Page 198 - 《软件学报》2026年第3期

丁炜超 等: 基于信息共享的改进双归档高维多目标进化算法 1161

表 3 Two-Arch/IS 和其他高维多目标进化算法在高维 DTLZ 问题上的 IGD 结果 (续)

测试问题 目标数目 Two-Arch/IS NSGA-III KnEA IBEA HEA TSNSGA-II MOEA/D SMS-EMOA
1.2400E+0 1.3177E+1 7.0634E+2 1.0566E+0 1.0200E+0 5.7914E+2 3.2063E+0 9.7090E+1
DTLZ3 20
(1.13E+0) (8.32E+0) – (1.46E+2) – (4.02E–2) + (1.24E–1) + (4.63E+2) – (2.19E+0) – (1.88E+1) –
1.8505E–1 2.3604E–1 1.5116E–1 1.9547E–1 4.4026E–1 1.4117E–1 4.4896E–1 2.8439E–1
4
(9.13E–2) (1.49E–1) – (5.38E–3) + (1.51E–1) = (2.34E–1) – (3.26E–4) + (2.62E–1) – (1.49E–1) –
3.2476E–1 4.0888E–1 3.0292E–1 3.6168E–1 5.0194E–1 2.8915E–1 6.1389E–1 4.5825E–1
6
(5.94E–2) (1.07E–1) = (5.46E–3) + (9.83E–2) = (1.49E–1) – (3.12E–3) + (1.70E–1) – (1.04E–1) –
4.1051E–1 4.9653E–1 4.0816E–1 4.5910E–1 5.5569E–1 4.0290E–1 7.5323E–1 5.2703E–1
8
(3.24E–2) (8.88E–2) = (5.25E–3) + (6.45E–2) – (1.24E–1) – (8.25E–3) + (1.76E–1) – (7.78E–2) –
DTLZ4
4.9340E–1 5.9139E–1 5.1116E–1 5.3693E–1 6.9389E–1 5.7143E–1 8.4894E–1 6.1417E–1
10
(1.69E–2) (5.80E–2) – (6.05E–3) – (4.58E–2) – (1.03E–1) – (1.84E–2) – (1.20E–1) – (5.65E–2) –
5.6024E–1 6.4324E–1 5.6668E–1 5.8213E–1 8.6827E–1 1.8669E+0 1.0643E+0 8.5864E–1
15
(2.17E–3) (1.69E–2) – (4.11E–3) – (3.97E–3) – (8.80E–2) – (4.50E–1) – (1.22E–1) – (1.50E–1) –
6.1600E–1 9.7055E–1 6.2212E–1 6.7551E–1 8.5697E–1 1.8520E+0 1.1450E+0 1.3938E+0
20
(1.17E–3) (3.53E–2) – (2.76E–3) – (1.04E–2) – (5.75E–2) – (4.47E–1) – (1.60E–1) – (1.41E–1) –
3.6911E–2 5.3657E–2 1.7661E–1 4.6158E–2 6.9234E–2 9.2373E–2 3.6030E–2 3.6174E–2
4
(6.06E–3) (8.68E–3) – (8.42E–2) – (4.77E–3) – (6.41E–3) – (1.62E–2) – (2.01E–4) = (8.38E–3) =
8.7485E–2 1.2939E–1 2.3360E–1 7.5383E–2 2.0267E–1 3.0272E–1 3.4729E–2 6.3997E–2
6
(1.50E–2) (4.50E–2) – (5.59E–2) – (1.44E–2) + (2.70E–2) – (1.55E–1) – (2.01E–3) + (1.29E–2) +
1.1496E–1 2.6392E–1 2.8287E–1 1.3056E–1 2.5294E–1 3.2348E–1 5.2388E–2 9.4036E–2
8
(1.89E–2) (8.64E–2) – (6.90E–2) – (4.92E–2) = (6.03E–2) – (1.52E–1) – (6.02E–3) + (3.33E–2) +
DTLZ5
1.3084E–1 2.3372E–1 3.9692E–1 1.9989E–1 2.1871E–1 3.5588E–1 7.3741E–2 1.9587E–1
10
(1.93E–2) (7.78E–2) – (1.19E–1) – (6.10E–2) – (5.79E–2) – (1.72E–1) – (1.17E–4) + (4.60E–2) –
1.4586E–1 2.4525E–1 4.9301E–1 2.4533E–1 3.2466E–1 4.8497E–1 3.2008E–1 2.4171E–1
15
(2.37E–2) (3.61E–2) – (1.84E–1) – (7.14E–2) – (5.53E–2) – (1.50E–1) – (1.68E–1) – (5.08E–2) –
1.4888E–1 1.1795E+0 7.8404E–1 2.7405E–1 3.5808E–1 4.7694E–1 2.3750E–1 2.5476E–1
20
(4.07E–2) (5.69E–1) – (3.18E–1) – (6.62E–2) – (5.63E–2) – (1.80E–1) – (6.34E–3) – (8.38E–2) –
5.7666E–2 1.0200E–1 2.0850E–1 5.4058E–2 1.4377E–1 2.2188E–1 3.5837E–2 6.0860E–1
4
(1.87E–2) (3.90E–2) – (1.08E–1) – (6.24E–3) = (4.01E–2) – (1.13E–1) – (7.54E–4) + (3.43E–1) –
1.4606E–1 9.8979E–1 6.9817E–1 1.5718E–1 2.7116E–1 5.6079E–1 2.1399E–1 9.0398E–1
6
(4.07E–2) (6.35E–1) – (2.68E–1) – (6.84E–2) = (1.17E–1) – (3.28E–1) – (6.25E–1) – (3.94E–1) –
2.4125E–1 1.9782E+0 1.5879E+0 2.6959E–1 4.1867E–1 8.4134E–1 2.4353E–1 1.6069E+0
8
(1.09E–1) (9.57E–1) – (5.36E–1) – (9.62E–2) = (1.15E–1) – (4.96E–1) – (4.51E–1) = (4.31E–1) –
DTLZ6
2.5337E–1 2.4700E+0 1.6960E+0 3.6169E–1 8.6637E–1 6.1502E–1 9.8692E–2 1.9697E+0
10
(7.45E–2) (9.62E–1) – (6.04E–1) – (6.21E–2) – (6.52E–1) – (3.30E–1) – (1.11E–1) + (3.33E–1) –
3.1577E–1 9.5553E–1 1.9657E+0 3.4408E–1 6.1859E–1 4.1840E+0 3.7859E–1 2.7613E+0
15
(1.18E–1) (4.80E–1) – (4.08E–1) – (4.89E–2) – (6.70E–2) – (1.49E+0) – (1.99E–1) – (5.05E–1) –
3.4380E–1 5.0266E+0 1.7892E+0 3.8950E–1 6.2069E–1 3.7691E+0 2.3879E–1 3.6442E+0
20
(8.85E–2) (1.49E+0) – (4.24E–1) – (5.41E–2) – (1.20E–1) – (1.80E+0) – (1.84E–5) + (7.39E–1) –
2.8423E–1 2.4341E–1 1.8077E–1 2.9288E–1 4.7072E–1 2.4657E–1 4.4063E–1 5.3515E–1
4
(1.62E–1) (6.70E–2) = (9.27E–2) = (1.52E–1) – (2.63E–1) – (7.43E–2) + (1.83E–1) – (4.39E–1) –
4.8491E–1 5.2044E–1 4.1047E–1 6.0894E–1 1.8803E+0 4.8930E–1 1.2888E+0 2.1103E+0
6
(9.02E–2) (2.15E–2) – (1.13E–2) + (1.79E–1) – (9.14E–1) – (9.74E–3) = (2.75E–1) – (6.09E–1) –
8.2499E–1 9.9353E–1 7.6044E–1 1.0877E+0 4.3103E+0 1.4236E+0 1.6565E+0 4.0956E+0
8
(1.24E–1) (8.44E–2) – (2.47E–2) = (3.82E–1) – (8.01E–1) – (1.52E–1) – (2.37E–1) – (3.60E–1) –
DTLZ7
9.9898E–1 2.5060E+0 1.2056E+0 1.8369E+0 3.8659E+0 3.1519E+0 2.0840E+0 5.6648E+0
10
(4.65E–2) (5.02E–1) – (5.96E–2) – (6.34E–1) – (1.19E+0) – (1.18E–1) – (2.95E–1) – (2.78E–1) –
1.4489E+0 8.0893E+0 2.4294E+0 3.9662E+0 1.1266E+1 9.1522E+0 6.1500E+0 1.3520E+1
15
(1.86E–2) (9.24E–1) – (2.73E–1) – (1.36E+0) – (7.20E–1) – (8.70E–1) – (8.49E–1) – (1.34E+0) –
1.8475E+0 1.4771E+1 4.2138E+0 1.1461E+1 1.4789E+1 1.3918E+1 3.4546E+0 8.0875E+1
20
(1.75E–2) (5.47E–1) – (7.29E–1) – (1.53E+0) – (1.04E+0) – (8.52E–1) – (4.08E–1) – (1.64E+1) –
+/=/– － 3/4/35 6/3/33 7/7/28 11/1/30 8/2/32 12/4/26 3/2/37