Table 10 Evaluation results of recent algorithms for the functions F31 to F51.
From: Learning cooking algorithm for solving global optimization problems
\({\text {Functions}}\) | \({\text {IGWO}}\) | \({\text {MWOA}}\) | \({\text {TLBO}}\) | \({\text {MTBO}}\) | \({\text {BWO}}\) | \({\text {HHO}}\) | \({\text {MGO}}\) | \({\text {SCSO}}\) | \({\text {LCA}}\) | |
|---|---|---|---|---|---|---|---|---|---|---|
\({\text {F31}}\) | Mean | –2600 | –2519.999983 | –2600 | –2580 | –2593.528239 | –2510 | –2600 | –2600 | \(-2600\) |
Std | 1.119E–11 | 1.005E+02 | 0 | 61.55870113 | 6.035411821 | 102.0835571 | 0 | 3.49179E–07 | 0.6545 | |
Best | –2600 | –2600 | –2600 | –2600 | –2599.959733 | –2600 | –2600 | –2600 | \(-2600\) | |
Worst | –2600 | –2399.999998 | –2600 | –2400 | –2576.88762 | –2400 | –2600 | –2599.999998 | \(-2600\) | |
Median | –2600 | –2599.999954 | –2600 | –2600 | –2594.802697 | –2600 | –2600 | –2600 | \(-2600\) | |
\({\text {F32}}\) | Mean | 1.513E–125 | 4.062E–158 | 9.256E–225 | 2.301E–63 | 0 | 3.147E–188 | 1.340E–234 | 1.891E–261 | 0 |
Std | 6.191E–125 | 0 | 0 | 9.040E–63 | 0 | 0 | 0 | 0 | 0 | |
Best | 1.384E–131 | 4.719E–173 | 2.284E–228 | 1.763E–70 | 0 | 3.332E–212 | 1.215E–252 | 1.143E–286 | 0 | |
Worst | 2.777E–124 | 6.563E–157 | 1.145E–223 | 4.036E–62 | 0 | 6.195E–187 | 2.679E–233 | 3.782E–260 | 0 | |
Median | 4.947E–128 | 3.070E–164 | 1.258E–226 | 2.639E–67 | 0 | 2.077E–200 | 8.613E–246 | 7.253E–276 | 0 | |
\({\text {F33}}\) | Mean | 2.328E–05 | 2.007E–06 | 1.240E–06 | 3.695E–03 | 0 | 5.520E–189 | 7.414E–20 | 2.249E–205 | 0 |
Std | 2.341E–05 | 3.478E–06 | 2.519E–06 | 7.070E–03 | 0 | 0 | 3.314E–19 | 0 | 0 | |
Best | 6.034E–07 | 6.492E–24 | 2.408E–09 | 1.681E–04 | 0 | 1.324E–209 | 7.169E–79 | 1.748E–223 | 0 | |
Worst | 9.158E–05 | 1.354E–05 | 8.784E–06 | 2.862E–02 | 0 | 1.017E–187 | 1.482E–18 | 2.604E–204 | 0 | |
Median | 1.398E–05 | 4.760E–07 | 9.067E–08 | 6.301E–04 | 0 | 3.412E–196 | 1.955E–39 | 2.576E–209 | 0 | |
\({\text {F34}}\) | Mean | 4.207E–08 | 9.121E–05 | 1.095E–09 | 1.103E–07 | 9.939E–04 | 1.374E–06 | 0 | 2.354E–09 | 0 |
Std | 8.795E–08 | 3.906E–04 | 4.863E–09 | 4.815E–07 | 1.486E–03 | 5.915E–06 | 0 | 6.571E–09 | 0 | |
Best | 9.802E–13 | 2.739E–13 | 1.758E–29 | 7.216E–29 | 5.463E–05 | 6.312E–19 | 0 | 1.378E–12 | 0 | |
Worst | 3.007E–07 | 1.750E–03 | 2.176E–08 | 2.155E–06 | 6.081E–03 | 2.649E–05 | 0 | 2.880E–08 | 0 | |
Median | 2.558E–09 | 7.092E–08 | 9.042E–15 | 8.723E–18 | 3.248E–04 | 7.162E–11 | 0 | 5.137E–11 | 0 | |
\({\text {F35}}\) | Mean | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
Std | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
Best | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
Worst | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
Median | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
\({\text {F36}}\) | Mean | 0 | 1.846E–04 | 0 | 0 | 1.316E–02 | 1.351E–05 | 0 | 1.507E–09 | 0 |
Std | 0 | 1.829E–04 | 0 | 0 | 1.094E–02 | 1.962E–05 | 0 | 1.625E–09 | 0 | |
Best | 0 | 1.547E–06 | 0 | 0 | 2.826E–04 | 5.889E–07 | 0 | 1.735E–10 | 0 | |
Worst | 0 | 6.420E–04 | 0 | 0 | 4.312E–02 | 8.616E–05 | 0 | 6.555E–09 | 0 | |
Median | 0 | 1.277E–04 | 0 | 0 | 1.146E–02 | 7.420E–06 | 0 | 9.423E–10 | 0 | |
\({\text {F37}}\) | Mean | –1.801E+00 | –1.761E+00 | –1.80130341 | –1.80130341 | –1.792931404 | –1.801303341 | –1.80130341 | –1.801303393 | –1.8013 |
Std | 2.278E–16 | 1.792E–01 | 2.27813E–16 | 2.27813E–16 | 0.007577534 | 1.0454E–07 | 2.27813E–16 | 2.12997E–08 | 2.27813E–16 | |
Best | –1.801E+00 | –1.801E+00 | –1.80130341 | –1.80130341 | –1.801118771 | –1.80130341 | –1.80130341 | –1.80130341 | \(-1.8013\) | |
Worst | –1.801E+00 | –1.000E+00 | –1.80130341 | –1.80130341 | –1.778829412 | –1.801303089 | –1.80130341 | –1.801303338 | \(-1.8013\) | |
Median | –1.801E+00 | –1.801E+00 | –1.80130341 | –1.80130341 | –1.795093528 | –1.801303403 | –1.80130341 | –1.801303402 | \(-1.8013\) | |
\({\text {F38}}\) | Mean | –4.688E+00 | –3.931E+00 | –4.599170064 | –4.525632059 | –4.533729173 | –3.972500532 | –4.619902565 | –3.838872176 | –3.25754 |
Std | 7.889E–06 | 4.832E–01 | 0.077337752 | 0.238929809 | 0.070670424 | 0.444660327 | 0.075397429 | 0.575059478 | 0.126028177 | |
Best | –4.688E+00 | –4.685E+00 | –4.687658179 | –4.687658179 | –4.642856136 | –4.644847481 | –4.687658179 | –4.687648188 | –3.426 | |
Worst | –4.688E+00 | –2.985E+00 | –4.495893207 | –3.694589796 | –4.424495995 | –3.42015395 | –4.483135734 | –2.79789007 | –3.0562 | |
Median | –4.688E+00 | –3.709E+00 | –4.644837995 | –4.645895026 | –4.518993699 | –3.972060041 | –4.645895368 | –3.694589523 | –3.22785 | |
\({\text {F39}}\) | Mean | –9.068E+00 | –6.008E+00 | –9.01522002 | –8.732242041 | –6.070391308 | –6.110441526 | –9.046555997 | –6.43592972 | –5.66115 |
Std | 3.435E–01 | 6.219E–01 | 0.321545056 | 0.504127326 | 0.508509705 | 0.696997939 | 0.275474881 | 0.98654883 | 0.431730696 | |
Best | –9.550E+00 | –7.019E+00 | –9.425864026 | –9.343178782 | –7.736882995 | –7.190986668 | –9.384751108 | –8.79614711 | –6.3366 | |
Worst | –7.953E+00 | –4.714E+00 | –8.356104448 | –7.569585751 | –5.446550181 | –4.883048814 | –8.458962888 | –4.650984325 | –5.2273 | |
Median | –9.098E+00 | –6.045E+00 | –9.079140438 | –8.78895874 | –6.008318134 | –6.078816149 | –9.066799789 | –6.312001237 | –5.4497 | |
\({\text {F40}}\) | Mean | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
Std | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
Best | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
Worst | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
Median | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
\({\text {F41}}\) | Mean | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
Std | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
Best | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
Worst | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
Median | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
\({\text {F42}}\) | Mean | 0 | 9.714E–17 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
Std | 0 | 1.669E–16 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
Best | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
Worst | 0 | 5.551E–16 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
Median | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
\({\text {F43}}\) | Mean | –24.99985224 | –24.99999928 | –24.99871775 | –24.99822699 | –24.99994621 | –24.99999994 | –25 | –24.99999945 | \(-25\) |
Std | 0.000327874 | 2.16995E–06 | 0.000874902 | 0.002140763 | 7.30727E–05 | 1.73922E–07 | 0 | 1.09684E–06 | 0 | |
Best | –24.99999926 | –25 | –24.9999503 | –24.99999999 | –24.99999993 | –25 | –25 | –25 | \(-25\) | |
Worst | –24.99851988 | –24.99999037 | –24.99727191 | –24.99074036 | –24.99970548 | –24.99999924 | –25 | –24.99999561 | \(-25\) | |
Median | –24.99995762 | –24.99999998 | –24.99867017 | –24.99867989 | –24.99996887 | –25 | –25 | –24.99999998 | \(-25\) | |
\({\text {F44}}\) | Mean | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
Std | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
Best | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
Worst | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
Median | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
\({\text {F45}}\) | Mean | 0 | 4.735E–12 | 0 | 0 | 0.000462133 | 0 | 0 | 3.76103E–08 | 0 |
Std | 0 | 1.073E–11 | 0 | 0 | 0.000831292 | 0 | 0 | 5.74829E–08 | 0 | |
Best | 0 | 2.251E–16 | 0 | 0 | 1.20274E–06 | 0 | 0 | 1.26264E–10 | 0 | |
Worst | 0 | 3.764E–11 | 0 | 0 | 0.003421027 | 0 | 0 | 2.1425E–07 | 0 | |
Median | 0 | 1.066E–13 | 0 | 0 | 7.17244E–05 | 0 | 0 | 9.08508E–09 | 0 | |
\({\text {F46}}\) | Mean | –1.034 | –1.014105252 | –1.034 | –1.034 | –1.029926715 | –1.034 | –1.034 | –1.008149999 | \(-1.0341\) |
Std | 0 | 0.088972017 | 0 | 0 | 0.006712129 | 1.51796E–11 | 0 | 0.115604714 | 0 | |
Best | –1.034 | –1.034 | –1.034 | –1.034 | –1.033991487 | –1.034 | –1.034 | –1.034 | \(-1.034\) | |
Worst | –1.034 | –0.636105042 | –1.034 | –1.034 | –1.006485061 | –1.034 | –1.034 | –0.517 | \(-1.034\) | |
Median | –1.034 | –1.034 | –1.034 | –1.034 | –1.032821904 | –1.034 | –1.034 | –1.034 | \(-1.034\) | |
\({\text {F47}}\) | Mean | –4.825 | –3.868825722 | –2.234366896 | –4.776750076 | –4.799467405 | –4.82143072 | –4.825 | –4.017799574 | –4.62031 |
Std | 9.11252E–16 | 0.680018044 | 0.062194668 | 0.215780221 | 0.014149513 | 0.002303213 | 9.11252E–16 | 0.649473866 | 0.288855 | |
Best | –4.825 | –4.824984594 | –2.248633351 | –4.825 | –4.823591842 | –4.824955173 | –4.825 | –4.824999894 | –4.6849 | |
Worst | –4.825 | –2.894993803 | –1.970212321 | –3.860001516 | –4.775673138 | –4.817382988 | –4.825 | –2.865683603 | –3.3931 | |
Median | –4.825 | –3.859971954 | –2.248633351 | –4.825 | –4.801538318 | –4.821446897 | –4.825 | –3.860003321 | –4.6849 | |
\({\text {F48}}\) | Mean | –8.759999994 | –5.087587315 | –8.453450888 | –7.806566271 | –4.473652447 | –7.395415441 | –8.7162 | –5.814601868 | –5.838515 |
Std | 1.02509E–08 | 0.708116778 | 0.428608666 | 0.53971358 | 0.270184415 | 0.540574512 | 0.195879555 | 0.843970291 | 0.2436643 | |
Best | –8.76 | –6.130314235 | –8.76 | –8.76 | –4.937067039 | –8.667871498 | –8.76 | –7.010837453 | –5.893 | |
Worst | –8.759999958 | –3.504007998 | –7.884000001 | –7.009513304 | –3.918868486 | –6.856856991 | –7.884 | –3.989170484 | –4.8033 | |
Median | –8.759999999 | –5.241225781 | –8.76 | –7.884009291 | –4.483067125 | –7.190286478 | –8.76 | –6.022940734 | –5.893 | |
\({\text {F49}}\) | Mean | 0 | 1.899E–13 | 0 | 2.426E–27 | 7.656E–06 | 0 | 0 | 7.467E–10 | 0 |
Std | 0 | 3.730E–13 | 0 | 1.085E–26 | 2.051E–05 | 0 | 0 | 1.196E–09 | 0 | |
Best | 0 | 1.140E–17 | 0 | 0 | 8.644E–10 | 0 | 0 | 1.181E–12 | 0 | |
Worst | 0 | 1.408E–12 | 0 | 4.852E–26 | 8.843E–05 | 0 | 0 | 5.049E–09 | 0 | |
Median | 0 | 1.728E–14 | 0 | 0 | 7.588E–07 | 0 | 0 | 2.711E–10 | 0 | |
\({\text {F50}}\) | Mean | 0 | 1.926E–13 | 0 | 0 | 5.142E–05 | 0 | 0 | 2.632E–09 | 0 |
Std | 0 | 4.177E–13 | 0 | 0 | 7.299E–05 | 0 | 0 | 6.959E–09 | 0 | |
Best | 0 | 1.223E–16 | 0 | 0 | 3.136E–09 | 0 | 0 | 6.075E–14 | 0 | |
Worst | 0 | 1.793E–12 | 0 | 0 | 2.227E–04 | 0 | 0 | 3.115E–08 | 0 | |
Median | 0 | 1.516E–14 | 0 | 0 | 1.174E–05 | 0 | 0 | 3.446E–10 | 0 | |
\({\text {F51}}\) | Mean | 0 | 1.331E–13 | 0 | 0 | 1.181E–06 | 0 | 0 | 2.443E–09 | 0 |
Std | 0 | 2.884E–13 | 0 | 0 | 2.723E–06 | 0 | 0 | 8.081E–09 | 0 | |
Best | 0 | 2.803E–17 | 0 | 0 | 4.846E–10 | 0 | 0 | 2.021E–13 | 0 | |
Worst | 0 | 1.185E–12 | 0 | 0 | 1.194E–05 | 0 | 0 | 3.535E–08 | 0 | |
Median | 0 | 1.094E–15 | 0 | 0 | 7.483E–08 | 0 | 0 | 1.222E–10 | 0 |
