
C1-DTLZ3 | 3 | 10000 | 8.0133e+0 (6.31e-3) - | 8.007e+0 (1.72e-3) - | 8.6610e-2 (3.05e-2) - | 5.7687e-2 (8.17e-3) + | 9.7757e-2 (3.55e-2) |
5 | 15000 | 1.1571e+1 (1.02e-2) - | 1.1554e+0 (3.69e-3) - | 2.1601e-1 (1.60e-2) - | 1.7177e-1 (3.19e-1) - | 6.6539e-1 (2.29e-3) | |
8 | 25000 | 1.1668e+1 (7.83e-2) - | 1.1610e+1 (2.64e-3) - | 3.1596e-1 (6.90e-2) ≈ | 2.1762e-1 (1.45e-2) + | 8.1711e-1 (1.31e-2) | |
10 | 35000 | 1.4267e+1 (5.12e-2) - | 1.4140e+1 (4.30e-2) - | 2.4128e-1 (5.72e-3) - | 5.8109e-1 (1.09e-3) + | 8.4374e-1 (4.23e-3) | |
15 | 50000 | 1.4630e+1 (2.26e-1) - | 1.4463e+1 (8.22e-2) - | 7.4207e-1 (1.24e-3) + | 8.6244e-1 (4.52e-2) - | 9.4453e-1 (3.09e-2) | |
+/≈/- | 3/0/7 | 1/3/6 | 3/2/5 | 6/1/3 |
测试问题 | M | Gmax | C-NSGA-III | C-MOEA/D | C-MOEA/DD | C-TAEA | CMaOEA-AI |
---|---|---|---|---|---|---|---|
C2-DTLZ2 | 3 | 2500 | 4.8195e-2 (1.86e-4) + | 4.9069e-2 (3.74e-4) + | 4.9725e-2 (5.80e-4) - | 4.4169e-2 (1.46e-3) - | 4.8765e-2 (5.05e-4) |
5 | 3500 | 1.4868e-1 (3.28e-4) ≈ | 1.4863e-1 (5.93e-4) ≈ | 1.4800e-1 (3.86e-4) - | 1.4569e-2 (1.63e-3) + | 1.4835e-1 (6.59e-4) | |
8 | 5000 | 4.0162e-1 (2.57e-1) - | 4.1220e-1 (7.64e-1) - | 2.9225e-1 (1.33e-3) - | 2.4970e-1 (1.70e-3) + | 3.5213e-1 (1.29e-3) | |
10 | 7500 | 2.7665e-1 (6.10e-2) - | 2.5412e-1 (5.57e-3) ≈ | 2.7047e-1 (2.43e-4) + | 1.9095e-1 (9.78e-4) + | 2.4783e-1 (1.86e-2) | |
15 | 10000 | 3.8095e-1 (8.77e-2) - | 3.9317e-1 (6.43e-2) - | 3.8126e-1 (1.13e-1) - | 2.5915e-1 (2.49e-3) + | 3.3123e-1 (4.97e-2) | |
C2-DTLZ2* | 3 | 2500 | 3.4636e-2 (5.26e-4) + | 3.9069e-2 (1.05e-3) + | 4.3562e-2 (2.19e-4) + | 4.1667e-2 (1.04e-3) + | 5.0590e-2 (2.21e-3) |
5 | 7500 | 6.5637e-2 (7.01e-4) + | 7.1074e-2 (1/84e-3) ≈ | 8.7447e-2 (1.35e-3) - | 6.3779e-2 (7.37e-4) + | 7.8708e-2 (4.52e-3) | |
8 | 15000 | 1.4006e-1 (1.06e-3) + | 1.6735e-1 (7.64e-3) + | 1.3209e-1 (1.13e-3) ≈ | 2.1033e-1 (9.76e-3) - | 2.8256e-1 (3.32e-3) | |
10 | 25000 | 1.1358e-1 (2.24e-3) - | 1.4919e-1 (1.03e-3) + | 1.4979e-1 (4.35e-4) - | 3.0437e-1 (2.34e-2) - | 3.1828e-1 (4.22e-2) | |
15 | 35000 | 2.4336e-1 (3.69e-2) - | 2.5052e-1 (2.38e-2) - | 2.8508e-1 (1.70e-2) - | 3.3610e-1 (1.61e-2) - | 3.5038e-1 (2.01e-2) | |
+/≈/- | 4/1/5 | 4/3/3 | 2/1/7 | 6/0/4 |
表3 5种算法在第二类约束问题上实验结果的IGD平均值与标准差
测试问题 | M | Gmax | C-NSGA-III | C-MOEA/D | C-MOEA/DD | C-TAEA | CMaOEA-AI |
---|---|---|---|---|---|---|---|
C2-DTLZ2 | 3 | 2500 | 4.8195e-2 (1.86e-4) + | 4.9069e-2 (3.74e-4) + | 4.9725e-2 (5.80e-4) - | 4.4169e-2 (1.46e-3) - | 4.8765e-2 (5.05e-4) |
5 | 3500 | 1.4868e-1 (3.28e-4) ≈ | 1.4863e-1 (5.93e-4) ≈ | 1.4800e-1 (3.86e-4) - | 1.4569e-2 (1.63e-3) + | 1.4835e-1 (6.59e-4) | |
8 | 5000 | 4.0162e-1 (2.57e-1) - | 4.1220e-1 (7.64e-1) - | 2.9225e-1 (1.33e-3) - | 2.4970e-1 (1.70e-3) + | 3.5213e-1 (1.29e-3) | |
10 | 7500 | 2.7665e-1 (6.10e-2) - | 2.5412e-1 (5.57e-3) ≈ | 2.7047e-1 (2.43e-4) + | 1.9095e-1 (9.78e-4) + | 2.4783e-1 (1.86e-2) | |
15 | 10000 | 3.8095e-1 (8.77e-2) - | 3.9317e-1 (6.43e-2) - | 3.8126e-1 (1.13e-1) - | 2.5915e-1 (2.49e-3) + | 3.3123e-1 (4.97e-2) | |
C2-DTLZ2* | 3 | 2500 | 3.4636e-2 (5.26e-4) + | 3.9069e-2 (1.05e-3) + | 4.3562e-2 (2.19e-4) + | 4.1667e-2 (1.04e-3) + | 5.0590e-2 (2.21e-3) |
5 | 7500 | 6.5637e-2 (7.01e-4) + | 7.1074e-2 (1/84e-3) ≈ | 8.7447e-2 (1.35e-3) - | 6.3779e-2 (7.37e-4) + | 7.8708e-2 (4.52e-3) | |
8 | 15000 | 1.4006e-1 (1.06e-3) + | 1.6735e-1 (7.64e-3) + | 1.3209e-1 (1.13e-3) ≈ | 2.1033e-1 (9.76e-3) - | 2.8256e-1 (3.32e-3) | |
10 | 25000 | 1.1358e-1 (2.24e-3) - | 1.4919e-1 (1.03e-3) + | 1.4979e-1 (4.35e-4) - | 3.0437e-1 (2.34e-2) - | 3.1828e-1 (4.22e-2) | |
15 | 35000 | 2.4336e-1 (3.69e-2) - | 2.5052e-1 (2.38e-2) - | 2.8508e-1 (1.70e-2) - | 3.3610e-1 (1.61e-2) - | 3.5038e-1 (2.01e-2) | |
+/≈/- | 4/1/5 | 4/3/3 | 2/1/7 | 6/0/4 |
测试问题 | M | Gmax | C-NSGA-III | C-MOEA/D | C-MOEA/DD | C-TAEA | CMaOEA-AI |
---|---|---|---|---|---|---|---|
C3-DTLZ1 | 3 | 7500 | 5.0031e-2 (1.27e-2) + | 5.9263e-2 (2.86e-2) - | 5.6206e-2 (1.00e-2) - | 5.5203e-2 (9.83e-3)- | 5.0761e-2 (1.21e-3) |
5 | 12500 | 1.0723e-1 (3.11e-4) + | 1.1073e-1 (5.84e-3) + | 1.0693e-1 (2.57e-4) + | 1.2539e-1 (4.86e-4) ≈ | 1.0695e-1 (1.80e-3) | |
8 | 20000 | 2.5019e-1 (1.12e-3) - | 2.4099e-1 (4.97e-3) - | 2.4226e-1 (3.48e-4) - | 2.4734e-1 (1.14e-3) ≈ | 2.4053e-1 (3.11e-3) | |
10 | 30000 | 2.6326e-1 (5.73e-4) - | 2.6151e-1 (2.72e-3) ≈ | 2.6568e-1 (2.60e-5) - | 2.7160e-1 (2.83e-2) - | 2.5216e-1 (2.77e-3) | |
15 | 40000 | 4.0143e-1 (1.82e-3) + | 4.3989e-1 (8.52e-3) - | 4.0194e-1 (1.17e-3) + | 5.0268e-1 (8.22e-2) ≈ | 4.0187e-1 (1.23e-2) | |
C3-DTLZ4 | 3 | 7500 | 2.4315e-1 (3.35e-1) + | 2.4841e-1 (4.21e-1) - | 2.7033e-1 (3.23e-1) - | 1.6168e-1 (2.53e-3) + | 2.1126e-1 (3.30e-1) |
5 | 12500 | 3.2141e-1 (1.62e-1) - | 3.0484e-1 (4.89e-1) ≈ | 2.4368e-1 (1.42e-4) + | 2.4255e-1 (1.27e-3) + | 3.0017e-1 (2.40e-3) | |
8 | 20000 | 5.9044e-1 (1.33e-1) ≈ | 5.5268e-1 (7.46e-3) + | 4.9654e-1 (2.27e-5) + | 5.8925e-1 (3.10e-3) - | 5.4185e-1 (6.57e-2) | |
10 | 30000 | 5.6901e-1 (6.20e-4) + | 5.5651e-1 (1.18e-3) ≈ | 5.6741e-1 (2.91e-5) + | 5.9013e-1 (2.02e-3) - | 5.4002e-1 (8.39e-2) | |
15 | 40000 | 1.1437e+0 (1.15e-1) - | 7.7589e-1 (4.40e-2) - | 7.9192e-1 (1.19e-2) + | 7.6794e-1 (2.59e-5) + | 7.6903e-1 (3.49e-2) | |
+/≈/- | 5/1/4 | 2/3/5 | 6/0/4 | 3/3/4 |
表4 5种算法在第三类约束问题上实验结果的IGD平均值与标准差
测试问题 | M | Gmax | C-NSGA-III | C-MOEA/D | C-MOEA/DD | C-TAEA | CMaOEA-AI |
---|---|---|---|---|---|---|---|
C3-DTLZ1 | 3 | 7500 | 5.0031e-2 (1.27e-2) + | 5.9263e-2 (2.86e-2) - | 5.6206e-2 (1.00e-2) - | 5.5203e-2 (9.83e-3)- | 5.0761e-2 (1.21e-3) |
5 | 12500 | 1.0723e-1 (3.11e-4) + | 1.1073e-1 (5.84e-3) + | 1.0693e-1 (2.57e-4) + | 1.2539e-1 (4.86e-4) ≈ | 1.0695e-1 (1.80e-3) | |
8 | 20000 | 2.5019e-1 (1.12e-3) - | 2.4099e-1 (4.97e-3) - | 2.4226e-1 (3.48e-4) - | 2.4734e-1 (1.14e-3) ≈ | 2.4053e-1 (3.11e-3) | |
10 | 30000 | 2.6326e-1 (5.73e-4) - | 2.6151e-1 (2.72e-3) ≈ | 2.6568e-1 (2.60e-5) - | 2.7160e-1 (2.83e-2) - | 2.5216e-1 (2.77e-3) | |
15 | 40000 | 4.0143e-1 (1.82e-3) + | 4.3989e-1 (8.52e-3) - | 4.0194e-1 (1.17e-3) + | 5.0268e-1 (8.22e-2) ≈ | 4.0187e-1 (1.23e-2) | |
C3-DTLZ4 | 3 | 7500 | 2.4315e-1 (3.35e-1) + | 2.4841e-1 (4.21e-1) - | 2.7033e-1 (3.23e-1) - | 1.6168e-1 (2.53e-3) + | 2.1126e-1 (3.30e-1) |
5 | 12500 | 3.2141e-1 (1.62e-1) - | 3.0484e-1 (4.89e-1) ≈ | 2.4368e-1 (1.42e-4) + | 2.4255e-1 (1.27e-3) + | 3.0017e-1 (2.40e-3) | |
8 | 20000 | 5.9044e-1 (1.33e-1) ≈ | 5.5268e-1 (7.46e-3) + | 4.9654e-1 (2.27e-5) + | 5.8925e-1 (3.10e-3) - | 5.4185e-1 (6.57e-2) | |
10 | 30000 | 5.6901e-1 (6.20e-4) + | 5.5651e-1 (1.18e-3) ≈ | 5.6741e-1 (2.91e-5) + | 5.9013e-1 (2.02e-3) - | 5.4002e-1 (8.39e-2) | |
15 | 40000 | 1.1437e+0 (1.15e-1) - | 7.7589e-1 (4.40e-2) - | 7.9192e-1 (1.19e-2) + | 7.6794e-1 (2.59e-5) + | 7.6903e-1 (3.49e-2) | |
+/≈/- | 5/1/4 | 2/3/5 | 6/0/4 | 3/3/4 |
M | Gmax | 测试问题 | C-NSGA-III | C-MOEA /D | C-MOEA /DD | C-TAEA | CMaO- EA-AI |
---|---|---|---|---|---|---|---|
3 | 5000 | C1-DTLZ1 | 19.00 | 20.88 | 18.50 | 19.20 | 18.43 |
10000 | C1-DTLZ3 | 21.43 | 20.52 | 20.34 | 21.78 | 20.10 | |
2500 | C2-DTLZ2 | 19.71 | 22.87 | 21.02 | 20.41 | 19.22 | |
2500 | C2-DTLZ2* | 19.53 | 21.52 | 22.50 | 26.83 | 19.44 | |
7500 | C3-DTLZ1 | 21.42 | 19.21 | 20.93 | 23.45 | 18.79 | |
7500 | C3-DTLZ4 | 22.01 | 20.70 | 20.30 | 21.54 | 19.91 | |
5 | 6000 | C1-DTLZ1 | 67.11 | 45.17 | 52.91 | 43.91 | 40.04 |
15000 | C1-DTLZ3 | 70.32 | 49.46 | 55.33 | 46.31 | 43.71 | |
3500 | C2-DTLZ2 | 65.86 | 47.01 | 53.03 | 43.33 | 41.22 | |
7500 | C2-DTLZ2* | 69.39 | 49.38 | 53.89 | 41.56 | 41.48 | |
12500 | C3-DTLZ1 | 70.19 | 50.74 | 56.60 | 44.06 | 43.08 | |
12500 | C3-DTLZ4 | 71.06 | 51.19 | 56.88 | 43.72 | 43.58 | |
8 | 8000 | C1-DTLZ1 | 120.29 | 80.32 | 103.63 | 84.24 | 54.58 |
25000 | C1-DTLZ3 | 132.40 | 85.18 | 111.07 | 89.58 | 58.15 | |
5000 | C2-DTLZ2 | 119.33 | 81.20 | 104.58 | 88.27 | 60.22 | |
15000 | C2-DTLZ2* | 114.39 | 86.01 | 103.26 | 85.01 | 62.12 | |
20000 | C3-DTLZ1 | 130.43 | 87.55 | 113.79 | 91.40 | 65.99 | |
20000 | C3-DTLZ4 | 127.21 | 86.12 | 109.51 | 93.15 | 65.10 | |
10 | 10000 | C1-DTLZ1 | 230.13 | 110.38 | 198.53 | 165.09 | 87.02 |
35000 | C1-DTLZ3 | 240.37 | 115.01 | 212.21 | 188.12 | 92.03 | |
7500 | C2-DTLZ2 | 225.38 | 107.23 | 203.79 | 171.20 | 90.15 | |
25000 | C2-DTLZ2* | 229.42 | 119.64 | 202.50 | 189.44 | 91.09 | |
30000 | C3-DTLZ1 | 239.92 | 120.26 | 210.27 | 183.13 | 94.01 | |
30000 | C3-DTLZ4 | 241.46 | 124.78 | 208.34 | 191.74 | 94.14 | |
15 | 15000 | C1-DTLZ1 | 563.66 | 179.86 | 400.71 | 273.14 | 136.81 |
50000 | C1-DTLZ3 | 575.32 | 189.11 | 412.64 | 290.93 | 150.71 | |
10000 | C2-DTLZ2 | 557.86 | 183.90 | 402.61 | 282.55 | 151.23 | |
35000 | C2-DTLZ2* | 567.34 | 194.83 | 404.96 | 285.86 | 159.25 | |
40000 | C3-DTLZ1 | 584.56 | 191.21 | 417.55 | 299.73 | 166.32 | |
40000 | C3-DTLZ4 | 578.62 | 191.20 | 402.78 | 283.51 | 168.99 |
表5 5种算法在不同目标维数的C-DTLZ测试集上的运行时间平均值(s)
M | Gmax | 测试问题 | C-NSGA-III | C-MOEA /D | C-MOEA /DD | C-TAEA | CMaO- EA-AI |
---|---|---|---|---|---|---|---|
3 | 5000 | C1-DTLZ1 | 19.00 | 20.88 | 18.50 | 19.20 | 18.43 |
10000 | C1-DTLZ3 | 21.43 | 20.52 | 20.34 | 21.78 | 20.10 | |
2500 | C2-DTLZ2 | 19.71 | 22.87 | 21.02 | 20.41 | 19.22 | |
2500 | C2-DTLZ2* | 19.53 | 21.52 | 22.50 | 26.83 | 19.44 | |
7500 | C3-DTLZ1 | 21.42 | 19.21 | 20.93 | 23.45 | 18.79 | |
7500 | C3-DTLZ4 | 22.01 | 20.70 | 20.30 | 21.54 | 19.91 | |
5 | 6000 | C1-DTLZ1 | 67.11 | 45.17 | 52.91 | 43.91 | 40.04 |
15000 | C1-DTLZ3 | 70.32 | 49.46 | 55.33 | 46.31 | 43.71 | |
3500 | C2-DTLZ2 | 65.86 | 47.01 | 53.03 | 43.33 | 41.22 | |
7500 | C2-DTLZ2* | 69.39 | 49.38 | 53.89 | 41.56 | 41.48 | |
12500 | C3-DTLZ1 | 70.19 | 50.74 | 56.60 | 44.06 | 43.08 | |
12500 | C3-DTLZ4 | 71.06 | 51.19 | 56.88 | 43.72 | 43.58 | |
8 | 8000 | C1-DTLZ1 | 120.29 | 80.32 | 103.63 | 84.24 | 54.58 |
25000 | C1-DTLZ3 | 132.40 | 85.18 | 111.07 | 89.58 | 58.15 | |
5000 | C2-DTLZ2 | 119.33 | 81.20 | 104.58 | 88.27 | 60.22 | |
15000 | C2-DTLZ2* | 114.39 | 86.01 | 103.26 | 85.01 | 62.12 | |
20000 | C3-DTLZ1 | 130.43 | 87.55 | 113.79 | 91.40 | 65.99 | |
20000 | C3-DTLZ4 | 127.21 | 86.12 | 109.51 | 93.15 | 65.10 | |
10 | 10000 | C1-DTLZ1 | 230.13 | 110.38 | 198.53 | 165.09 | 87.02 |
35000 | C1-DTLZ3 | 240.37 | 115.01 | 212.21 | 188.12 | 92.03 | |
7500 | C2-DTLZ2 | 225.38 | 107.23 | 203.79 | 171.20 | 90.15 | |
25000 | C2-DTLZ2* | 229.42 | 119.64 | 202.50 | 189.44 | 91.09 | |
30000 | C3-DTLZ1 | 239.92 | 120.26 | 210.27 | 183.13 | 94.01 | |
30000 | C3-DTLZ4 | 241.46 | 124.78 | 208.34 | 191.74 | 94.14 | |
15 | 15000 | C1-DTLZ1 | 563.66 | 179.86 | 400.71 | 273.14 | 136.81 |
50000 | C1-DTLZ3 | 575.32 | 189.11 | 412.64 | 290.93 | 150.71 | |
10000 | C2-DTLZ2 | 557.86 | 183.90 | 402.61 | 282.55 | 151.23 | |
35000 | C2-DTLZ2* | 567.34 | 194.83 | 404.96 | 285.86 | 159.25 | |
40000 | C3-DTLZ1 | 584.56 | 191.21 | 417.55 | 299.73 | 166.32 | |
40000 | C3-DTLZ4 | 578.62 | 191.20 | 402.78 | 283.51 | 168.99 |
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