Complexity / 2019 / Article / Tab 3

Research Article

Evolutionary Search with Multiple Utopian Reference Points in Decomposition-Based Multiobjective Optimization

Table 3

Mean and standard deviation of IH values obtained by four classical algorithms and MOEA/D-MUP.

ProblemNSGA-IISMS-EMOAMOEA/D-DRAMOEA/D-DRA-UTMOEA/D-MUP

F14.70E-01 (1.59E-03)-4.65E-01 (3.24E-03)-4.80E-01 (3.07E-03)-4.93E-01 (1.02E-03)-4.95E-01 (2.93E-04)
F24.66E-01 (1.86E-03)-4.58E-01 (1.63E-03)-4.71E-01 (2.75E-03)-4.93E-01 (7.69E-04)-4.95E-01 (2.81E-04)
F34.50E-01 (3.39E-03)-4.39E-01 (4.60E-03)-4.64E-01 (7.66E-03)-4.91E-01 (2.66E-03)-4.93E-01 (4.57E-04)
F44.45E-01 (2.94E-03)-4.31E-01 (2.38E-03)-4.57E-01 (6.22E-03)-4.91E-01 (2.38E-03)-4.93E-01 (9.87E-04)
F54.31E-01 (1.22E-02)-4.14E-01 (1.21E-02)-4.42E-01 (2.13E-02)-4.91E-01 (1.28E-03)-4.92E-01 (7.98E-04)
F64.19E-01 (8.72E-03)-3.98E-01 (6.95E-03)-4.36E-01 (1.99E-02)-4.89E-01 (2.22E-03)=4.90E-01 (1.42E-03)
F73.27E-01 (4.10E-03)-3.29E-01 (2.78E-03)-3.35E-01 (1.07E-02)-3.64E-01 (1.10E-02)+3.56E-01 (4.01E-03)
F87.93E-01 (2.26E-03)-7.81E-01 (2.23E-03)-7.83E-01 (1.60E-02)-8.25E-01 (2.79E-03)=8.24E-01 (3.87E-03)
F95.72E-01 (3.92E-02)-6.16E-01 (2.45E-02)-6.76E-01 (2.27E-02)-7.40E-01 (2.53E-02)=7.38E-01 (7.61E-03)
F105.60E-01 (3.54E-02)-5.97E-01 (1.08E-02)-6.70E-01 (2.31E-02)-6.99E-01 (1.08E-02)-7.26E-01 (6.19E-03)
F115.21E-01 (5.42E-02)-5.71E-01 (3.13E-02)-6.34E-01 (3.49E-02)-6.92E-01 (2.56E-02)-7.00E-01 (8.77E-03)
F125.04E-01 (4.19E-02)-5.57E-01 (1.89E-02)-6.22E-01 (2.51E-02)-6.73E-01 (1.42E-02)-6.89E-01 (8.42E-03)
F134.54E-01 (7.91E-02)-5.37E-01 (6.65E-02)-5.80E-01 (5.73E-02)-6.48E-01 (1.63E-02)=6.50E-01 (7.62E-03)
F144.58E-01 (3.27E-02)-5.02E-01 (3.22E-02)-5.69E-01 (2.89E-02)-6.36E-01 (1.54E-02)=6.39E-01 (9.76E-03)
F154.13E-01 (1.40E-02)-4.17E-01 (3.52E-03)-4.75E-01 (1.57E-02)-4.91E-01 (5.18E-03)=4.90E-01 (4.29E-03)
F169.18E-01 (7.53E-03)-4.65E-01 (3.24E-03)-9.27E-01 (9.17E-03)-9.51E-01 (3.97E-03)-9.59E-01 (1.51E-03)
+/-/=0/16/00/16/00/16/01/9/6

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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