Table 6 Average and standard deviation of the HV values obtained by the five algorithms on the DTLZ test suite with different numbers of objectives.
From: An improved farmland fertility algorithm for many-objective optimization problems
Text Suite | M | NSGA-III | MOEA/D | RVEA | ARMOEA | MOIFF |
|---|---|---|---|---|---|---|
DTLZ1 | 3 | 8.40E−01 (1.85E−03)− | 8.38E−01 (2.55E−03)− | 8.40E−01 (1.51E−03)− | 8.40E−01 (1.57E−03)− | 9.60E−01 (3.48E−02) |
5 | 9.80E−01 (1.77E−04)− | 9.80E−01 (1.87E−04)− | 9.80E−01 (1.44E−04)− | 9.80E−01 (1.53E−04)− | 9.98E−01 (1.89E−03) | |
8 | 9.88E−01 (4.43E−02)− | 9.97E−01 (1.34E−04)− | 9.98E−01 (5.52E−05)− | 9.98E−01 (6.10E−05)− | 1.00E + 00 (1.99E−04) | |
10 | 9.96E−01 (1.73E−02) =  | 1.00E + 00 (2.73E−05) =  | 1.00E + 00 (1.56E−05) =  | 1.00E + 00 (2.10E−05) =  | 9.99E−01 (6.63E−04) | |
15 | 9.87E−01 (1. 69E−02) =  | 1.00E + 00 (2.73E−04)− | 1.00E + 00 (1.26E−05) +  | 1.00E + 00 (5.47E−05) +  | 1.00E + 00 (2.07E−04) | |
DTLZ2 | 3 | 5.59E−01 (7.35E−05)− | 5.59E−01 (6.76E−05)− | 5.59E−01 (2.95E−04)− | 5.59E−01 (1.84E−04)− | 9.26E−01 (2.96E−03) |
5 | 8.12E−01 (4.27E−04)− | 8.12E−01 (4.57E−04)− | 8.12E−01 (3.97E−04)− | 8.12E−01 (3.82E−04)− | 9.90E−01 (9.91E−04) | |
8 | 9.14E−01 (2.81E−02)− | 9.24E−01 (2.69E−04)− | 9.24E−01 (2.41E−04)− | 9.25E−01 (4.83E−04)− | 9.99E−01 (2.27E−03) | |
10 | 9.30E−01 (4.26E−02)− | 9.70E−01 (1.85E−04)− | 9.70E−01 (1.82E−04)− | 9.71E−01 (1.94E−04)− | 1.00E + 00 (1.05E−03) | |
15 | 8.55E−01 (6.01E−02)− | 9.91E−01 (1.30E−04)− | 9.90E−01 (2.21E−03)− | 9.91E−01 (5.50E−04)− | 1.00E + 00 (1.80E−05) | |
DTLZ3 | 3 | 5.55E−01 (2.89E−03)− | 5.54E−01 (4.35E−03)− | 5.55E−01 (3.15E−03)− | 5.55E−01 (3.39E−03)− | 8.81E−01 (1.33E−01) |
5 | 8.11E−01 (2.35E−03)− | 8.10E−01 (1.88E−03)− | 8.12E−01 (6.77E−04)− | 8.11E−01 (1.77E−03)− | 9.89E−01 (2.41E−03) | |
8 | 7.65E−01 (3.12E−01)− | 8.22E−01 (2.30E−01)− | 9.22E−01 (1.70E−03)− | 9.26E−01 (2.85E−03)− | 9.96E−01 (4.74E−03) | |
10 | 8.40E−01 (2.80E−01)− | 9.70E−01 (6.71E−04)− | 9.70E−01 (3.72E−04)− | 9.71E−01 (3.71E−03)− | 1.00E + 00 (4.97E−04) | |
15 | 0.00E + 00 (0.00E + 00)− | 5.18E−01 (4.41E−01)− | 9.91E−01 (1.33E−04)− | 9.82E−01 (5.05E−03)− | 1.00E + 00 (6.70E−05) | |
DTLZ4 | 3 | 4.56E−01 (1.26E−01)− | 4.13E−01 (1.65E−01)− | 5.52E−01 (3.95E−02)− | 4.64E−01 (1.38E−01)− | 8.76E−01 (6.36E−02) |
5 | 8.09E−01 (2.03E−02)− | 7.43E−01 (8.12E−02)− | 8.13E−01 (4.30E−04)− | 8.09E−01 (1.69E−02)− | 9.80E−01 (1.99E−02) | |
8 | 8.97E−01 (4.70E−02)− | 8.68E−01 (4.18E−02)− | 9.22E−01 (5.72E−03)− | 9.25E−01 (3.41E−04)− | 9.97E−01 (3.98E−03) | |
10 | 9.63E−01 (2.13E−02)− | 9.43E−01 (2.42E−02)− | 9.70E−01 (1.97E−04)− | 9.70E−01 (1.84E−04)− | 1.00E + 00 (2.08E−04) | |
15 | 8.97E−01 (4.70E−02)− | 9.70E−01 (1.43E−02)− | 9.90E−01 (1.48E−03)− | 9.91E−01 (1.42E−04)− | 1.00E + 00 (1.80E−05) | |
DTLZ5 | 3 | 1.94E−01 (1.11E−03)− | 1.82E−01 (1.05E−05)− | 1.56E−01 (6.29E−03)− | 1.99E−01 (1.16E−04)− | 7.26E−01 (3.45E−03) |
5 | 1.14E−01 (4.05E−03)− | 1.27E−01 (3.49E−04)− | 1.06E−01 (2.79E−03)− | 1.14E−01 (1.83E−03)− | 6.55E−01 (7.12E−03) | |
8 | 2.88E−02 (3.24E−02)− | 1.04E−01 (3.84E−04)− | 9.09E−02 (4.36E−05)− | 9.17E−02 (2.41E−03)− | 6.23E−01 (6.25E−03) | |
10 | 1.33E−02 (2.64E−02)− | 1.00E−01 (3.87E−04)− | 9.09E−02 (8.85E−05)− | 8.86E−02 (1.67E−03)− | 6.24E−01 (6.73E−03) | |
15 | 9.04E−02 (3.03E−03)− | 9.44E−02 (2.27E−04)− | 9.09E−02 (2.42E−04)− | 9.12E−02 (5.54E−04)− | 6.01E−01 (9.33E−03) | |
DTLZ6 | 3 | 1.90E−01 (1.48E−03)− | 1.82E−01 (1.26E−05)− | 1.46E−01 (1.10E−02)− | 2.00E−01 (6.13E−05)− | 7.18E−01 (5.37E−03) |
5 | 9.76E−02 (1.78E−02)− | 1.27E−01 (1.78E−03)− | 8.67E−02 (3.39E−02)− | 1.09E−01 (5.81E−03)− | 6.61E−01 (4.19E−03) | |
8 | 5.14E−02 (4.35E−02)− | 1.04E−01 (2.93E−04)− | 9.39E−02 (1.42E−03)− | 9.24E−02 (1.37E−03)− | 6.19E−01 (5.69E−03) | |
10 | 3.03E−03 (1.63E−02)− | 9.99E−02 (2.35E−04)− | 9.23E−02 (7.82E−04)− | 9.18E−02 (7.95E−04)− | 6.14E−01 (6.80E−03) | |
15 | 0.00E + 00 (0.00E + 00)− | 9.44E−02 (3.15E−04)− | 8.95E−02 (8.17E−03)− | 9.15E−02 (6.17E−04)− | 5.88E−01 (1.77E−02) | |
DTLZ7 | 3 | 2.68E−01 (1.02E−02)− | 2.47E−01 (6.21E−03)− | 2.65E−01 (1.76E−03)− | 2.49E−01 (2.38E−02)− | 4.10E−01 (7.32E−02) |
5 | 2.53E−01 (4.72E−03)− | 1.47E−01 (1.26E−02)− | 2.20E−01 (2.89E−03)− | 2.54E−01 (1.81E−03)− | 4.41E−01 (1.24E−02) | |
8 | 2.01E−01 (4.29E−03)− | 4.17E−03 (1.52E−02)− | 1.55E−01 (2.37E−02)− | 1.87E−01 (2.88E−03)− | 3.47E−01 (8.37E−03) | |
10 | 1.87E−01 (7.01E−03)− | 7.97E−06 (2.37E−05)− | 1.45E−01 (2.95E−02)− | 1.67E−01 (8.07E−03)− | 3.13E−01 (6.30E−03) | |
15 | 1.40E−01 (1.04E−02)− | 2.46E−04 (1.27E−03)− | 1.20E−01 (5.26E−03)− | 7.16E−02 (1.62E−02)− | 1.67E−01 (1.87E−02) | |
+/=/− |  | 0/2/33 | 0/1/34 | 1/1/33 | 1/1/33 |  |
