Table 14 Wilcoxon rank–sum test and t-test results for LCA versus recent algorithms for 51 benchmark functions.
From: Learning cooking algorithm for solving global optimization problems
Functions | LCA vs | LCA vs | LCA vs | LCA vs | LCA vs | LCA vs | LCA vs | LCA vs | |
|---|---|---|---|---|---|---|---|---|---|
IGWO | MWOA | TLBO | MTBO | BWO | HHO | MGO | SCSO | ||
\({\text {F1}}\) | \(p-value\) | 9.207E–05 | 9.207E–05 | 9.207E–05 | 9.207E–05 | NA | 9.207E–05 | 9.207E–05 | 9.207E–05 |
\(t-test\) | –1.763E+00 | –1.000E+00 | 0 | –1.022E+00 | 0 | 0 | –1.370E+00 | 0 | |
\({\text {F2}}\) | \(p-value\) | 9.207E–05 | 9.207E–05 | 9.207E–05 | 9.207E–05 | 9.207E–05 | 9.207E–05 | 9.207E–05 | 9.207E–05 |
\(t-test\) | –5.016E+00 | –1.238E+00 | –2.380E+00 | –1.603E+00 | 0 | –1.368E+00 | –2.021E+00 | –1.170E+00 | |
\({\text {F3}}\) | \(p-value\) | 9.207E–05 | 9.207E–05 | 9.207E–05 | 9.207E–05 | NA | 9.207E–05 | 9.207E–05 | 9.207E–05 |
\(t-test\) | –1.530E+00 | –9.865E+00 | –3.498E+00 | –3.487E+00 | 0 | –1.000E+00 | –1.150E+00 | 0 | |
\({\text {F4}}\) | \(p-value\) | 9.207E–05 | 9.207E–05 | 9.207E–05 | 9.207E–05 | 9.207E–05 | 9.207E–05 | 9.207E–05 | 9.207E–05 |
\(t-test\) | –3.149E+00 | –6.969E+00 | –3.963E+00 | –1.489E+01 | 0 | –1.000E+00 | –1.531E+00 | –1.017E+00 | |
\({\text {F5}}\) | \(p-value\) | 9.207E–05 | 9.207E–05 | 9.207E–05 | 9.207E–05 | 9.207E–05 | 9.207E–05 | 9.207E–05 | 9.207E–05 |
\(t-test\) | –5.212E+02 | –3.337E+02 | –1.552E+02 | –8.142E+00 | –1.193E+00 | –4.900E+00 | –1.916E+00 | –1.650E+02 | |
\({\text {F6}}\) | \(p-value\) | 9.207E–05 | 9.207E–05 | 9.207E–05 | 9.207E–05 | 9.207E–05 | 9.207E–05 | 9.207E–05 | 9.207E–05 |
\(t-test\) | –9.998E+00 | –3.888E+00 | –1.866E+00 | –1.462E+00 | –2.308E+00 | –2.829E+00 | –1.208E+00 | –2.114E+01 | |
\({\text {F7}}\) | \(p-value\) | 9.207E–05 | 1.251E–04 | 9.207E–05 | 9.207E–05 | 8.259E–03 | 9.207E–05 | 9.207E–05 | 9.207E–05 |
\(t-test\) | –1.429E+01 | –3.814E+00 | –1.097E+01 | –9.742E+00 | –3.488E+00 | –1.615E+00 | –6.536E+00 | –2.104E+00 | |
\({\text {F8}}\) | \(p-value\) | 9.207E–05 | 9.207E–05 | 9.207E–05 | 9.207E–05 | 8.139E–06 | 1.074E–04 | 8.139E–06 | 9.207E–05 |
\(t-test\) | –1.163E+01 | –1.279E+01 | –3.337E+01 | –2.168E+01 | 1.948E+07 | –2.639E+00 | 5.682E+05 | –4.581E+01 | |
\({\text {F9}}\) | \(p-value\) | 9.207E–05 | NA | 1.373E–04 | 9.207E–05 | NA | NA | NA | NA |
\(t-test\) | –1.136E+01 | 0 | –9.747E+00 | –1.854E+01 | 0 | 0 | 0 | 0 | |
\({\text {F10}}\) | \(p-value\) | 3.813E–05 | 3.813E–05 | 5.276E–05 | 9.207E–05 | 8.139E–06 | 8.139E–06 | 8.139E–06 | 8.139E–06 |
\(t-test\) | –2.433E+01 | –4.765E+00 | –1.424E+01 | –2.239E+01 | –1.949E+00 | –1.949E+00 | –2.179E+00 | –1.949E+00 | |
\({\text {F11}}\) | \(p-value\) | 4.883E–04 | 1.000E+00 | NA | 9.207E–05 | NA | NA | NA | NA |
\(t-test\) | –3.599E+00 | –1.000E+00 | 0 | –3.597E+00 | 0 | 0 | 0 | 0 | |
\({\text {F12}}\) | \(p-value\) | 9.207E–05 | 9.207E–05 | 9.194E–05 | 9.207E–05 | 9.207E–05 | 9.207E–05 | NA | 9.207E–05 |
\(t-test\) | –1.332E+01 | –3.689E+00 | –1.453E+00 | –4.331E+00 | –3.078E+00 | –4.427E+00 | –3.189E+11 | –1.239E+01 | |
\({\text {F13}}\) | \(p-value\) | 9.207E–05 | 9.207E–05 | 9.142E–05 | 9.207E–05 | 9.207E–05 | 9.207E–05 | NA | 9.207E–05 |
\(t-test\) | –1.832E+00 | –6.255E+00 | –4.574E+00 | –5.870E+00 | –2.635E+00 | –2.462E+00 | –1.154E+11 | –3.808E+01 | |
\({\text {F14}}\) | \(p-value\) | 8.139E–06 | 7.022E–05 | 8.139E–06 | 8.139E–06 | 8.139E–06 | 1.792E–05 | 8.139E–06 | 6.312E–05 |
\(t-test\) | –7.534E+10 | –2.386E+00 | –7.534E+10 | –7.534E+10 | –1.478E+07 | –1.000E+00 | –7.534E+10 | –3.410E+00 | |
\({\text {F15}}\) | \(p-value\) | 1.504E–03 | 1.455E–04 | 7.245E–02 | 1.555E–03 | 2.630E–04 | 3.508E–04 | 7.159E–02 | 2.510E–01 |
\(t-test\) | –9.253E–01 | –3.063E+00 | –9.984E–01 | –1.280E+00 | –4.042E+00 | –4.427E+00 | –1.785E+00 | –1.449E+00 | |
\({\text {F16}}\) | \(p-value\) | 8.139E–06 | 8.139E–06 | 8.139E–06 | 8.139E–06 | 9.216E–03 | 8.139E–06 | 8.139E–06 | 8.139E–06 |
\(t-test\) | 2.793E+11 | 8.951E+05 | 2.793E+11 | 2.793E+11 | –2.608E+00 | 2.849E+06 | 2.793E+11 | 1.262E+06 | |
\({\text {F17}}\) | \(p-value\) | 8.575E–05 | 9.181E–05 | 8.575E–05 | 8.575E–05 | 9.207E–05 | 9.181E–05 | 8.575E–05 | 9.181E–05 |
\(t-test\) | 5.426E+00 | 5.318E+00 | 5.426E+00 | 5.426E+00 | –4.235E+00 | 5.402E+00 | 5.426E+00 | 5.424E+00 | |
\({\text {F18}}\) | \(p-value\) | NA | 1.373E–04 | NA | NA | 9.207E–05 | NA | NA | 9.207E–05 |
\(t-test\) | 3.879E+02 | –1.571E+00 | 3.879E+02 | 3.879E+02 | –3.427E+00 | –1.710E+00 | 1.369E+02 | –4.464E+00 | |
\({\text {F19}}\) | \(p-value\) | 6.629E–05 | 1.587E–01 | 6.629E–05 | 6.629E–05 | 4.168E–01 | 4.166E–03 | 6.629E–05 | 1.191E–01 |
\(t-test\) | 4.978E+00 | 1.206E+00 | –3.815E+03 | 4.978E+00 | 9.358E–01 | 3.901E+00 | 4.978E+00 | 1.543E+00 | |
\({\text {F20}}\) | \(p-value\) | 8.824E–05 | 9.207E–05 | 7.225E–05 | 8.612E–05 | 9.207E–05 | 1.074E–04 | 8.649E–05 | 9.207E–05 |
\(t-test\) | 1.251E+01 | 1.060E+01 | 1.301E+01 | 1.140E+01 | 1.239E+01 | 8.124E+00 | 1.100E+01 | 1.002E+01 | |
\({\text {F21}}\) | \(p-value\) | 1.792E–05 | 9.207E–05 | 1.252E–05 | 7.118E–05 | 9.129E–05 | 9.207E–05 | 8.139E–06 | 9.207E–05 |
\(t-test\) | –1.000E+00 | –4.238E+00 | –1.000E+00 | –5.286E+00 | –6.203E+00 | –3.939E+04 | –7.875E+08 | –7.917E+00 | |
\({\text {F22}}\) | \(p-value\) | 1.252E–05 | 9.207E–05 | 5.427E–02 | 5.957E–01 | 9.194E–05 | 9.207E–05 | 8.139E–06 | 4.043E–04 |
\(t-test\) | 3.922E+05 | –4.777E+00 | –1.445E+00 | –3.183E+00 | 1.213E+02 | –1.345E+01 | 4.977E+10 | –7.719E+00 | |
\({\text {F23}}\) | \(p-value\) | 8.139E–06 | 9.207E–05 | 4.088E–04 | 5.659E–01 | 9.207E–05 | 9.207E–05 | 8.139E–06 | 1.961E–04 |
\(t-test\) | 1.871E+09 | –5.936E+00 | –1.000E+00 | –2.512E+00 | 4.571E+01 | –1.434E+01 | 5.678E+09 | –1.038E+01 | |
\({\text {F24}}\) | \(p-value\) | NA | NA | NA | NA | NA | NA | NA | NA |
\(t-test\) | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
\({\text {F25}}\) | \(p-value\) | 9.207E–05 | 9.207E–05 | 9.207E–05 | 9.207E–05 | NA | 9.207E–05 | 9.207E–05 | 9.207E–05 |
\(t-test\) | –2.451E+00 | –1.001E+00 | 0 | –1.284E+00 | 0 | 0 | –1.041E+00 | 0 | |
\({\text {F26}}\) | \(p-value\) | 4.570E–05 | 1.410E–02 | 4.570E–05 | 4.570E–05 | 1.820E–01 | 9.078E–05 | 4.570E–05 | 9.207E–05 |
\(t-test\) | 1.388E+01 | –1.448E+00 | 1.388E+01 | 1.388E+01 | –2.192E+00 | 1.388E+01 | 1.388E+01 | 1.388E+01 | |
\({\text {F27}}\) | \(p-value\) | NA | 2.033E–04 | NA | NA | NA | 9.194E–05 | NA | 1.780E–04 |
\(t-test\) | 0 | –1.961E+00 | 0 | 0 | 0 | –3.215E+00 | 0 | –3.886E+00 | |
\({\text {F28}}\) | \(p-value\) | 9.207E–05 | NA | 9.207E–05 | 9.207E–05 | NA | 9.207E–05 | NA | NA |
\(t-test\) | 0 | 0 | 0 | –1.013E+00 | 0 | 0 | 0 | 0 | |
\({\text {F29}}\) | \(p-value\) | 9.207E–05 | 9.207E–05 | 9.207E–05 | 9.207E–05 | 9.207E–05 | 9.207E–05 | 9.207E–05 | 9.207E–05 |
\(t-test\) | –5.334E+00 | –3.372E+00 | –2.291E+00 | –1.877E+00 | –3.875E+00 | –4.152E+00 | –3.365E+00 | –5.027E+00 | |
\({\text {F30}}\) | \(p-value\) | 1.217E–03 | 3.173E–01 | 1.273E–03 | 1.273E–03 | 9.207E–05 | 2.451E–01 | 6.371E–05 | 8.416E–05 |
\(t-test\) | –9.997E–01 | –3.559E+00 | –9.997E–01 | –9.997E–01 | –4.094E–02 | –2.179E+00 | 0 | –7.670E–07 | |
\({\text {F31}}\) | \(p-value\) | 1.788E–05 | 3.163E–01 | 1.788E–05 | 8.926E–03 | 2.273E–04 | 1.391E–01 | 1.788E–05 | 2.415E–05 |
\(t-test\) | 1.083E–05 | –3.559E+00 | 1.083E–05 | –1.453E+00 | –4.768E+00 | –3.943E+00 | 1.083E–05 | 9.499E–06 | |
\({\text {F32}}\) | \(p-value\) | 9.207E–05 | 9.207E–05 | 9.207E–05 | 9.207E–05 | NA | 9.207E–05 | 9.207E–05 | 9.207E–05 |
\(t-test\) | –1.093E+00 | 0 | 0 | –1.138E+00 | 0 | 0 | 0 | 0 | |
\({\text {F33}}\) | \(p-value\) | 9.207E–05 | 9.207E–05 | 9.207E–05 | 9.207E–05 | NA | 9.207E–05 | 9.207E–05 | 9.207E–05 |
\(t-test\) | –4.446E+00 | –2.581E+00 | –2.200E+00 | –2.337E+00 | 0 | 0 | –1.000E+00 | 0 |
\({\text {F34}}\) | \(p-value\) | 9.207E–05 | 9.207E–05 | 9.207E–05 | 9.194E–05 | 9.207E–05 | 9.207E–05 | NA | 9.207E–05 |
\(t-test\) | –2.139E+00 | –1.044E+00 | –1.007E+00 | –1.025E+00 | –2.991E+00 | –1.038E+00 | 0 | –1.602E+00 | |
\({\text {F35}}\) | \(p-value\) | NA | NA | NA | NA | NA | NA | NA | NA |
\(t-test\) | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
\({\text {F36}}\) | \(p-value\) | 9.207E–05 | 9.207E–05 | 9.207E–05 | 9.207E–05 | 9.207E–05 | 9.207E–05 | 9.207E–05 | 9.207E–05 |
\(t-test\) | 0 | –3.164E+00 | 0 | 0 | –5.381E+00 | –3.079E+00 | 0 | –4.146E+00 | |
\({\text {F37}}\) | \(p-value\) | 8.139E–06 | 1.551E–03 | 8.139E–06 | 8.139E–06 | 9.207E–05 | 9.014E–05 | 8.139E–06 | 9.103E–05 |
\(t-test\) | 4.734E+10 | –9.999E–01 | 4.734E+10 | 4.734E+10 | –4.939E+00 | 1.429E+02 | 4.734E+10 | 7.124E+02 | |
\({\text {F38}}\) | \(p-value\) | 9.207E–05 | 1.691E–04 | 9.129E–05 | 9.168E–05 | 9.207E–05 | 9.207E–05 | 9.039E–05 | 7.042E–04 |
\(t-test\) | 5.075E+01 | 6.035E+00 | 4.058E+01 | 2.099E+01 | 3.950E+01 | 6.918E+00 | 4.149E+01 | 4.416E+00 | |
\({\text {F39}}\) | \(p-value\) | 9.207E–05 | 3.412E–02 | 9.207E–05 | 9.207E–05 | 1.732E–02 | 2.274E–03 | 9.207E–05 | 5.900E–03 |
\(t-test\) | 2.761E+01 | 2.051E+00 | 2.786E+01 | 2.069E+01 | 2.744E+00 | 2.451E+00 | 2.956E+01 | 3.218E+00 | |
\({\text {F40}}\) | \(p-value\) | NA | NA | NA | NA | NA | NA | NA | NA |
\(t-test\) | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
\({\text {F41}}\) | \(p-value\) | NA | NA | NA | NA | NA | NA | NA | NA |
\(t-test\) | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
\({\text {F42}}\) | \(p-value\) | NA | 7.813E–03 | NA | NA | NA | NA | NA | NA |
\(t-test\) | 0 | –2.603E+00 | 0 | 0 | 0 | 0 | 0 | 0 | |
\({\text {F43}}\) | \(p-value\) | 9.207E–05 | 4.883E–04 | 9.207E–05 | 9.207E–05 | 9.207E–05 | 1.563E–02 | NA | 4.456E–04 |
\(t-test\) | –2.015E+00 | –1.475E+00 | –6.554E+00 | –3.704E+00 | –3.292E+00 | –1.602E+00 | 0 | –2.259E+00 | |
\({\text {F44}}\) | \(p-value\) | NA | NA | NA | NA | NA | NA | NA | NA |
\(t-test\) | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
\({\text {F45}}\) | \(p-value\) | NA | 9.207E–05 | NA | NA | 9.207E–05 | NA | NA | 9.207E–05 |
\(t-test\) | 0 | –1.973E+00 | 0 | 0 | –2.486E+00 | 0 | 0 | –2.926E+00 | |
\({\text {F46}}\) | \(p-value\) | NA | 1.000E+00 | NA | NA | 9.207E–05 | NA | NA | 7.813E–03 |
\(t-test\) | 0 | –1.000E+00 | 0 | 0 | –2.714E+00 | –1.540E+00 | 0 | –1.000E+00 | |
\({\text {F47}}\) | \(p-value\) | 9.078E–05 | 9.207E–05 | 9.207E–05 | 9.091E–05 | 9.207E–05 | 9.207E–05 | 9.078E–05 | 9.207E–05 |
\(t-test\) | 3.169E+00 | –4.549E+00 | –3.611E+01 | 1.940E+00 | 2.770E+00 | 3.114E+00 | 3.169E+00 | –3.791E+00 | |
\({\text {F48}}\) | \(p-value\) | 9.181E–05 | 9.207E–05 | 9.168E–05 | 9.207E–05 | 9.207E–05 | 9.207E–05 | 9.091E–05 | 9.207E–05 |
\(t-test\) | 5.362E+01 | –4.484E+00 | 2.372E+01 | 1.486E+01 | –1.678E+01 | 1.174E+01 | 4.116E+01 | –1.217E–01 | |
\({\text {F49}}\) | \(p-value\) | NA | 9.207E–05 | NA | 1.000E+00 | 9.207E–05 | NA | NA | 9.207E–05 |
\(t-test\) | 0 | –2.277E+00 | 0 | –1.000E+00 | –1.669E+00 | 0 | 0 | –2.793E+00 | |
\({\text {F50}}\) | \(p-value\) | NA | 9.207E–05 | NA | NA | 9.207E–05 | NA | NA | 9.207E–05 |
\(t-test\) | 0 | –2.062E+00 | 0 | 0 | –3.150E+00 | 0 | 0 | –1.692E+00 | |
\({\text {F51}}\) | \(p-value\) | NA | 9.207E–05 | NA | NA | 9.207E–05 | NA | NA | 9.207E–05 |
\(t-test\) | 0 | –2.064E+00 | 0 | 0 | –1.940E+00 | 0 | 0 | –1.352E+00 |
