Table 11 Results of various HBWO on CEC2019
F | Index | Algorithm | |||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
PSO | SSA | WOA | HHO | DO | SCSO | AO | AOA | BWO | LHHO | LSMA | HBWO | ||
F1 | Mean | 8.269E + 06 | 1 | 8.204E + 06 | 1 | 1 | 1 | 1 | 7.992E + 03 | 1 | 1 | 1 | 1 |
Std | 9.505E + 06 | 4.651E-15 | 1.205E + 07 | 0 | 0 | 2.010E-12 | 1.368E-08 | 3.574E + 04 | 0 | 0 | 0 | 0 | |
Best | 2.469E + 05 | 1 | 6.605E + 00 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | |
Worst | 3.718E + 07 | 1 | 4.881E + 07 | 1 | 1 | 1.000E + 00 | 1.000E + 00 | 1.598E + 05 | 1 | 1 | 1 | 1 | |
Rank | 12 | 7 | 11 | 1 | 1 | 8 | 9 | 10 | 1 | 1 | 1 | 1 | |
F2 | Mean | 4.331E + 03 | 4.666E + 00 | 7.376E + 03 | 4.963E + 00 | 5 | 4.523E + 00 | 4.977E + 00 | 8.498E + 03 | 4.997E + 00 | 5 | 5 | 4.551E + 00 |
Std | 3.541E + 03 | 5.455E-01 | 2.771E + 03 | 1.049E-01 | 0 | 3.602E-01 | 8.121E-02 | 1.882E + 03 | 1.175E-02 | 1.977E-03 | 8.662E-06 | 3.760E-01 | |
Best | 4.822E + 02 | 4.222E + 00 | 3.115E + 03 | 4.569E + 00 | 5 | 4.217E + 00 | 4.651E + 00 | 5.426E + 03 | 4.947E + 00 | 4.991E + 00 | 5 | 4.217E + 00 | |
Worst | 1.305E + 04 | 6.479E + 00 | 1.543E + 04 | 5 | 5 | 5 | 5 | 1.206E + 04 | 5 | 5 | 5 | 5 | |
Rank | 10 | 3 | 11 | 4 | 9 | 1 | 5 | 12 | 6 | 7 | 8 | 2 | |
F3 | Mean | 7.968E + 00 | 7.200E + 00 | 3.913E + 00 | 4.097E + 00 | 5.816E + 00 | 2.549E + 00 | 5.556E + 00 | 9.578E + 00 | 4.138E + 00 | 3.582E + 00 | 3.561E + 00 | 2.143E + 00 |
Std | 2.390E + 00 | 2.182E + 00 | 2.005E + 00 | 1.318E + 00 | 1.799E + 00 | 9.844E-01 | 1.835E + 00 | 1.093E + 00 | 8.606E-01 | 1.386E + 00 | 2.202E + 00 | 6.181E-01 | |
Best | 1.901E + 00 | 3.738E + 00 | 1.485E + 00 | 1.761E + 00 | 1.518E + 00 | 1.409E + 00 | 2.907E + 00 | 7.311E + 00 | 2.729E + 00 | 1.429E + 00 | 1.000E + 00 | 1.296E + 00 | |
Worst | 1.071E + 01 | 1.069E + 01 | 7.711E + 00 | 6.429E + 00 | 8.629E + 00 | 5.236E + 00 | 9.760E + 00 | 1.174E + 01 | 5.792E + 00 | 6.237E + 00 | 8.612E + 00 | 3.562E + 00 | |
Rank | 11 | 10 | 5 | 6 | 9 | 2 | 8 | 12 | 7 | 4 | 3 | 1 | |
F4 | Mean | 2.528E + 01 | 4.324E + 01 | 5.244E + 01 | 3.968E + 01 | 5.508E + 01 | 4.050E + 01 | 2.733E + 01 | 4.368E + 01 | 5.647E + 01 | 3.786E + 01 | 1.995E + 01 | 1.034E + 01 |
Std | 1.085E + 01 | 1.613E + 01 | 2.092E + 01 | 9.130E + 00 | 9.215E + 00 | 1.225E + 01 | 9.203E + 00 | 1.078E + 01 | 6.157E + 00 | 1.236E + 01 | 9.604E + 00 | 3.678E + 00 | |
Best | 9.955E + 00 | 1.493E + 01 | 2.395E + 01 | 2.309E + 01 | 3.088E + 01 | 1.794E + 01 | 1.605E + 01 | 2.688E + 01 | 4.320E + 01 | 1.006E + 01 | 7.965E + 00 | 5.029E + 00 | |
Worst | 4.659E + 01 | 6.965E + 01 | 9.797E + 01 | 5.595E + 01 | 6.567E + 01 | 6.512E + 01 | 4.595E + 01 | 6.313E + 01 | 6.805E + 01 | 5.579E + 01 | 4.279E + 01 | 1.917E + 01 | |
Rank | 3 | 8 | 10 | 6 | 11 | 7 | 4 | 9 | 12 | 5 | 2 | 1 | |
F5 | Mean | 1.578E + 01 | 1.652E + 00 | 2.074E + 00 | 2.056E + 00 | 1.634E + 00 | 6.153E + 00 | 1.860E + 00 | 6.858E + 01 | 6.586E + 01 | 2.024E + 00 | 1.191E + 00 | 1.004E + 00 |
Std | 1.208E + 01 | 3.375E-01 | 4.019E-01 | 3.427E-01 | 2.737E-01 | 6.486E + 00 | 2.274E-01 | 2.138E + 01 | 2.121E + 01 | 3.171E-01 | 7.736E-02 | 1.063E-02 | |
Best | 1.071E + 00 | 1.239E + 00 | 1.420E + 00 | 1.536E + 00 | 1.194E + 00 | 1.153E + 00 | 1.590E + 00 | 2.711E + 01 | 2.326E + 01 | 1.584E + 00 | 1.092E + 00 | 1.000E + 00 | |
Worst | 3.920E + 01 | 2.706E + 00 | 3.014E + 00 | 2.767E + 00 | 2.187E + 00 | 2.857E + 01 | 2.644E + 00 | 1.071E + 02 | 1.084E + 02 | 2.714E + 00 | 1.391E + 00 | 1.123E + 00 | |
Rank | 10 | 4 | 8 | 7 | 3 | 9 | 5 | 12 | 11 | 6 | 2 | 1 | |
F6 | Mean | 4.782E + 00 | 6.881E + 00 | 9.165E + 00 | 8.013E + 00 | 8.910E + 00 | 7.093E + 00 | 6.527E + 00 | 1.126E + 01 | 1.099E + 01 | 8.763E + 00 | 4.794E + 00 | 2.047E + 00 |
Std | 1.691E + 00 | 1.572E + 00 | 1.262E + 00 | 1.905E + 00 | 2.096E + 00 | 1.713E + 00 | 1.355E + 00 | 1.560E + 00 | 5.897E-01 | 1.499E + 00 | 1.612E + 00 | 1.048E + 00 | |
Best | 1.491E + 00 | 4.125E + 00 | 7.307E + 00 | 5.066E + 00 | 5.516E + 00 | 3.665E + 00 | 4.325E + 00 | 8.417E + 00 | 9.676E + 00 | 5.980E + 00 | 1.389E + 00 | 1.001E + 00 | |
Worst | 7.707E + 00 | 9.412E + 00 | 1.236E + 01 | 1.179E + 01 | 1.267E + 01 | 9.779E + 00 | 9.607E + 00 | 1.387E + 01 | 1.222E + 01 | 1.107E + 01 | 7.433E + 00 | 3.832E + 00 | |
Rank | 2 | 5 | 10 | 7 | 9 | 6 | 4 | 12 | 11 | 8 | 3 | 1 | |
F7 | Mean | 9.908E + 02 | 1.136E + 03 | 1.220E + 03 | 1.125E + 03 | 1.611E + 03 | 9.988E + 02 | 8.380E + 02 | 1.053E + 03 | 1.653E + 03 | 1.091E + 03 | 8.153E + 02 | 5.140E + 02 |
Std | 2.409E + 02 | 2.747E + 02 | 3.528E + 02 | 3.660E + 02 | 3.946E + 02 | 3.416E + 02 | 3.177E + 02 | 2.977E + 02 | 2.099E + 02 | 2.555E + 02 | 2.860E + 02 | 2.256E + 02 | |
Best | 6.217E + 02 | 7.492E + 02 | 7.505E + 02 | 3.595E + 02 | 8.104E + 02 | 3.924E + 02 | 3.286E + 02 | 5.270E + 02 | 1.239E + 03 | 6.393E + 02 | 2.698E + 02 | 1.402E + 02 | |
Worst | 1.556E + 03 | 1.626E + 03 | 1.961E + 03 | 1.770E + 03 | 2.431E + 03 | 1.711E + 03 | 1.455E + 03 | 1.694E + 03 | 2.012E + 03 | 1.666E + 03 | 1.229E + 03 | 9.344E + 02 | |
Rank | 4 | 9 | 10 | 8 | 11 | 5 | 3 | 6 | 12 | 7 | 2 | 1 | |
F8 | Mean | 4.061E + 00 | 4.583E + 00 | 4.526E + 00 | 4.507E + 00 | 4.808E + 00 | 3.964E + 00 | 4.234E + 00 | 4.400E + 00 | 4.517E + 00 | 4.341E + 00 | 3.619E + 00 | 3.407E + 00 |
Std | 3.110E-01 | 2.816E-01 | 3.428E-01 | 2.942E-01 | 2.564E-01 | 4.520E-01 | 3.078E-01 | 3.010E-01 | 1.215E-01 | 3.900E-01 | 5.501E-01 | 2.421E-01 | |
Best | 3.528E + 00 | 3.871E + 00 | 3.492E + 00 | 3.932E + 00 | 4.287E + 00 | 3.136E + 00 | 3.775E + 00 | 3.565E + 00 | 4.261E + 00 | 3.565E + 00 | 1.934E + 00 | 2.905E + 00 | |
Worst | 4.644E + 00 | 5.019E + 00 | 5.043E + 00 | 4.935E + 00 | 5.158E + 00 | 4.593E + 00 | 4.857E + 00 | 4.914E + 00 | 4.705E + 00 | 4.849E + 00 | 4.397E + 00 | 4.153E + 00 | |
Rank | 4 | 11 | 10 | 8 | 12 | 3 | 5 | 7 | 9 | 6 | 2 | 1 | |
F9 | Mean | 1.319E + 00 | 1.744E + 00 | 1.515E + 00 | 1.589E + 00 | 1.645E + 00 | 1.386E + 00 | 1.534E + 00 | 1.747E + 00 | 2.014E + 00 | 1.593E + 00 | 1.265E + 00 | 1.247E + 00 |
Std | 1.220E-01 | 1.606E-01 | 1.572E-01 | 1.568E-01 | 1.595E-01 | 1.429E-01 | 2.051E-01 | 1.481E-01 | 1.382E-01 | 2.152E-01 | 8.216E-02 | 3.834E-02 | |
Best | 1.100E + 00 | 1.436E + 00 | 1.299E + 00 | 1.353E + 00 | 1.404E + 00 | 1.188E + 00 | 1.221E + 00 | 1.443E + 00 | 1.724E + 00 | 1.246E + 00 | 1.137E + 00 | 1.206E + 00 | |
Worst | 1.554E + 00 | 2.081E + 00 | 1.877E + 00 | 1.898E + 00 | 1.946E + 00 | 1.686E + 00 | 2.015E + 00 | 2.103E + 00 | 2.296E + 00 | 1.967E + 00 | 1.394E + 00 | 1.348E + 00 | |
Rank | 3 | 10 | 5 | 7 | 9 | 4 | 6 | 11 | 12 | 8 | 2 | 1 | |
F10 | Mean | 21.07486 | 21.01216 | 21.18397 | 21.06706 | 21.02644 | 21.09288 | 21.27971 | 21.07935 | 21.41832 | 21.10596 | 21.07634 | 20.2073 |
Std | 9.771E-02 | 5.828E-02 | 1.414E-01 | 6.087E-02 | 5.503E-02 | 9.155E-02 | 1.281E-01 | 2.768E-02 | 1.024E-01 | 1.426E-01 | 5.656E-02 | 4.521E + 00 | |
Best | 20.1000 | 20.9978 | 21.0467 | 21.0019 | 20.9997 | 21.0018 | 21.0827 | 21.0441 | 21.1929 | 20.9983 | 21.0015 | 1.0003 | |
Worst | 21.2659 | 21.2597 | 21.5129 | 21.2196 | 21.2451 | 21.2914 | 21.4906 | 21.16560 | 21.5801 | 21.5156 | 21.1799 | 21.3154 | |
Rank | 5 | 2 | 10 | 4 | 3 | 8 | 11 | 7 | 12 | 9 | 6 | 1 | |
Average rank | 6.4 | 6.9 | 9 | 5.8 | 7.7 | 5.3 | 6 | 9.8 | 9.3 | 6.1 | 3.1 | 1.1 | |
Final rank | 7 | 8 | 10 | 4 | 9 | 3 | 5 | 12 | 11 | 6 | 2 | 1 | |