Table 2.
Evaluation results of unimodal functions.
| PEOA | RSA | MPA | TSA | WOA | GWO | MVO | TLBO | GSA | PSO | GA | ||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| F1 | Mean | 0 | 0 | 5.87E−50 | 2.61E−47 | 1.69E−152 | 1.62E−01 | 1.16E−58 | 4.15E−74 | 1.19E−16 | 0.0362664 | 34.230951 |
| Best | 0 | 0.00E+00 | 2.84E−52 | 1.24E−50 | 2.41E−168 | 9.82E−02 | 1.12E−60 | 2.27E−77 | 6.70E−17 | 2.073E−05 | 16.574816 | |
| Worst | 0 | 0 | 3.48E−49 | 3.20E−46 | 2.59E−151 | 2.27E−01 | 8.48E−58 | 7.17E−73 | 3.64E−16 | 0.483779 | 49.532216 | |
| Std | 0 | 0 | 8.40E−50 | 7.29E−47 | 5.84E−152 | 3.66E−02 | 2.50E−58 | 1.59E−73 | 7.38E−17 | 0.1078096 | 10.467117 | |
| Median | 0 | 0 | 2.42E−50 | 1.06E−48 | 1.55E−159 | 1.58E−01 | 1.43E−59 | 3.50E−76 | 9.51E−17 | 0.0019868 | 32.065603 | |
| Rank | 1 | 1 | 5 | 6 | 2 | 9 | 4 | 3 | 7 | 8 | 10 | |
| F2 | Mean | 0 | 0 | 1.01E−27 | 9.02E−29 | 1E−103 | 2.56E−01 | 1.07E−34 | 7.74E−39 | 4.93E−08 | 0.9707812 | 3.3228995 |
| Best | 0 | 0 | 5.97E−30 | 1.72E−30 | 3.17E−113 | 1.53E−01 | 1.76E−35 | 6.07E−40 | 3.45E−08 | 0.1235284 | 2.2410278 | |
| Worst | 0 | 0 | 4.31E−27 | 5.47E−28 | 1.54E−102 | 3.73E−01 | 7.83E−34 | 4.79E−38 | 6.48E−08 | 5.2619108 | 4.9763673 | |
| Std | 0 | 0 | 1.13E−27 | 1.67E−28 | 3.53E−103 | 5.40E−02 | 1.73E−34 | 1.09E−38 | 8.64E−09 | 1.2057648 | 0.7100882 | |
| Median | 0 | 0 | 6.94E−28 | 1.96E−29 | 5.94E−108 | 2.53E−01 | 4.26E−35 | 4.56E−39 | 4.98E−08 | 0.5893712 | 3.1159037 | |
| Rank | 1 | 1 | 6 | 5 | 2 | 8 | 4 | 3 | 7 | 9 | 10 | |
| F3 | Mean | 0 | 0 | 1.315E−11 | 2.48E−10 | 18,858.845 | 1.29 E+01 | 2.649E−14 | 2.49E−25 | 5.12 E+02 | 1054.4577 | 2195.5586 |
| Best | 0 | 0 | 2.652E−16 | 1.90E−18 | 2032.3297 | 4.20 E+00 | 3.816E−19 | 2.02E−27 | 2.11 E+02 | 27.156302 | 1279.3432 | |
| Worst | 0 | 0 | 1.82E−10 | 4.87E−09 | 33,406.826 | 2.07 E+01 | 4.419E−13 | 1.29E−24 | 7.25 E+02 | 10,037.204 | 3685.8776 | |
| Std | 0 | 0 | 4.047E−11 | 1.09E−09 | 8589.6075 | 4.86 E+00 | 9.822E−14 | 4.02E−25 | 1.41 E+02 | 2392.5678 | 557.05946 | |
| Median | 0 | 0 | 5.931E−13 | 3.76E−14 | 18,946.43 | 1.29 E+01 | 4.75E−16 | 2.52E−26 | 5.43 E+02 | 284.32942 | 2155.0394 | |
| Rank | 1 | 1 | 4 | 5 | 10 | 6 | 3 | 2 | 7 | 8 | 9 | |
| F4 | Mean | 0 | 0 | 2.362E−19 | 1.37E−02 | 25.164909 | 5.60E−01 | 1.229E−14 | 1.389E−30 | 1.69 E+00 | 6.2895249 | 2.9507205 |
| Best | 0 | 0 | 2.66E−20 | 1.57E−04 | 0.0159905 | 2.41E−01 | 6.529E−16 | 6.32E−32 | 1.18E−08 | 3.0734408 | 2.0354827 | |
| Worst | 0 | 0 | 9.464E−19 | 2.08E−01 | 66.772408 | 1.19 E+00 | 5.365E−14 | 7.472E−30 | 6.57 E+00 | 11.646481 | 4.3222951 | |
| Std | 0 | 0 | 2.231E−19 | 4.59E−02 | 21.758362 | 1.99E−01 | 1.297E−14 | 1.765E−30 | 1.67 E+00 | 2.6353934 | 0.647295 | |
| Median | 0 | 0 | 1.621E−19 | 1.62E−03 | 23.196445 | 5.23E−01 | 7.145E−15 | 7.971E−31 | 1.69 E+00 | 6.0689463 | 2.9578029 | |
| Rank | 1 | 1 | 3 | 5 | 10 | 6 | 4 | 2 | 7 | 9 | 8 | |
| F5 | Mean | 0.0004425 | 8.6946598 | 23.549145 | 28.63252 | 27.239329 | 576.06487 | 26.523222 | 26.678885 | 43.865848 | 85.688829 | 465.03333 |
| Best | 4.577E−07 | 1.575E−28 | 22.951247 | 27.130444 | 26.744112 | 27.656243 | 25.534928 | 25.726694 | 24.573464 | 9.50 E+00 | 259.28355 | |
| Worst | 0.0032013 | 28.990103 | 24.176305 | 29.081852 | 28.73628 | 2095.1885 | 27.900939 | 27.97673 | 312.33572 | 174.484 | 836.20012 | |
| Std | 0.000918 | 13.62634 | 0.3563753 | 0.4518025 | 0.554927 | 747.12125 | 0.5842817 | 0.6800463 | 64.674449 | 50.026782 | 174.72182 | |
| Median | 5.048E−05 | 1.299E−26 | 23.548934 | 28.822767 | 27.012342 | 230.13846 | 26.214753 | 26.37307 | 26.300628 | 7.51 E+01 | 405.1663 | |
| Rank | 1 | 2 | 3 | 7 | 6 | 11 | 4 | 5 | 8 | 9 | 10 | |
| F6 | Mean | 0 | 6.6398929 | 1.43E−09 | 3.8285078 | 0.0832617 | 0.1433226 | 0.508549 | 1.142094 | 1.22E−16 | 2.7244767 | 33.438664 |
| Best | 0 | 4.16 E+00 | 5.07E−10 | 2.802989 | 0.0115735 | 8.98E−02 | 1.907E−05 | 0.4090807 | 5.64E−17 | 6.881E−05 | 17.553177 | |
| Worst | 0 | 7.2500944 | 3.28E−09 | 5.0317017 | 0.2700173 | 0.2076179 | 1.250753 | 2.0796222 | 2.09E−16 | 54.106228 | 65.046009 | |
| Std | 0 | 0.8369605 | 6.47E−10 | 0.6222018 | 0.0794334 | 0.0313493 | 0.3354954 | 0.4035729 | 4.34E−17 | 12.094085 | 14.218234 | |
| Median | 0 | 6.9757851 | 1.38E−09 | 3.5684783 | 0.040989 | 0.1380778 | 0.5003995 | 1.1671963 | 1.07E−16 | 0.0027714 | 28.503061 | |
| Rank | 1 | 10 | 3 | 9 | 4 | 5 | 6 | 7 | 2 | 8 | 11 | |
| F7 | Mean | 1.328E−05 | 9.22E−05 | 0.0006545 | 0.0046427 | 0.0015207 | 0.0122507 | 0.0008299 | 0.0023495 | 0.0532191 | 0.1673299 | 1.03E−02 |
| Best | 6.54E−07 | 1.03E−05 | 0.0001747 | 0.0016636 | 0.0001157 | 0.0060462 | 1.64E−04 | 0.0004908 | 0.014482 | 8.17E−02 | 4.29E−03 | |
| Worst | 5.028E−05 | 0.0003552 | 0.0021105 | 0.0167963 | 0.0059269 | 0.0180807 | 0.001983 | 0.0051277 | 0.0968921 | 0.3189685 | 1.69E−02 | |
| Std | 1.438E−05 | 8.699E−05 | 0.0004314 | 0.0035579 | 0.0015071 | 0.0032761 | 0.0004305 | 0.0013534 | 0.0257839 | 6.52E−02 | 3.68E−03 | |
| Median | 3.606E−06 | 7.175E−05 | 0.0005529 | 0.0037002 | 0.000804 | 0.0123418 | 0.0007959 | 0.0020168 | 0.0547296 | 1.62E−01 | 9.20E−03 | |
| Rank | 1 | 2 | 3 | 7 | 5 | 9 | 4 | 6 | 10 | 11 | 8 | |
| Sum rank | 7 | 18 | 27 | 44 | 39 | 54 | 29 | 28 | 48 | 62 | 66 | |
| Mean rank | 1 | 2.5714286 | 3.8571429 | 6.2857143 | 5.5714286 | 7.7142857 | 4.1428571 | 4 | 6.8571429 | 8.8571429 | 9.4285714 | |
| Total rank | 1 | 2 | 3 | 7 | 6 | 9 | 5 | 4 | 8 | 10 | 11 | |