Table 8.
Results of HV for considered MO algorithms on ZDT benchmark problems.
| Problem | FE | MOSCA | MODA | MOWHO | MOMFO | NSGA-II | DEMO | MOCS | MOCS2Arc |
|---|---|---|---|---|---|---|---|---|---|
| ZDT1 | 10,000 | 6.9594e–1 (5.99e–3) – | 1.7165e–1 (7.41e–2) – | 5.4817e–1 (2.53e–2) – | 5.5701e–1 (4.32e–2) – | 7.0541e–1 (3.14e–3) = | 6.7620e–1 (6.57e–2) = | 7.0570e–1 (3.50e–3) = | 7.0708e-1 (3.32e-3) |
| ZDT2 | 10,000 | 3.9970e–1 (2.24e–2) – | 0.0000e + 0 (0.00e + 0) – | 2.2055e–1 (3.56e–2) – | 3.4876e–2 (7.16e–2) – | 4.1847e–1 (2.33e–2) = | 2.0055e–1 (9.95e–2) – | 4.1890e–1 (2.55e–2) = | 4.2010e-1 (1.92e-2) |
| ZDT3 | 10,000 | 5.9948e–1 (3.16e–2) + | 2.8124e–1 (6.51e–2) – | 4.8256e–1 (2.89e–2) – | 5.3523e–1 (3.63e–2) – | 5.9245e–1 (1.88e–3) = | 6.1319e–1 (5.50e–2) + | 5.9496e–1 (1.66e–2) = | 5.9780e–1 (2.30e–2) |
| ZDT4 | 10,000 | 2.4013e–1 (1.68e–1) – | 0.0000e + 0 (0.00e + 0) – | 3.2122e–2 (9.18e–2) – | 4.0462e–2 (8.07e–2) – | 5.1933e–1 (1.47e–1) = | 0.0000e + 0 (0.00e + 0) – | 2.3181e–1 (1.39e–1) – | 4.9915e–1 (1.58e–1) |
| ZDT5 | 10,000 | 7.7699e–1 (3.96e–3) – | 7.8458e–1 (9.61e–3) = | 7.4650e–1 (1.41e–2) – | 7.8314e–1 (9.72e–3) = | 7.8564e–1 (8.33e–3) = | 8.3456e–1 (2.21e–2) + | 7.3314e–1 (1.20e–2) – | 7.8273e–1 (6.11e–3) |
| ZDT6 | 10,000 | 1.7020e–1 (5.66e–2) – | 2.7901e–1 (1.49e–1) = | 8.8886e–2 (4.13e–2) – | 3.3483e–2 (5.49e–2) – | 3.1493e–1 (4.04e–2) = | 3.0111e–1 (1.18e–1) = | 1.8934e–1 (5.90e–2) – | 3.2383e–1 (3.10e–2) |
| + /-/ = | 1/5/0 | 0/4/2 | 0/6/0 | 0/5/1 | 0/0/6 | 2/2/2 | 0/3/3 | ||