Table 5 Average and standard deviation of the IGD 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 | NSGAIII | MOEA/D | RVEA | ARMOEA | MOIFF |
|---|---|---|---|---|---|---|
DTLZ1 | 3 | 2.07E−02 (2.99E−04) +  | 2.10E−02 (4.73E−04) +  | 2.07E−02 (1.86E−04) +  | 2.08E−02 (2.27E−04) +  | 3.08E−02 (6.00E−02) |
5 | 5.27E−02 (4.60E−05)− | 5.28E−02 (8.10E−05)− | 5.27E−02 (2.80E−05)− | 5.27E−02 (5.62E−05)− | 2.42E−02 (4.39E−02) | |
8 | 1.06E−01 (2.94E−02)− | 9.63E−02 (3.28E−04)− | 9.71E−02 (2.71E−04)- | 9.90E−02 (5.84E−04)− | 2.45E−02 (2.10E−02) | |
10 | 1.15E−01 (2.37E−02)− | 1.09E−01 (1.85E−04)− | 1.08E−01 (2.90E−04)− | 1.12E−01 (1.21E−03)− | 9.14E−02 (4.82E−02) | |
15 | 2.04E−01 (2.37E−02) +  | 1.64E−01 (7.84E−03) +  | 1.77E−01 (5.60E−03) +  | 1.70E−01 (1.54E−02)− | 2.49E−01 (1.13E−02) | |
DTLZ2 | 3 | 5.45E−02 (1.45E−05)− | 5.45E−02 (3.84E−06)− | 5.46E−02 (1.60E−04)− | 5.46E−02 (7.97E−05)− | 2.43E−02 (9.89E−03) |
5 | 1.65E−01 (2.72E−05)− | 1.65E−01 (9.43E−06)− | 1.65E−01 (2.28E−05)− | 1.65E−01 (8.57E−05)− | 4.60E−02 (8.90E−03) | |
8 | 3.37E−01 (6.22E−02)− | 3.15E−01 (3.34E−05)− | 3.15E−01 (1.41E−04)− | 3.26E−01 (1.90E−03)− | 9.83E−02 (9.74E−02) | |
10 | 4.93E−01 (8.03E−02)− | 4.22E−01 (1.69E−04)− | 4.20E−01 (4.72E−04)− | 4.27E−01 (2.47E−03)− | 1.59E−01 (1.16E−01) | |
15 | 7.50E−01 (5.07E−02)− | 6.23E−01 (7.47E−04)− | 6.24E−01 (4.18E−03)− | 6.11E−01 (3.01E−03)− | 1.39E−01 (1.40E−01) | |
DTLZ3 | 3 | 5.48E−02 (3.04E−04) +  | 5.49E−02 (6.97E−04) +  | 5.48E−02 (3.88E−04) +  | 5.49E−02 (4.29E−04) +  | 1.19E−01 (2.50E−01) |
5 | 1.65E−01 (3.05E−04)− | 1.65E−01 (2.15E−04)− | 1.65E−01 (7.46E−05)− | 1.66E−01 (3.26E−03)− | 7.27E−02 (3.70E−02) | |
8 | 5.51E−01 (5.16E−01)− | 3.89E−01 (1.88E−01) =  | 3.16E−01 (4.96E−04) =  | 3.45E−01 (7.68E−03) =  | 2.83E−01 (1.84E−01) | |
10 | 6.50E−01 (6.61E−01)− | 4.22E−01 (1.06E−03)− | 4.20E−01 (7.19E−04)− | 4.29E−01 (4.27E−03)− | 2.25E−01 (1.79E−01) | |
15 | 1.99E + 01 (1.42E + 01)− | 9.40E−01 (2.98E−01)− | 6.23E−01 (1.26E−03)− | 6.14E−01 (8.73E−03)− | 5.12E−01 (9.88E−02) | |
DTLZ4 | 3 | 2.79E−01 (2.66E−01)− | 3.55E−01 (3.25E−01)− | 7.07E−02 (8.75E−02) =  | 2.60E−01 (2.86E−01)− | 2.19E−01 (2.57E−01) |
5 | 1.73E−01 (4.37E−02)− | 3.18E−01 (1.58E−01)− | 1.65E−01 (6.97E−06)− | 1.73E−01 (4.20E−02)− | 1.62E−01 (2.07E−01) | |
8 | 3.74E−01 (1.00E−01) =  | 4.82E−01 (9.67E−02)− | 3.23E−01 (2.80E−02) =  | 3.23E−01 (1.52E−03) =  | 2.94E−01 (1.76E−01) | |
10 | 4.38E−01 (4.80E−02)− | 5.19E−01 (6.77E−02)− | 4.21E−01 (4.41E−04)− | 4.27E−01 (2.48E−03)− | 1.62E−01 (1.40E−01) | |
15 | 7.31E−01 (5.09E−02)− | 6.84E−01 (3.13E−02)− | 6.25E−01 (1.63E−03)− | 6.07E−01 (2.42E−03)− | 3.21E−01 (1.11E−01) | |
DTLZ5 | 3 | 1.24E−02 (1.56E−03) +  | 3.39E−02 (1.83E−05)− | 7.03E−02 (8.02E−03)− | 5.42E−03 (1.25E−04) +  | 2.96E−02 (4.26E−03) |
5 | 9.03E−02 (3.22E−02) =  | 2.27E−02 (4.54E−06) +  | 1.99E−01 (1.90E−02)− | 5.50E−02 (7.22E−03) +  | 8.29E−02 (1.94E−02) | |
8 | 3.59E−01 (9.03E−02)− | 2.59E−02 (6.37E−06) +  | 3.60E−01 (4.04E−02)− | 1.04E−01 (2.51E−02) +  | 1.22E−01 (2.69E−02) | |
10 | 5.02E−01 (1.27E−01)− | 1.99E−02 (1.02E−05) +  | 3.08E−01 (3.64E−02)− | 9.14E−02 (1.39E−02) +  | 1.49E−01 (3.10E−02) | |
15 | 2.51E−01 (5.64E−02)− | 9.57E−02 (5.05E−06) +  | 3.06E−01 (9.70E−02)− | 1.12E−01 (1.98E−02) +  | 2.16E−01 (5.19E−02) | |
DTLZ6 | 3 | 2.00E−02 (2.70E−03) +  | 3.39E−02 (2.04E−05) +  | 8.53E−02 (1.60E−02)− | 5.00E−03 (6.98E−05) +  | 4.74E−02 (9.10E−03) |
5 | 1.66E−01 (7.91E−02)− | 2.26E−02 (1.71E−04) +  | 1.50E−01 (2.38E−02)− | 7.12E−02 (2.11E−02) +  | 7.78E−02 (1.19E−02) | |
8 | 6.59E−01 (3.43E−01)− | 2.53E−02 (5.79E−04) +  | 2.92E−01 (6.01E−02)− | 1.07E−01 (2.23E−02) +  | 1.43E−01 (1.86E−02) | |
10 | 2.66E + 00 (1.15E + 00)− | 1.90E−02 (4.56E−04) +  | 2.40E−01 (5.44E−02)− | 1.03E−01 (2.37E−02) +  | 1.42E−01 (1.90E−02) | |
15 | 4.90E + 00 (1.15E + 00)− | 9.57E−02 (2.53E−06) +  | 1.87E−01 (1.18E−02)− | 1.04E−01 (2.35E−02) +  | 1.82E−01 (7.98E−02) | |
DTLZ7 | 3 | 9.79E−02 (8.05E−02) +  | 1.51E−01 (4.39E−03) =  | 1.07E−01 (2.76E−03) =  | 3.06E−01 (2.33E−01) =  | 2.80E−01 (2.66E−01) |
5 | 2.79E−01 (1.02E−02) +  | 5.76E−01 (1.72E−01)− | 5.02E−01 (7.27E−03)− | 2.60E−01 (4.14E−03) +  | 3.46E−01 (3.90E−02) | |
8 | 7.81E−01 (2.26E−02) +  | 1.86E + 00 (2.16E−01)− | 1.89E + 00 (9.58E−02)− | 1.00E + 00 (5.71E−02) =  | 9.86E−01 (1.17E−01) | |
10 | 9.68E−01 (7.45E−02) +  | 3.01E + 00 (3.61E−01)− | 2.67E + 00 (1.71E−01)− | 1.49E + 00 (1.43E−01) +  | 2.11E + 00 (3.86E−01) | |
15 | 7.34E + 00 (1.05E + 00)− | 2.77E + 00 (2.93E−01) =  | 6.07E + 00 (8.95E−01)− | 5.03E + 00 (9.02E−01)− | 4.59E + 00 (2.58E + 00) | |
+/=/− |  | 9/2/24 | 12/3/20 | 3/4/28 | 14/4/17 |  |
