Table 4.
Fitness values generated by competitor algorithms over 30 experiments conducted for CEC'2020.
| Function | Metric | WOA | SCA | TSA | SMA | HHO | RUN | AHA | mAHA |
|---|---|---|---|---|---|---|---|---|---|
| F1 | Mean | 6.473E+06 | 8.199E+08 | 2.565E+09 | 6.759E+03 | 5.652E+05 | 3.830E+03 | 1.829E+03 | 1.000E+02 |
| Std | 8.747E+06 | 3.019E+08 | 2.068E+09 | 4.193E+03 | 5.827E+05 | 2.234E+03 | 1.629E+03 | 1.828E−02 | |
| Best | 6.949E+05 | 2.944E+08 | 1.078E+07 | 2.415E+02 | 9.659E+04 | 1.572E+02 | 1.159E+02 | 1.000E+02 | |
| Worst | 4.477E+07 | 1.481E+09 | 7.693E+09 | 1.271E+04 | 3.162E+06 | 9.526E+03 | 6.359E+03 | 1.001E+02 | |
| F2 | Mean | 2.175E+03 | 2.370E+03 | 2.077E+03 | 1.594E+03 | 2.080E+03 | 1.693E+03 | 1.471E+03 | 1.336E+03 |
| Std | 2.943E+02 | 1.937E+02 | 3.455E+02 | 2.244E+02 | 2.491E+02 | 2.079E+02 | 1.985E+02 | 1.548E+02 | |
| Best | 1.615E+03 | 1.927E+03 | 1.414E+03 | 1.226E+03 | 1.605E+03 | 1.324E+03 | 1.115E+03 | 1.100E+03 | |
| Worst | 2.750E+03 | 2.899E+03 | 2.863E+03 | 2.051E+03 | 2.698E+03 | 2.078E+03 | 1.936E+03 | 1.699E+03 | |
| F3 | Mean | 7.777E+02 | 7.766E+02 | 7.936E+02 | 7.284E+02 | 7.819E+02 | 7.609E+02 | 7.365E+02 | 7.255E+02 |
| Std | 2.592E+01 | 1.088E+01 | 3.091E+01 | 8.521E+00 | 1.784E+01 | 1.656E+01 | 1.138E+01 | 8.629E+00 | |
| Best | 7.261E+02 | 7.532E+02 | 7.470E+02 | 7.176E+02 | 7.418E+02 | 7.208E+02 | 7.216E+02 | 7.135E+02 | |
| Worst | 8.416E+02 | 7.971E+02 | 8.598E+02 | 7.558E+02 | 8.185E+02 | 8.084E+02 | 7.717E+02 | 7.505E+02 | |
| F4 | Mean | 1.908E+03 | 1.928E+03 | 1.634E+04 | 1.901E+03 | 1.908E+03 | 1.902E+03 | 1.901E+03 | 1.901E+03 |
| Std | 9.512E+00 | 1.970E+01 | 2.714E+04 | 5.555E−01 | 2.992E+00 | 1.465E+00 | 7.627E−01 | 7.439E−01 | |
| Best | 1.903E+03 | 1.909E+03 | 1.903E+03 | 1.901E+03 | 1.903E+03 | 1.900E+03 | 1.900E+03 | 1.900E+03 | |
| Worst | 1.955E+03 | 2.007E+03 | 1.252E+05 | 1.903E+03 | 1.913E+03 | 1.906E+03 | 1.904E+03 | 1.903E+03 | |
| F5 | Mean | 3.308E+05 | 4.694E+04 | 4.427E+05 | 7.437E+03 | 5.209E+04 | 4.211E+03 | 6.619E+03 | 2.719E+03 |
| Std | 5.992E+05 | 6.608E+04 | 3.475E+05 | 5.520E+03 | 6.303E+04 | 1.377E+03 | 4.882E+03 | 1.507E+03 | |
| Best | 9.792E+03 | 1.029E+04 | 2.724E+03 | 1.854E+03 | 2.861E+03 | 2.302E+03 | 1.744E+03 | 1.719E+03 | |
| Worst | 2.614E+06 | 3.812E+05 | 9.381E+05 | 1.939E+04 | 2.084E+05 | 7.488E+03 | 2.291E+04 | 8.325E+03 | |
| F6 | Mean | 1.612E+03 | 1.603E+03 | 1.630E+03 | 1.601E+03 | 1.620E+03 | 1.601E+03 | 1.602E+03 | 1.601E+03 |
| Std | 1.299E+01 | 2.398E+00 | 2.318E+01 | 3.053E−01 | 8.626E+00 | 2.714E−01 | 3.043E+00 | 3.210E−01 | |
| Best | 1.601E+03 | 1.601E+03 | 1.601E+03 | 1.601E+03 | 1.601E+03 | 1.601E+03 | 1.601E+03 | 1.601E+03 | |
| Worst | 1.660E+03 | 1.615E+03 | 1.667E+03 | 1.602E+03 | 1.632E+03 | 1.602E+03 | 1.618E+03 | 1.602E+03 | |
| F7 | Mean | 1.756E+05 | 1.368E+04 | 4.182E+04 | 6.657E+03 | 1.341E+04 | 4.414E+03 | 3.288E+03 | 2.125E+03 |
| Std | 2.557E+05 | 7.169E+03 | 7.349E+04 | 6.060E+03 | 2.811E+04 | 3.051E+03 | 2.278E+03 | 3.179E+01 | |
| Best | 1.131E+04 | 4.463E+03 | 2.654E+03 | 2.241E+03 | 2.451E+03 | 2.144E+03 | 2.102E+03 | 2.100E+03 | |
| Worst | 9.505E+05 | 3.215E+04 | 2.038E+05 | 2.112E+04 | 1.573E+05 | 1.391E+04 | 9.947E+03 | 2.235E+03 | |
| F8 | Mean | 2.348E+03 | 2.392E+03 | 2.620E+03 | 2.412E+03 | 2.410E+03 | 2.305E+03 | 2.300E+03 | 2.299E+03 |
| Std | 1.612E+02 | 4.104E+01 | 4.015E+02 | 3.440E+02 | 3.016E+02 | 1.645E+01 | 1.187E+01 | 1.670E+01 | |
| Best | 2.261E+03 | 2.298E+03 | 2.234E+03 | 2.228E+03 | 2.264E+03 | 2.222E+03 | 2.237E+03 | 2.211E+03 | |
| Worst | 3.199E+03 | 2.481E+03 | 4.127E+03 | 3.540E+03 | 3.562E+03 | 2.324E+03 | 2.305E+03 | 2.308E+03 | |
| F9 | Mean | 2.770E+03 | 2.773E+03 | 2.793E+03 | 2.739E+03 | 2.829E+03 | 2.748E+03 | 2.654E+03 | 2.647E+03 |
| Std | 5.640E+01 | 6.138E+01 | 1.038E+02 | 6.552E+01 | 5.099E+01 | 8.740E+00 | 1.218E+02 | 1.224E+02 | |
| Best | 2.561E+03 | 2.545E+03 | 2.554E+03 | 2.500E+03 | 2.739E+03 | 2.734E+03 | 2.500E+03 | 2.500E+03 | |
| Worst | 2.829E+03 | 2.813E+03 | 2.906E+03 | 2.776E+03 | 2.936E+03 | 2.766E+03 | 2.768E+03 | 2.768E+03 | |
| F10 | Mean | 2.948E+03 | 2.980E+03 | 3.039E+03 | 2.936E+03 | 2.932E+03 | 2.921E+03 | 2.932E+03 | 2.930E+03 |
| Std | 3.155E+01 | 2.636E+01 | 1.671E+02 | 3.068E+01 | 3.452E+01 | 2.464E+01 | 2.180E+01 | 2.205E+01 | |
| Best | 2.902E+03 | 2.941E+03 | 2.899E+03 | 2.898E+03 | 2.899E+03 | 2.898E+03 | 2.898E+03 | 2.898E+03 | |
| Worst | 3.030E+03 | 3.064E+03 | 3.648E+03 | 3.024E+03 | 3.028E+03 | 2.956E+03 | 2.951E+03 | 2.947E+03 | |
| Friedman mean rank | 5.19 | 5.80 | 6.15 | 4.60 | 4.85 | 4.22 | 3.23 | 2.02 | |
| rank | 6 | 7 | 8 | 4 | 5 | 3 | 2 | 1 | |