Complexity / 2019 / Article / Tab 5

Research Article

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.

ProblemMOEA/D-STMMOEA/D-M2MMOEA/D-AWAMOEA/D-PaSMOEA/D-MUP

F14.84E-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)
F24.78E-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)
F34.71E-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)
F44.63E-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)
F54.73E-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)
F64.51E-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)
F73.49E-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)
F87.97E-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)
F96.83E-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)
F106.67E-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)
F116.41E-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)
F126.23E-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)
F136.06E-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)
F145.88E-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)
F154.81E-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)
F169.16E-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)
+/-/=0/16/01/13/20/16/00/16/0

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.

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