Research Article
Kriging-Based Space Exploration Global Optimization Method in Aerodynamic Design
Table 3
Average number of function evaluations (over 30 trials) to get a relative error of <1%.
| | Problems | KSE | MLSL-SQP | MPS | MADS | EGO | The best-published results from the comparison of TR-ARSM, MSSR, AQUARS, and TRIKE-Restart | | Results | | Results | | Results | | Results | | Results | | Results | Algorithm |
| | Branin | 22.7 (3.69) | 30 | 24.4 (1.52) | 30 | 57.3 (2.15) | 30 | 31.5 (1.35) | 30 | 40.8 (2.33) | 30 | 25.6 | TRIKE-restart | | Goldstein-Price | 43.6 (4.31) | 30 | 56.8 (9.63) | 30 | 132.4 (6.25) | 30 | 63.6 (4.77) | 30 | 98.5 (10.77) | 30 | 36.2 | TR-ARSM | | Hartman3 | 23.4 (2.21) | 30 | 42.3 (3.36) | 30 | >38.9(-) | 27 | 41.7 (2.55) | 30 | 42.1 (3.88) | 30 | 26.5 | TRIKE-restart | | Shekel5 | 164.9 (33.3) | 30 | >368.9(-) | 25 | >446.3(-) | 5 | 213.5 (37.1) | 30 | >139.9(-) | 9 | 202.4 | TRIKE-restart | | Hartman6 | 131.1 (11.4) | 30 | 157.1 (12.6) | 30 | >500(-) | 0 | 144.6 (13.62) | 30 | 154.2 (9.63) | 30 | 54.5 | MSSR | | SC | 21.6 (3.46) | 30 | 37.5 (2.77) | 30 | 32.3 (5.66) | 30 | 26.4 (2.11) | 30 | 49 (6.37) | 30 | 22.5 | MSSR | | Shekel7 | 144.3 (22.5) | 30 | >362.3(-) | 22 | >137.6(-) | 13 | 168.5 (19.5) | 30 | >500 (30) | 0 | 152.7 | AQUARS | | Shekel10 | 137.5 (9.62) | 30 | >414.2(-) | 17 | >455.7(-) | 7 | 136.8 (11.2) | 30 | >500 (30) | 0 | 121.1 | AQUARS | | Shubert | 124.5 (11.3) | 30 | 237.1 (21.7) | 30 | >500(-) | 0 | 143.7 (12.6) | 30 | >437.5 (22) | 8 | 122.9 | MSSR | | Trid10 | 114.7 (13.5) | 30 | 189.4 (11.4) | 30 | 125.2 (5.74) | 30 | 145.6 (4.55) | 30 | >500 (30) | 0 | 142.4 | MSSR | | Sphere10 | 107.6 (9.85) | 30 | 172.5 (8.96) | 30 | 131.5 (9.68) | 30 | 177.6 (11.12) | 30 | >500 (30) | 0 | 115.4 | MSSR | | F16 | 135.2 (8.57) | 30 | 165.1 (7.3) | 30 | >500(-) | 0 | 159.7 (8.55) | 30 | 337.4 (15.9) | 30 | 137.7 | MSSR |
|
|
