Complexity / 2019 / Article / Tab 2

Research Article

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.

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

F12.73E-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)
F23.28E-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)
F34.84E-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)
F45.73E-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)
F56.35E-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)
F68.19E-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)
F71.92E-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)
F85.86E-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)
F91.35E-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)
F101.29E-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)
F111.60E-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)
F121.65E-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)
F132.03E-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)
F141.88E-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)
F152.18E-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)
F165.35E-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)
+/-/=0/16/00/16/00/15/12/13/1

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.

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