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

Table 1.

Results of GD metric for WFG problems.

Problem M D MaOALO MaOPSO MaOSOS MaOMVO NSGA-III MaOMPA
WFG1 5 14 0.13172 ± 0.0101 0.13651 ± 0.0279 0.073159 ± 0.00582 0.11919 ± 0.0151 0.13177 ± 0.0212 0.12470 ± 0.00945
7 16 0.17367 ± 0.0216 0.16982 ± 0.0129 0.10871 ± 0.0123 0.20466 ± 0.0132 0.17841 ± 0.0233 0.14767 ± 0.0163
WFG2 5 14 0.029799 ± 0.00541 0.027105 ± 0.00275 0.034787 ± 0.0151 0.10411 ± 0.0233 0.023066 ± 0.00407 0.023279 ± 0.00105
7 16 0.051870 ± 0.00780 0.064284 ± 0.0203 0.039006 ± 0.00495 0.21056 ± 0.0418 0.032534 ± 0.00461 0.050524 ± 0.0144
WFG3 5 14 0.30812 ± 0.0105 0.26770 ± 0.0140 0.25243 ± 0.00821 0.30934 ± 0.00678 0.17234 ± 0.0240 0.28212 ± 0.00773
7 16 0.17491 ± 0.0342 0.16081 ± 0.0906 0.41418 ± 0.00931 0.51572 ± 0.0141 0.26102 ± 0.0159 0.47257 ± 0.0162
WFG4 5 14 0.032634 ± 0.000966 0.036244 ± 0.00227 0.032057 ± 0.00105 0.042044 ± 0.00158 0.041787 ± 0.00127 0.032906 ± 0.000815
7 16 0.064241 ± 0.00254 0.072984 ± 0.00295 0.089381 ± 0.00348 0.11314 ± 0.00456 0.10776 ± 0.00571 0.074592 ± 0.0389
WFG5 5 14 0.035738 ± 0.00165 0.040818 ± 0.000909 0.036890 ± 0.000782 0.045242 ± 0.000778 0.045624 ± 0.000822 0.034320 ± 0.00155
7 16 0.072556 ± 0.00297 0.088378 ± 0.00485 0.094693 ± 0.00528 0.12391 ± 0.00632 0.11511 ± 0.00445 0.060505 ± 0.00203
WFG6 5 14 0.041607 ± 0.00383 0.048270 ± 0.00304 0.042809 ± 0.00427 0.051311 ± 0.00446 0.055199 ± 0.00332 0.040414 ± 0.00107
7 16 0.071349 ± 0.00164 0.085160 ± 0.00165 0.088507 ± 0.00301 0.12780 ± 0.00647 0.12373 ± 0.00347 0.064165 ± 0.00739
WFG7 5 14 0.037593 ± 0.00275 0.041430 ± 0.00381 0.033270 ± 0.00307 0.060270 ± 0.00162 0.046807 ± 0.00363 0.038189 ± 0.00206
7 16 0.069899 ± 0.00654 0.078722 ± 0.00278 0.083790 ± 0.00372 0.13754 ± 0.00805 0.12229 ± 0.00366 0.067060 ± 0.00738
WFG8 5 14 0.066477 ± 0.00249 0.069660 ± 0.00123 0.065908 ± 0.00209 0.076401 ± 0.00784 0.073621 ± 0.00164 0.064398 ± 0.000938
7 16 0.14561 ± 0.00550 0.14702 ± 0.00448 0.14288 ± 0.00636 0.15815 ± 0.00404 0.17744 ± 0.00861 0.12734 ± 0.00398
WFG9 5 14 0.046216 ± 0.00479 0.052682 ± 0.00617 0.040496 ± 0.000831 0.066813 ± 0.00338 0.053583 ± 0.00569 0.051786 ± 0.00300
7 16 0.11204 ± 0.00719 0.11811 ± 0.00773 0.12465 ± 0.00746 0.17626 ± 0.0127 0.14048 ± 0.00513 0.10828 ± 0.0103

Significant values are in bold.