Page 195 - 《软件学报》2026年第3期

1158 软件学报 2026 年第 37 卷第 3 期

表 2 Two-Arch/IS 和不同类型的 Two-Arch 算法在高维 DTLZ 问题上的 IGD 结果 (续)

测试问题 目标数目 Two-Arch/IS Two-Arch Two_Arch2 C-TAEA TriMOEATAR TwoArchM TwoArchA
3.9197E–1 5.2125E–1 4.0623E–1 4.3577E–1 3.8357E–1 3.8057E–1 3.9894E–1
8
(2.74E–3) (2.93E–2) – (4.83E–3) – (6.78E–3) – (6.97E–4) + (1.59E–3) + (5.66E–3) –
4.7686E–1 6.6423E–1 4.9208E–1 5.7275E–1 5.1608E–1 5.1379E–1 5.4042E–1
10
(2.90E–3) (4.06E–2) – (6.56E–3) – (4.50E–3) – (3.53E–3) – (4.38E–2) – (4.65E–3) –
DTLZ2
5.4409E–1 8.2740E–1 5.9202E–1 6.3952E–1 6.6315E–1 5.4458E–1 6.2912E–1
15
(4.84E–3) (3.49E–2) – (5.70E–3) – (2.49E–3) – (3.59E–3) – (1.42E–3) = (8.50E–3) –
6.2367E–1 9.5963E–1 8.0332E–1 7.6521E–1 7.3567E–1 6.2401E–1 8.1567E–1
20
(2.29E–3) (3.02E–2) – (6.63E–3) – (3.55E–3) – (3.07E–3) – (6.07E–3) = (4.52E–3) –
4.8838E+0 2.0920E+0 1.4226E+0 4.7195E+0 1.3868E+0 1.0245E+0 4.6880E+0
4
(2.05E+0) (1.43E+0) + (1.19E+0) + (2.14E+0) = (7.83E–1) + (7.23E–1) + (1.87E+1) +
4.4899E+0 1.2354E+1 2.6970E+0 9.3593E+0 5.1102E+0 4.2738E+0 6.9498E+0
6
(1.70E+0) (4.76E+0) – (1.84E+0) + (6.29E+0) – (2.20E+0) = (2.34E+0) = (6.97E+0) –
4.5326E+0 2.7480E+1 4.6125E+0 1.8487E+1 7.0781E+0 1.2865E+1 5.8237E+0
8
(1.95E+0) (8.49E+0) – (1.74E+0) – (9.79E+0) – (2.50E+0) – (5.57E+0) – (1.23E+1) –
DTLZ3
5.7788E+0 3.5272E+1 9.9040E+0 2.8174E+1 8.2047E+0 2.3020E+1 5.1378E+0
10
(1.67E+0) (1.11E+1) – (4.17E+0) – (1.01E+1) – (2.75E+0) – (2.17E+1) – (1.48E+1) +
1.5993E+0 1.4042E+1 6.8737E+0 1.9758E+1 3.4872E+0 1.9801E+2 1.1152E+1
15
(8.97E–1) (6.47E+0) – (4.18E+0) – (1.27E+1) – (1.42E+0) – (7.38E+1) – (1.74E+1) –
1.2400E+0 1.7800E+1 2.0461E+1 6.0088E+0 2.8924E+0 2.5155E+2 2.2450E+1
20
(1.13E+0) (7.30E+0) – (1.02E+1) – (2.69E+0) – (1.00E+0) – (1.16E+2) – (9.83E+0) –
1.8505E–1 3.7697E–1 1.3501E–1 1.6681E–1 1.8376E–1 2.1614E–1 2.1775E–1
4
(9.13E–2) (1.39E–1) – (2.19E–3) + (3.88E–3) + (1.11E–1) = (1.37E–1) – (1.34E–1) –
3.2476E–1 5.7929E–1 2.8777E–1 3.3092E–1 2.9723E–1 2.9026E–1 2.9859E–1
6
(5.94E–2) (1.17E–1) – (4.75E–3) + (3.32E–3) = (2.68E–2) = (3.55E–2) + (7.25E–2) +
4.1051E–1 7.3008E–1 4.1431E–1 4.2757E–1 4.0921E–1 3.8080E–1 4.4106E–1
8
(3.24E–2) (1.21E–1) – (5.56E–3) – (4.66E–3) = (1.93E–2) = (1.61E–3) + (3.73E–2) –
DTLZ4
4.9340E–1 7.9086E–1 4.9152E–1 5.6421E–1 5.3762E–1 5.1511E–1 5.1245E–1
10
(1.69E–2) (8.29E–2) – (6.70E–3) = (4.01E–3) – (9.47E–3) – (2.62E–2) – (3.92E–3) –
5.6024E–1 8.8176E–1 5.7441E–1 6.2956E–1 7.0307E–1 5.6563E–1 6.4545E–1
15
(2.17E–3) (5.37E–2) – (4.36E–3) – (5.64E–3) – (2.30E–3) – (9.48E–4) = (1.47E–2) –
6.1600E–1 1.1044E+0 7.3714E–1 7.6289E–1 7.4930E–1 6.2008E–1 6.9606E–1
20
(1.17E–3) (4.48E–2) – (6.87E–3) – (2.01E–3) – (2.26E–3) – (1.03E–3) – (1.28E–2) –
3.6911E–2 7.1100E–2 4.4714E–2 6.6650E–2 4.5610E–2 8.8868E–2 5.5790E–2
4
(6.06E–3) (1.32E–2) – (4.67E–3) – (1.20E–2) – (7.30E–3) – (1.69E–2) – (1.06E–2) –
8.7485E–2 8.7812E–2 1.1159E–1 1.4483E–1 1.3845E–1 1.6663E–1 9.6713E–2
6
(1.50E–2) (2.03E–2) = (1.87E–2) – (4.61E–2) – (6.56E–2) – (3.77E–2) – (1.21E–2) –
1.1496E–1 1.1649E–1 1.7261E–1 1.8186E–1 2.4139E–1 3.1275E–1 1.0946E–1
8
(1.89E–2) (2.94E–2) = (3.38E–2) – (5.01E–2) – (6.66E–2) – (5.23E–2) – (2.09E–2) +
DTLZ5
1.3084E–1 1.3479E–1 2.3506E–1 2.7374E–1 4.8692E–1 3.3988E–1 1.3139E–1
10
(1.93E–2) (4.19E–2) = (4.65E–2) – (7.93E–2) – (7.16E–2) – (7.38E–2) – (1.84E–2) =
1.4586E–1 1.5312E–1 3.4937E–1 3.1887E–1 5.9429E–1 5.6431E–1 1.6282E–1
15
(2.37E–2) (3.83E–2) – (1.10E–1) – (1.07E–1) – (2.73E–2) – (1.21E–1) – (1.24E–2) –
1.4888E–1 1.9812E–1 5.5643E–1 3.5739E–1 6.0261E–1 8.1851E–1 1.7683E–1
20
(4.07E–2) (3.32E–2) – (1.06E–1) – (8.27E–2) – (2.91E–2) – (7.54E–2) – (1.60E–2) –
5.7666E–2 4.1950E–1 5.5910E–2 2.2642E–1 4.7171E–2 1.7017E–1 1.2714E–1
4
(1.87E–2) (2.44E–1) – (4.74E–3) = (1.81E–1) – (1.05E–2) + (3.94E–2) – (2.24E–1) –
1.4606E–1 8.7755E–1 1.9906E–1 6.5559E–1 2.2789E–1 3.2013E–1 2.8997E–1
6
(4.07E–2) (6.00E–1) – (6.11E–2) – (3.57E–1) – (5.35E–2) – (5.62E–2) – (2.25E–1) –
DTLZ6
2.4125E–1 1.9573E+0 3.2116E–1 8.6451E–1 2.4875E–1 8.4913E–1 3.8178E–1
8
(1.09E–1) (8.21E–1) – (9.65E–2) – (4.12E–1) – (7.49E–2) = (2.81E–1) – (4.94E–1) –
2.5337E–1 2.7224E+0 6.9154E–1 2.6388E+0 5.1617E–1 9.6385E–1 2.9570E–1
10
(7.45E–2) (8.31E–1) – (2.84E–1) – (9.54E–1) – (2.00E–1) – (3.24E–1) – (8.09E–1) –