Evolutionary Search with Multiple Utopian Reference Points in Decomposition-Based Multiobjective Optimization
Table 4
Mean and standard deviation of IGD values obtained by four representative MOEA/Ds and MOEA/D-MUP.
Problem
MOEA/D-STM
MOEA/D-M2M
MOEA/D-AWA
MOEA/D-PaS
MOEA/D-MUP
F1
1.47E-02 (4.39E-03)-
8.58E-03 (2.01E-03)-
8.43E-02 (2.18E-03)-
1.74E-02 (2.19E-03)-
2.87E-03 (1.44E-04)
F2
2.14E-02 (4.00E-03)-
1.25E-02 (2.80E-03)-
8.95E-02 (2.12E-03)-
2.07E-02 (2.09E-03)-
3.02E-03 (1.50E-04)
F3
2.80E-02 (7.22E-03)-
1.07E-02 (2.18E-03)-
1.47E-01 (3.64E-03)-
3.12E-02 (3.03E-03)-
3.56E-03 (2.52E-04)
F4
3.81E-02 (6.41E-03)-
1.41E-02 (3.25E-03)-
1.54E-01 (2.54E-03)-
3.59E-02 (2.67E-03)-
4.00E-03 (5.85E-04)
F5
2.61E-02 (1.95E-02)-
1.52E-02 (4.28E-03)-
2.29E-01 (3.30E-03)-
7.30E-02 (7.81E-02)-
4.58E-03 (4.94E-04)
F6
5.16E-02 (1.96E-02)-
1.75E-02 (4.56E-03)-
2.37E-01 (3.00E-03)-
1.39E-01 (1.37E-01)-
5.49E-03 (8.24E-04)
F7
1.73E-01 (1.16E-02)=
6.62E-02 (8.57E03)+
2.54E-01 (1.90E-02)-
2.02E-01 (6.36E-02)-
1.71E-01 (9.01E-03)
F8
4.41E-02 (9.46E-03)-
2.16E-02 (6.39E-03)-
1.90E-01 (2.92E-03)-
5.84E-02 (5.55E-02)-
8.41E-03 (2.91E-03)
F9
4.51E-02 (2.60E-03)-
7.07E-02 (2.40E-03)-
4.96E-02 (2.15E-03)-
4.18E-02 (2.42E-03)-
3.56E-02 (8.63E-04)
F10
4.75E-02 (1.47E-03)-
7.39E-02 (2.33E-03)-
5.17E-02 (2.22E-03)-
4.52E-02 (3.95E-03)-
3.64E-02 (1.11E-03)
F11
6.05E-02 (6.23E-03)-
8.91E-02 (5.95E-03)-
6.91E-02 (3.65E-03)-
5.27E-02 (4.14E-03)-
4.20E-02 (1.74E-03)
F12
6.49E-02 (2.65E-03)-
9.83E-02 (1.03E-02)-
7.25E-02 (2.49E-03)-
5.96E-02 (5.30E-03)-
4.41E-02 (1.90E-03)
F13
7.92E-02 (1.28E-02)-
9.35E-02 (1.04E-02)-
1.06E-01 (3.93E-03)-
7.12E-02 (7.55E-03)-
5.60E-02 (2.69E-03)
F14
8.45E-02 (1.02E-02)-
9.93E-02 (1.65E-02)-
1.13E-01 (5.05E-03)-
8.06E-02 (2.07E-02)-
5.99E-02 (3.59E-03)
F15
1.40E-01 (3.81E-03)-
2.14E-01 (5.36E-03)-
1.72E-01 (8.14E-03)-
1.45E-01 (5.10E-03)-
1.37E-01 (5.16E-03)
F16
7.10E-02 (5.00E-03)-
5.16E-02 (2.78E-03)-
8.78E-02 (6.21E-03)-
6.85E-02 (4.07E-03)-
3.72E-02 (3.25E-03)
+/-/=
0/15/1
1/15/0
0/16/0
0/16/0
∖
According to Wilcoxon’s rank sum test with a significant level , +, − and = indicate that the corresponding MOEA is significantly better than, worse than or similar to MOEA/D-MUP.
