Evolutionary Search with Multiple Utopian Reference Points in Decomposition-Based Multiobjective Optimization
Table 5
Mean and standard deviation of IH 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
4.84E-01 (4.07E-03)-
4.86E-01 (3.43E-03)-
4.35E-01 (1.19E-03)-
4.80E-01 (2.94E-03)-
4.95E-01 (2.93E-04)
F2
4.78E-01 (3.77E-03)-
4.80E-01 (4.69E-03)-
4.32E-01 (1.26E-03)-
4.77E-01 (2.22E-03)-
4.95E-01 (2.81E-04)
F3
4.71E-01 (6.77E-03)-
4.81E-01 (3.98E-03)-
3.90E-01 (1.77E-03)-
4.67E-01 (3.34E-03)-
4.93E-01 (4.57E-04)
F4
4.63E-01 (5.40E-03)-
4.76E-01 (5.16E-03)-
3.86E-01 (1.57E-03)-
4.63E-01 (3.18E-03)-
4.93E-01 (9.87E-04)
F5
4.73E-01 (1.80E-02)-
4.73E-01 (8.50E-03)-
3.34E-01 (1.80E-03)-
4.32E-01 (6.19E-02)-
4.92E-01 (7.98E-04)
F6
4.51E-01 (1.74E-02)-
4.69E-01 (8.67E-03)-
3.28E-01 (1.68E-03)-
3.78E-01 (1.10E-01)-
4.90E-01 (1.42E-03)
F7
3.49E-01 (7.79E-03)-
3.92E-01 (1.19E02)+
3.04E-01 (1.14E-02)-
3.21E-01 (5.39E-02)-
3.56E-01 (4.01E-03)
F8
7.97E-01 (5.39E-03)-
8.10E-01 (5.14E-03)-
7.33E-01 (1.40E-03)-
7.78E-01 (7.00E-02)-
8.24E-01 (3.87E-03)
F9
6.83E-01 (1.98E-02)-
6.60E-01 (1.36E-02)-
6.99E-01 (3.22E-03)-
7.09E-01 (1.37E-02)-
7.38E-01 (7.61E-03)
F10
6.67E-01 (4.42E-03)-
6.45E-01 (6.63E-03)-
6.91E-01 (2.99E-03)-
6.92E-01 (6.82E-03)-
7.26E-01 (6.19E-03)
F11
6.41E-01 (3.00E-02)-
6.39E-01 (2.69E-02)-
6.47E-01 (4.72E-03)-
6.72E-01 (1.22E-02)-
7.00E-01 (8.77E-03)
F12
6.23E-01 (6.72E-03)-
6.23E-01 (2.90E-02)-
6.39E-01 (3.32E-03)-
6.61E-01 (1.42E-02)-
6.89E-01 (8.42E-03)
F13
6.06E-01 (5.73E-02)-
6.40E-01 (2.84E02)=
5.74E-01 (2.90E-03)-
6.28E-01 (2.39E-02)-
6.50E-01 (7.62E-03)
F14
5.88E-01 (4.53E-02)-
6.33E-01 (3.94E02)=
5.65E-01 (3.76E-03)-
6.15E-01 (1.35E-02)-
6.39E-01 (9.76E-03)
F15
4.81E-01 (6.37E-03)-
4.03E-01 (8.49E-03)-
4.56E-01 (9.47E-03)-
4.84E-01 (5.15E-03)-
4.90E-01 (4.29E-03)
F16
9.16E-01 (3.50E-03)-
9.26E-01 (2.18E-03)-
9.36E-01 (1.35E-03)-
9.31E-01 (2.83E-03)-
9.59E-01 (1.51E-03)
+/-/=
0/16/0
1/13/2
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.
