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

Table 3.

Results of spacing metric for WFG problems.

Problem M D MaOALO MaOPSO MaOSOS MaOMVO NSGA-III MaOMPA
WFG1 5 14 1.0127 ± 0.0334 0.83688 ± 0.0308 0.54804 ± 0.195 0.87886 ± 0.0841 0.98270 ± 0.0681 0.60345 ± 0.0730
7 16 1.2070 ± 0.110 1.1975 ± 0.0841 1.1607 ± 0.0941 1.3319 ± 0.186 1.7650 ± 0.155 0.82687 ± 0.0699
WFG2 5 14 0.66067 ± 0.146 0.55353 ± 0.0622 0.65075 ± 0.103 0.48623 ± 0.127 0.69233 ± 0.103 0.31764 ± 0.0284
7 16 1.1717 ± 0.125 0.94543 ± 0.182 1.0307 ± 0.0685 0.72535 ± 0.238 0.86137 ± 0.202 0.53823 ± 0.0984
WFG3 5 14 0.57144 ± 0.0203 0.58385 ± 0.0752 0.40364 ± 0.0365 0.39771 ± 0.0766 0.75537 ± 0.113 0.32180 ± 0.0901
7 16 0.64281 ± 0.0795 0.59643 ± 0.174 0.76160 ± 0.0296 0.69554 ± 0.0693 1.2777 ± 0.128 0.67988 ± 0.0453
WFG4 5 14 0.83411 ± 0.0197 0.92290 ± 0.0764 0.63476 ± 0.0702 0.69457 ± 0.0392 0.85124 ± 0.0460 0.45077 ± 0.0103
7 16 1.4517 ± 0.112 1.6718 ± 0.106 1.5248 ± 0.123 1.6934 ± 0.126 1.4678 ± 0.161 0.95666 ± 0.0829
WFG5 5 14 0.83560 ± 0.0331 0.83906 ± 0.0416 0.68450 ± 0.102 0.76683 ± 0.0664 0.82498 ± 0.0353 0.45602 ± 0.0359
7 16 1.3680 ± 0.0403 1.6719 ± 0.119 1.4471 ± 0.110 1.6074 ± 0.240 1.3521 ± 0.0443 0.88467 ± 0.0778
WFG6 5 14 0.83239 ± 0.0388 0.90446 ± 0.0816 0.69513 ± 0.0794 0.76519 ± 0.0917 0.78216 ± 0.0461 0.48755 ± 0.0574
7 16 1.4039 ± 0.0968 1.5898 ± 0.176 1.4921 ± 0.188 1.5026 ± 0.106 1.4441 ± 0.0449 0.86176 ± 0.0328
WFG7 5 14 0.87242 ± 0.0303 0.91209 ± 0.110 0.67231 ± 0.105 0.82402 ± 0.0331 0.82415 ± 0.0390 0.43260 ± 0.0522
7 16 1.4478 ± 0.134 1.8465 ± 0.165 1.4757 ± 0.139 1.5959 ± 0.153 1.6457 ± 0.101 0.81158 ± 0.106
WFG8 5 14 1.0789 ± 0.113 0.86796 ± 0.0633 0.60454 ± 0.0680 0.75985 ± 0.0542 0.88828 ± 0.0381 0.47769 ± 0.0432
7 16 2.0619 ± 0.133 1.6931 ± 0.102 1.4614 ± 0.0773 1.4699 ± 0.164 2.2170 ± 0.160 0.90960 ± 0.0471
WFG9 5 14 0.79169 ± 0.0634 0.82298 ± 0.0286 0.59598 ± 0.0653 0.74638 ± 0.0932 0.84979 ± 0.0741 0.42837 ± 0.0400
7 16 1.4849 ± 0.0957 1.5817 ± 0.131 1.2436 ± 0.150 1.5077 ± 0.111 1.5772 ± 0.108 0.78615 ± 0.0752

Significant values are in bold.