Table 3.
Evaluation results of high-dimensional multimodal functions.
| PEOA | RSA | MPA | TSA | WOA | GWO | MVO | TLBO | GSA | PSO | GA | ||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| F8 | Mean | −12,340.563 | −5479.3915 | −9.76 E+03 | −6.09 E+03 | −10,835.776 | −8.09 E+03 | −6.02 E+03 | −5.17 E+03 | −2.71 E+03 | −6452.3236 | −8453.7272 |
| Best | −12,569.487 | −5.66 E+03 | −1.04 E+04 | −7.73 E+03 | −12,569.483 | −9.23 E+03 | −7.81 E+03 | −7.52 E+03 | −3.58 E+03 | −7836.8201 | −9627.5786 | |
| Worst | −9015.5801 | −5255.8756 | −8.83 E+03 | −5.23 E+03 | −7160.1437 | −6.70 E+03 | −3.01 E+03 | −4.32 E+03 | −2.15 E+03 | −5185.7055 | −7561.2263 | |
| Std | 792.57825 | 141.02969 | 4.03 E+02 | 6.47 E+02 | 1757.8744 | 7.09 E+02 | 9.25 E+02 | 7.25 E+02 | 4.85 E+02 | 761.06762 | 601.23332 | |
| Median | −12,559.187 | −5489.1157 | −9.81 E+03 | −6.10 E+03 | −11,531.955 | −8.10 E+03 | −6.21 E+03 | −5.04 E+03 | −2.69 E+03 | −6400.0566 | −8333.607 | |
| Rank | 1 | 9 | 3 | 7 | 2 | 5 | 8 | 10 | 11 | 6 | 4 | |
| F9 | Mean | 0 | 0 | 0.00 E+00 | 1.61 E+02 | 0 | 1.11 E+02 | 8.28E−01 | 0.00 E+00 | 2.77 E+01 | 62.148683 | 54.625233 |
| Best | 0 | 0 | 0.00 E+00 | 8.42 E+01 | 0 | 4.09 E+01 | 0.00 E+00 | 0.00 E+00 | 1.39 E+01 | 21.889242 | 27.874075 | |
| Worst | 0 | 0 | 0.00 E+00 | 2.29 E+02 | 0 | 1.61 E+02 | 1.22 E+01 | 0.00 E+00 | 3.88 E+01 | 95.516848 | 86.612784 | |
| Std | 0 | 0 | 0.00 E+00 | 4.21 E+01 | 0 | 2.80 E+01 | 2.78 E+00 | 0.00 E+00 | 7.33 E+00 | 17.331681 | 16.779213 | |
| Median | 0 | 0 | 0.00 E+00 | 1.67 E+02 | 0 | 1.11 E+02 | 0.00 E+00 | 0.00 E+00 | 2.84 E+01 | 67.171546 | 54.639675 | |
| Rank | 1 | 1 | 1 | 7 | 1 | 6 | 2 | 1 | 3 | 5 | 4 | |
| F10 | Mean | 8.882E−16 | 8.882E−16 | 4.086E−15 | 2.21 E+00 | 3.908E−15 | 8.18E−01 | 1.563E−14 | 4.09E−15 | 7.66E−09 | 3.2833888 | 3.5478982 |
| Best | 8.882E−16 | 8.882E−16 | 8.882E−16 | 7.99E−15 | 8.882E−16 | 9.40E−02 | 1.155E−14 | 8.88E−16 | 5.32E−09 | 1.5021109 | 2.8115873 | |
| Worst | 8.882E−16 | 8.882E−16 | 4.441E−15 | 3.45 E+00 | 7.994E−15 | 2.91 E+00 | 1.865E−14 | 4.44E−15 | 9.76E−09 | 5.1787822 | 4.3093529 | |
| Std | 0 | 0 | 1.094E−15 | 1.33 E+00 | 2.647E−15 | 8.53E−01 | 1.739E−15 | 1.09E−15 | 1.07E−09 | 1.0404378 | 0.3787695 | |
| Median | 8.882E−16 | 8.882E−16 | 4.441E−15 | 2.81 E+00 | 4.441E−15 | 1.58E−01 | 1.51E−14 | 4.44E−15 | 7.75E−09 | 3.402404 | 3.5164526 | |
| Rank | 1 | 1 | 3 | 7 | 2 | 6 | 4 | 3 | 5 | 8 | 9 | |
| F11 | Mean | 0 | 0 | 0 | 8.98E−03 | 0.0096082 | 3.94E−01 | 0.0034191 | 0 | 7.99 E+00 | 0.0981329 | 1.4848734 |
| Best | 0 | 0 | 0.00 E+00 | 0.00 E+00 | 0 | 2.84E−01 | 0 | 0.00 E+00 | 3.64 E+00 | 0.0030975 | 1.241286 | |
| Worst | 0 | 0 | 0 | 2.38E−02 | 0.1097843 | 5.12E−01 | 0.017904 | 0 | 1.41 E+01 | 0.3900938 | 1.743239 | |
| Std | 0 | 0 | 0 | 7.61E−03 | 0.0299058 | 6.04E−02 | 0.006312 | 0 | 2.79 E+00 | 0.0920983 | 0.1329458 | |
| Median | 0 | 0 | 0 | 9.92E−03 | 0 | 3.93E−01 | 0 | 0 | 7.87 E+00 | 0.0737275 | 1.4632312 | |
| Rank | 1 | 1 | 1 | 3 | 4 | 6 | 2 | 1 | 8 | 5 | 7 | |
| F12 | Mean | 3.137E−08 | 1.16244 | 1.57E−07 | 8.0074137 | 0.0167428 | 0.6392239 | 0.0329332 | 0.0751404 | 0.1702449 | 1.1511137 | 0.1626114 |
| Best | 4.736E−10 | 0.557437 | 3.842E−08 | 1.0769903 | 0.0010716 | 0.000628 | 0.0065876 | 0.03806 | 2.277E−19 | 3.54E−05 | 0.0336148 | |
| Worst | 1.695E−07 | 1.6688946 | 2.913E−07 | 16.998566 | 0.1908087 | 2.4615261 | 0.0664481 | 0.1133911 | 1.0440811 | 4.5874462 | 0.5244877 | |
| Std | 4.053E−08 | 0.3387055 | 6.877E−08 | 4.5096676 | 0.042204 | 0.7935942 | 0.0159373 | 0.0184989 | 0.2682654 | 1.2331964 | 0.125602 | |
| Median | 1.432E−08 | 1.106103 | 1.461E−07 | 8.0094012 | 0.0037323 | 0.3815718 | 0.0293849 | 0.0756851 | 0.0856922 | 8.52E−01 | 0.1211823 | |
| Rank | 1 | 10 | 2 | 11 | 3 | 8 | 4 | 5 | 7 | 9 | 6 | |
| F13 | Mean | 5.337E−07 | 0.3927599 | 2.82E−03 | 2.8688846 | 0.2466066 | 0.036827 | 0.4665474 | 1.111075 | 1.42E−02 | 5.3795073 | 2.9235075 |
| Best | 7.965E−11 | 5.35E−31 | 1.86E−09 | 1.6791696 | 0.0158998 | 1.42E−02 | 0.2003169 | 0.5959632 | 5.42E−18 | 0.0286689 | 1.3610917 | |
| Worst | 6.244E−06 | 2.9 | 1.31E−02 | 4.1956798 | 0.6945697 | 0.0691117 | 0.8138707 | 1.6022415 | 1.18E−01 | 17.838499 | 5.2426649 | |
| Std | 1.395E−06 | 0.9634638 | 5.06E−03 | 0.6638534 | 0.1993274 | 0.0180155 | 0.1651567 | 0.296759 | 2.96E−02 | 4.3403151 | 0.9803997 | |
| Median | 7.624E−08 | 8.367E−31 | 3.62E−09 | 2.8262039 | 0.1936396 | 0.0320078 | 0.417461 | 1.1361137 | 1.32E−17 | 4.8528038 | 2.8760768 | |
| Rank | 1 | 6 | 2 | 9 | 5 | 4 | 7 | 8 | 3 | 11 | 10 | |
| Sum rank | 6 | 28 | 12 | 44 | 17 | 35 | 27 | 28 | 37 | 44 | 40 | |
| Mean rank | 1 | 4.6666667 | 2 | 7.3333333 | 2.8333333 | 5.8333333 | 4.5 | 4.6666667 | 6.1666667 | 7.3333333 | 6.6666667 | |
| Total rank | 1 | 5 | 2 | 9 | 3 | 6 | 4 | 5 | 7 | 9 | 8 | |