Table 7 Wilcoxon rank sum test results of other optimization algorithms CEC2017 test set based on HBWO
F | Algorithm | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
PSO | SSA | WOA | HHO | DO | SCSO | AO | AOA | BWO | LHHO | LSMA | |
F1 | 6.79560E-08 | 1.20090E-06 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 | 0.0071135 |
F3 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 | 1.65710E-07 |
F4 | 6.79560E-08 | 1.04730E-06 | 6.79560E-08 | 6.01480E-07 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 | 7.94790E-07 | 0.0036388 |
F5 | 9.12660E-07 | 6.79560E-08 | 6.79560E-08 | 7.89800E-08 | 6.79560E-08 | 1.06460E-07 | 0.000011045 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 | 0.0065572 |
F6 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 | 2.95980E-07 |
F7 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 | 9.17280E-08 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 | 0.0003048 |
F8 | 5.87360E-06 | 6.79560E-08 | 1.06460E-07 | 2.95980E-07 | 6.79560E-08 | 6.79560E-08 | 5.87360E-06 | 6.79560E-08 | 6.79560E-08 | 1.65710E-07 | 0.4093600 |
F9 | 2.56290E-07 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 | 0.0315170 |
F10 | 0.0003048 | 1.91770E-07 | 6.79560E-08 | 7.57740E-06 | 9.12660E-07 | 2.68980E-06 | 0.0001159 | 6.79560E-08 | 6.79560E-08 | 2.35570E-06 | 0.2732900 |
F11 | 6.79560E-08 | 1.91770E-07 | 6.79560E-08 | 6.91660E-07 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 | 0.000082924 | 3.93880E-07 |
F12 | 6.79560E-08 | 3.06910E-06 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 |
F13 | 4.53900E-07 | 0.3369200 | 6.79560E-08 | 6.79560E-08 | 7.89800E-08 | 7.89800E-08 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 | 7.89800E-08 |
F14 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 |
F15 | 6.79560E-08 | 0.0065572 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 |
F16 | 0.000066104 | 0.0036388 | 7.89800E-08 | 1.91770E-07 | 7.94790E-07 | 0.000023025 | 7.94790E-07 | 6.79560E-08 | 6.79560E-08 | 1.04730E-06 | 0.0315170 |
F17 | 0.00033819 | 2.35570E-06 | 6.91660E-07 | 0.00002596 | 6.91660E-07 | 0.012345 | 0.00068682 | 7.89800E-08 | 7.89800E-08 | 4.53900E-07 | 0.0023413 |
F18 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 |
F19 | 5.22690E-07 | 0.00604030 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 |
F20 | 5.16580E-06 | 3.41560E-07 | 6.79560E-08 | 4.53900E-07 | 2.21780E-07 | 1.79360E-04 | 5.09070E-04 | 0.000011045 | 6.79560E-08 | 0.00012941 | 0.0179390 |
F21 | 9.17280E-08 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 | 2.21780E-07 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 | 0.0764310 |
F22 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 |
F23 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 | 0.5608500 |
F24 | 9.17280E-08 | 4.54010E-06 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 | 2.95980E-07 | 1.04730E-06 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 | 0.0467920 |
F25 | 6.79560E-08 | 2.47060E-04 | 6.79560E-08 | 1.43090E-07 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 | 2.06160E-06 | 0.015479 |
F26 | 1.23460E-07 | 7.57740E-06 | 6.79560E-08 | 1.91770E-07 | 4.54010E-06 | 6.67370E-06 | 0.0083548 | 6.79560E-08 | 6.79560E-08 | 6.01480E-07 | 0.0764310 |
F27 | 0.0097865 | 0.285300 | 0.000082924 | 0.0004155 | 0.0004155 | 0.033718 | 0.0438800 | 6.79560E-08 | 6.79560E-08 | 0.0097865 | 5.87360E-06 |
F28 | 6.79560E-08 | 1.23460E-07 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 | 2.06160E-06 |
F29 | 6.79560E-08 | 2.56290E-07 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 | 1.91770E-07 | 7.89800E-08 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 | 0.00014438 |
F30 | 6.79560E-08 | 0.0065572 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 | 6.79560E-08 |
 + / = / −  | 0/0/29 | 0/2/27 | 0/0/29 | 0/0/29 | 0/0/29 | 0/0/29 | 0/0/29 | 0/0/29 | 0/0/29 | 0/0/29 | 3/5/21 |