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

Table 8.

Results of IGD metric for WFG problems.

Problem M D MaOALO MaOPSO MaOSOS MaOMVO NSGA-III MaOMPA
WFG1 5 14 1.3121 ± 0.210 1.2991 ± 0.190 1.2490 ± 0.0869 1.2221 ± 0.131 1.3190 ± 0.0932 0.82160 ± 0.0547
7 16 1.8111 ± 0.144 1.8523 ± 0.177 1.5342 ± 0.114 2.0687 ± 0.214 1.7773 ± 0.184 1.2237 ± 0.0620
WFG2 5 14 0.52196 ± 0.0105 0.52245 ± 0.0222 0.50760 ± 0.00789 0.83375 ± 0.0563 0.50608 ± 0.0113 0.50794 ± 0.0107
7 16 0.93491 ± 0.0742 0.84288 ± 0.0556 0.87093 ± 0.0322 1.8378 ± 0.280 0.84085 ± 0.0157 0.82816 ± 0.0142
WFG3 5 14 0.73275 ± 0.0649 0.72681 ± 0.0938 0.82682 ± 0.114 0.76119 ± 0.101 0.89805 ± 0.0769 0.55459 ± 0.0395
7 16 0.81544 ± 0.281 1.1664 ± 0.0586 1.6205 ± 0.0489 1.5918 ± 0.216 0.84288 ± 0.0345 0.84514 ± 0.0878
WFG4 5 14 1.2697 ± 0.00929 1.2581 ± 0.0105 1.2203 ± 0.00302 1.2100 ± 0.00982 1.2294 ± 0.00597 1.1982 ± 0.0142
7 16 2.7721 ± 0.0714 2.5806 ± 0.0332 2.7509 ± 0.220 2.5554 ± 0.0189 2.6313 ± 0.0131 2.6233 ± 0.0392
WFG5 5 14 1.2696 ± 0.0221 1.2561 ± 0.0177 1.2077 ± 0.00334 1.1948 ± 0.00648 1.2091 ± 0.00712 1.2352 ± 0.00822
7 16 2.6563 ± 0.00329 2.6900 ± 0.0415 2.6280 ± 0.0183 2.5415 ± 0.0315 2.5685 ± 0.0122 2.5929 ± 0.0330
WFG6 5 14 1.3241 ± 0.0230 1.3040 ± 0.0217 1.2353 ± 0.00556 1.2387 ± 0.0168 1.2371 ± 0.00644 1.2680 ± 0.0236
7 16 2.8373 ± 0.132 2.7803 ± 0.0693 2.6550 ± 0.0183 2.5956 ± 0.0373 2.6369 ± 0.0170 2.7012 ± 0.0246
WFG7 5 14 1.2938 ± 0.00875 1.2636 ± 0.00981 1.2383 ± 0.00598 1.2629 ± 0.0167 1.2482 ± 0.0119 1.2619 ± 0.0237
7 16 2.6793 ± 0.0173 2.5931 ± 0.0528 2.6440 ± 0.0182 2.6297 ± 0.0449 2.6264 ± 0.0148 2.6866 ± 0.0172
WFG8 5 14 1.3512 ± 0.0104 1.3332 ± 0.0216 1.2765 ± 0.0101 1.3055 ± 0.0291 1.3026 ± 0.00874 1.3003 ± 0.0161
7 16 2.7561 ± 0.172 2.7775 ± 0.0212 2.6999 ± 0.0248 2.7132 ± 0.0214 2.6508 ± 0.0221 2.6508 ± 0.0285
WFG9 5 14 1.2693 ± 0.0103 1.2622 ± 0.0274 1.2237 ± 0.0118 1.2564 ± 0.0194 1.1989 ± 0.0144 1.1971 ± 0.00488
7 16 2.5677 ± 0.0379 2.5958 ± 0.0261 2.5686 ± 0.0136 2.7492 ± 0.0745 2.5386 ± 0.0574 2.5182 ± 0.0332

Significant values are in bold.