Table 6.
HV values for 5 MOPSO and ASDMOPSO.
| Problem | M | D | CMOPSO | NMPSO | MOPSOCD | MOPSO | MPSOD | ASDMOPSO | |
|---|---|---|---|---|---|---|---|---|---|
| ZDT1 | 2 | 30 |
Mean Std |
7.1997e−1 (5.99e−4)− |
6.8912e−1 (1.27e−2)− |
7.2098e−1 (1.21e−3)≈ |
0.0000e + 0 (0.00e + 0)− |
5.9247e−1 (4.19e−2)− |
7.2129e−01 (6.03e−05) |
| ZDT2 | 2 | 30 |
Mean Std |
4.4443e−1 (1.05e−3)− |
4.3373e−1 (1.34e−2)− |
3.5891e−1 (1.42e−1)− |
0.0000e + 0 (0.00e + 0)− |
2.8091e−1 (8.73e−2)− |
4.4657e−01 (2.05e−05) |
| ZDT3 | 2 | 30 |
Mean Std |
5.9994e−1 (1.39e−3)− |
5.7102e−1 (7.16e−3)− |
5.8591e−1 (2.77e−2)− |
6.5564e−4 (1.75e−3)− |
4.6280e−1 (4.59e−2)− |
6.0005e−01 (1.37e−04) |
| ZDT4 | 2 | 10 |
Mean Std |
0.0000e + 0 (0.00e + 0)− |
0.0000e + 0 (0.00e + 0)− |
0.0000e + 0 (0.00e + 0)− |
0.0000e + 0 (0.00e + 0)− |
6.9846e−01 (1.33e−01) |
|
| ZDT6 | 2 | 10 |
Mean Std |
3.9035e−1 (4.98e−5) + |
3.8978e−1 (2.06e−4)− |
3.8905e−1 (1.22e−3)− |
0.0000e + 0 (0.00e + 0)− |
3.7749e−1 (8.73e−3)− |
3.9015e−01 (1.31e−05) |
| UF1 | 2 | 30 |
Mean Std |
5.7482e−1 (1.77e−2) + |
5.3366e−1 (2.34e−2)− |
9.2488e−2 (9.05e−2)− |
1.7961e−1 (5.35e−2)− |
3.6349e−1 (5.50e−2)− |
4.9805e−01 (1.61e−02) |
| UF2 | 2 | 30 |
Mean Std |
6.4681e−1 (7.49e−3) + |
6.1819e−1 (6.27e−3)− |
5.3943e−1 (2.07e−2)− |
6.1132e−1 (8.75e−3)− |
5.7994e−1 (1.11e−2)− |
6.4061e−01 (4.58e−03) |
| UF3 | 2 | 30 |
Mean Std |
2.6683e−1 (3.81e−2)− |
2.8723e−1 (4.79e−2)− |
2.2645e−1 (7.63e−2)− |
1.7937e−1 (2.64e−2)− |
1.7360e−1 (1.69e−2)− |
3.4111e−01 (3.21e−02) |
| UF4 | 2 | 30 |
Mean Std |
2.8868e−1 (1.20e−2) |
3.6166e−1 (1.28e−2) + |
3.3391e−1 (1.08e−2)− |
2.1306e−1 (4.15e−3)− |
3.0658e−1 (4.40e−3)− |
1.2726e−01 (3.36e−03) |
| UF5 | 2 | 30 |
Mean Std |
9.4110e−3 (2.20e−2) + |
0.0000e + 0 (0.00e + 0)≈ |
0.0000e + 0 (0.00e + 0)≈ |
0.0000e + 0 (0.00e + 0)≈ |
0.0000e + 0 (0.00e + 0)≈ |
0.0000e + 00 (0.00e + 0) |
| UF6 | 2 | 30 |
Mean Std |
1.5727e−1 (5.15e−2) + |
2.2070e−2 (3.27e−2)≈ |
0.0000e + 0 (0.00e + 0)− |
0.0000e + 0 (0.00e + 0)− |
0.0000e + 00(0.00e + 0)− |
7.1557e−03 (6.25e−02) |
| UF7 | 2 | 30 |
Mean Std |
4.5126e−1 (7.87e−2) + |
3.9036e−1 (9.47e−2)≈ |
2.6253e−2 (3.79e−2)− |
3.8297e−2 (2.33e−2)− |
2.7589e−1 (5.15e−2)− |
4.1627e−01 (1.26e−02) |
| UF8 | 3 | 30 |
Mean Std |
1.8293e−2 (1.78e−2)− |
2.7633e−1 (6.28e−2)− |
1.0132e−2 (1.28e−2)− |
2.5649e−1 (3.32e−2)− |
5.7408e−2 (1.93e−2)− |
3.4690e−01 (2.89e−02) |
| UF9 | 3 | 30 |
Mean Std |
1.8081e−2 (2.69e−2)− |
3.1197e−1 (5.18e−2) + |
3.0344e−2 (3.39e−2) |
2.5578e−1 (2.39e−2)− |
1.1504e−1 (2.81e−2)− |
2.8639e−01 (2.11e−02) |
| UF10 | 3 | 30 |
Mean Std |
0.0000e + 0 ( 0.00e + 0)− |
0.0000e + 0 (0.00e + 0)− |
0.0000e + 0 (0.00e + 0)− |
0.0000e + 0 (0.00e + 0)− |
0.0000e + 0 (0.00e + 0)− |
2.7421e−01 (3.86e−02) |
| DTLZ1 | 3 | 7 |
Mean Std |
0.0000e + 0 (0.00e + 0)− |
0.0000e + 0 (0.00e + 0)− |
0.0000e + 0 (0.00e + 0)− |
0.0000e + 0 (0.00e + 0)− |
0.0000e + 0 (0.00e + 0)− |
5.9780e−04 (6.98e + 00) |
| DTLZ2 | 3 | 12 |
Mean Std |
5.5924e−1 (1.11e−3)− |
5.6875e−1 (9.49e−4) + |
4.7859e−1 (1.87e−2)− |
5.4019e−1 (7.15e−3)− |
5.4961e−1 (2.17e−3)− |
4.1042e−02 (8.54e−03) |
| DTLZ3 | 3 | 12 |
Mean Std |
0.0000e + 0 (0.00e + 0)− |
0.0000e + 0 (0.00e + 0)− |
0.0000e + 0 (0.00e + 0)− |
0.0000e + 0 (0.00e + 0)− |
0.0000e + 0 (0.00e + 0)− |
4.1886e−03 (2.53e + 01) |
| DTLZ4 | 3 | 12 |
Mean Std |
5.4030e−1 (8.49e−2)− |
5.5358e−1 (5.63e−2) + |
2.8241e−1 (5.10e−2)− |
4.6129e−1 (6.25e−2)− |
4.2632e−1 (4.24e−2)− |
3.7090e−01 (8.65e−01) |
| DTLZ5 | 3 | 12 |
Mean Std |
1.9895e−1 (2.56e−4) + |
1.9818e−1 (3.83e−4)− |
1.7164e−1 (9.56e−3)− |
1.9858e−1 (9.37e−4)− |
1.4248e−1 (7.36e−3)− |
2.4535e−02 (1.29e + 00) |
| DTLZ6 | 3 | 12 |
Mean Std |
1.6476e−1 (7.55e−2)− |
1.9804e−1 (6.40e−4) + |
1.7311e−1 (5.43e−2)− |
0.0000e + 0 (0.00e + 0)− |
5.8464e−3 (1.80e−2)− |
1.3678e−02 (1.99e−04) |
| DTLZ7 | 3 | 22 |
Mean Std |
2.6967e−1 (1.30e−2)− |
2.8095e−1 (6.92e−4) + |
2.6843e−1 (7.06e−3)− |
0.0000e + 0 (0.00e + 0)− |
7.1984e−2 (4.17e−2)− |
1.6227e−01 (2.03e−02) |
| Best/all | 7/22 | 6/22 | 0/22 | 0/22 | 0/22 | 9/22 | |||
| ± /≈ | 7/15/0 | 6/13/3 | 0/20/2 | 0/21/1 | 0/21/1 | – |