Evolutionary Search with Multiple Utopian Reference Points in Decomposition-Based Multiobjective Optimization
Table 2
Mean and standard deviation of IGD values obtained by four classical algorithms and MOEA/D-MUP.
Problem
NSGA-II
SMS-EMOA
MOEA/D-DRA
MOEA/D-DRA-UT
MOEA/D-MUP
F1
2.73E-02 (3.07E-03)-
3.43E-02 (5.81E-03)-
1.88E-02 (1.59E-03)-
3.93E-03 (3.07E-03)-
2.87E-03 (1.44E-04)
F2
3.28E-02 (2.75E-03)-
4.47E-02 (3.22E-03)-
2.90E-02 (1.86E-03)-
4.02E-03 (2.75E-03)-
3.02E-03 (1.50E-04)
F3
4.84E-02 (7.66E-03)-
6.39E-02 (9.64E-03)-
3.80E-02 (3.39E-03)-
5.09E-03 (7.66E-03)-
3.56E-03 (2.52E-04)
F4
5.73E-02 (6.22E-03)-
7.50E-02 (5.05E-03)-
4.48E-02 (2.94E-03)-
5.21E-03 (6.22E-03)-
4.00E-03 (5.85E-04)
F5
6.35E-02 (2.13E-02)-
8.43E-02 (2.54E-02)-
6.34E-02 (1.22E-02)-
5.14E-03 (2.13E-02)-
4.58E-03 (4.94E-04)
F6
8.19E-02 (1.99E-02)-
1.13E-01 (1.55E-02)-
7.10E-02 (8.72E-03)-
6.19E-03 (1.99E-02)-
5.49E-03 (8.24E-04)
F7
1.92E-01 (1.07E-02)-
1.77E-01 (6.64E-03)-
1.74E-01 (4.10E-03)=
1.35E-01 (1.07E-02)+
1.71E-01 (9.01E-03)
F8
5.86E-02 (1.60E-02)-
9.17E-02 (1.65E-02)-
6.32E-02 (2.26E-03)-
6.14E-03 (1.60E-02)+
8.41E-03 (2.91E-03)
F9
1.35E-01 (2.27E-02)-
1.02E-01 (7.36E-03)-
5.42E-02 (3.92E-02)-
4.97E-02 (2.27E-02)-
3.56E-02 (8.63E-04)
F10
1.29E-01 (2.31E-02)-
1.02E-01 (3.36E-03)-
5.66E-02 (3.54E-02)-
5.62E-02 (2.31E-02)-
3.64E-02 (1.11E-03)
F11
1.60E-01 (3.49E-02)-
1.16E-01 (3.48E-03)-
6.89E-02 (5.42E-02)-
6.17E-02 (3.49E-02)-
4.20E-02 (1.74E-03)
F12
1.65E-01 (2.51E-02)-
1.18E-01 (3.88E-03)-
7.40E-02 (4.19E-02)-
6.30E-02 (2.51E-02)-
4.41E-02 (1.90E-03)
F13
2.03E-01 (5.73E-02)-
1.36E-01 (1.27E-02)-
9.21E-02 (7.91E-02)-
7.32E-02 (5.73E-02)-
5.60E-02 (2.69E-03)
F14
1.88E-01 (2.89E-02)-
1.46E-01 (6.56E-03)-
9.80E-02 (3.27E-02)-
7.59E-02 (2.89E-02)-
5.99E-02 (3.59E-03)
F15
2.18E-01 (1.57E-02)-
1.99E-01 (3.88E-03)-
1.40E-01 (1.40E-02)-
1.37E-01 (1.57E-02)=
1.37E-01 (5.16E-03)
F16
5.35E-02 (9.17E-03)-
7.61E-02 (6.07E-03)-
6.58E-02 (7.53E-03)-
4.23E-02 (9.17E-03)-
3.72E-02 (3.25E-03)
+/-/=
0/16/0
0/16/0
0/15/1
2/13/1
∖
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.
