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. 2025 Apr 12;15:12690. doi: 10.1038/s41598-025-96901-y

Table 2.

Statistical test results of GD and p-values for WFG problems.

Problem M D MaOALO MaOPSO MaOSOS MaOMVO NSGA-III MaOMPA p-values
WFG1 5 14 4 4.8 1 3 4.6 3.6 0.0169
7 16 3.6 3.8 1 5.8 4.4 2.4 0.0015
WFG2 5 14 4.2 3.6 3.4 6 2 1.8 0.0045
7 16 3.8 4.4 2.2 6 1.2 3.4 0.0012
WFG3 5 14 5.4 3.2 2.2 5.6 1 3.6 0.0003
7 16 1.6 1.6 4 6 2.8 5 0.0003
WFG4 5 14 2.2 3.8 1.6 5.6 5.4 2.4 0.0009
7 16 1.6 2.8 3.8 5.4 5.2 2.2 0.0034
WFG5 5 14 2 4 2.4 5.4 5.6 1.6 0.0005
7 16 2 3 4 5.8 5.2 1 0.0002
WFG6 5 14 1.6 4 2.8 5.2 5.6 1.8 0.0009
7 16 1.8 3 4 5.6 5.4 1.2 0.0002
WFG7 5 14 2.6 3.6 1.2 6 5 2.6 0.0005
7 16 1.8 2.8 4 6 5 1.4 0.0003
WFG8 5 14 2.6 3.8 2.2 5.4 5.6 1.4 0.0007
7 16 3.2 3.4 2.4 5 6 1 0.0003
WFG9 5 14 2.2 3.6 1.2 6 4 4 0.0015
7 16 2 2.6 3.4 6 5 2 0.0014

Significant values are in bold.