Table 8 Evaluation results of recent algorithms for the functions F1 to F15.
From: Learning cooking algorithm for solving global optimization problems
\({\text {Functions}}\) | \({\text {IGWO}}\) | \({\text {MWOA}}\) | \({\text {TLBO}}\) | \({\text {MTBO}}\) | \({\text {BWO}}\) | \({\text {HHO}}\) | \({\text {MGO}}\) | \({\text {SCSO}}\) | \({\text {LCA}}\) | |
|---|---|---|---|---|---|---|---|---|---|---|
\({\text {F1}}\) | Mean | 1.267E–60 | 2.658E–149 | 7.817E–183 | 8.815E–08 | 0 | 4.070E–189 | 9.615E–146 | 1.087E–223 | 0 |
Std | 3.214E–60 | 1.188E–148 | 0 | 3.859E–07 | 0 | 0 | 3.139E–145 | 0 | 0 | |
Best | 7.650E–64 | 6.649E–167 | 7.903E–186 | 2.228E–13 | 0 | 5.979E–204 | 6.557E–163 | 1.355E–241 | 0 | |
Worst | 1.309E–59 | 5.315E–148 | 3.515E–182 | 1.727E–06 | 0 | 7.215E–188 | 1.400E–144 | 2.174E–222 | 0 | |
Median | 2.321E–61 | 1.459E–155 | 1.663E–183 | 5.748E–11 | 0 | 2.199E–195 | 1.211E–148 | 7.329E–237 | 0 | |
\({\text {F2}}\) | Mean | 4.710E–37 | 1.212E–103 | 7.484E–92 | 1.613E–01 | 1.480E–259 | 2.994E–97 | 4.230E–84 | 5.858E–123 | 0 |
Std | 4.200E–37 | 4.381E–103 | 1.407E–91 | 4.500E–01 | 0 | 9.789E–97 | 9.363E–84 | 2.239E–122 | 0 | |
Best | 7.989E–38 | 5.944E–113 | 2.094E–93 | 7.179E–04 | 4.975E–269 | 1.223E–105 | 1.906E–89 | 1.096E–129 | 0 | |
Worst | 1.412E–36 | 1.953E–102 | 6.495E–91 | 2.027E+00 | 2.954E–258 | 4.176E–96 | 3.041E–83 | 1.000E–121 | 0 | |
Median | 2.867E–37 | 5.907E–109 | 3.171E–92 | 3.228E–02 | 3.320E–265 | 1.812E–100 | 2.422E–85 | 6.140E–127 | 0 | |
\({\text {F3}}\) | Mean | 3.280E–10 | 1.909E+04 | 5.176E–41 | 1.494E+02 | 0 | 4.056E–147 | 7.074E–18 | 8.844E–195 | 0 |
Std | 9.589E–10 | 8.656E+03 | 6.618E–41 | 1.916E+02 | 0 | 1.814E–146 | 2.752E–17 | 0 | 0 | |
Best | 7.621E–14 | 2.357E+03 | 1.985E–44 | 7.682E+00 | 0 | 1.479E–180 | 8.967E–29 | 6.248E–214 | 0 | |
Worst | 4.149E–09 | 3.869E+04 | 1.954E–40 | 6.363E+02 | 0 | 8.113E–146 | 1.228E–16 | 1.769E–193 | 0 | |
Median | 5.332E–12 | 1.654E+04 | 2.223E–41 | 5.639E+01 | 0 | 1.584E–163 | 4.292E–23 | 1.076E–205 | 0 | |
\({\text {F4}}\) | Mean | 1.150E–11 | 4.610E+01 | 8.366E–75 | 1.007E+01 | 1.359E–252 | 1.031E–90 | 2.942E–47 | 8.172E–101 | 0 |
Std | 1.633E–11 | 2.958E+01 | 9.442E–75 | 3.024E+00 | 0 | 4.611E–90 | 8.594E–47 | 3.595E–100 | 0 | |
Best | 9.717E–13 | 1.765E–01 | 4.521E–76 | 5.932E+00 | 1.728E–260 | 5.362E–103 | 4.449E–57 | 2.272E–111 | 0 | |
Worst | 6.413E–11 | 9.001E+01 | 4.347E–74 | 2.032E+01 | 2.706E–251 | 2.062E–89 | 3.530E–46 | 1.609E–99 | 0 | |
Median | 4.784E–12 | 5.984E+01 | 5.792E–75 | 9.785E+00 | 5.736E–257 | 5.788E–99 | 3.281E–50 | 2.826E–105 | 0 | |
\({\text {F5}}\) | Mean | 2.296E+01 | 2.700E+01 | 2.406E+01 | 6.069E+01 | 1.451E–13 | 1.817E–03 | 1.652E–30 | 2.800E+01 | 0 |
Std | 1.971E–01 | 3.619E–01 | 6.934E–01 | 3.333E+01 | 5.440E–13 | 1.658E–03 | 3.857E–30 | 7.589E–01 | 0 | |
Best | 2.261E+01 | 2.639E+01 | 2.267E+01 | 7.835E+00 | 1.344E–19 | 2.044E–05 | 0 | 2.711E+01 | 0 | |
Worst | 2.337E+01 | 2.796E+01 | 2.530E+01 | 1.315E+02 | 2.445E–12 | 6.287E–03 | 1.514E–29 | 2.887E+01 | 0 | |
Median | 2.294E+01 | 2.692E+01 | 2.417E+01 | 7.178E+01 | 1.104E–15 | 1.547E–03 | 0 | 2.804E+01 | 0 | |
\({\text {F6}}\) | Mean | 4.734E–06 | 5.520E–02 | 1.071E–10 | 1.279E–06 | 9.033E–28 | 4.384E–05 | 2.708E–15 | 1.930E+00 | 0 |
Std | 2.118E–06 | 6.349E–02 | 2.568E–10 | 3.912E–06 | 1.751E–27 | 6.932E–05 | 1.002E–14 | 4.083E–01 | 0 | |
Best | 2.518E–06 | 9.860E–03 | 2.253E–14 | 8.527E–13 | 3.236E–31 | 1.710E–07 | 1.594E–19 | 1.260E+00 | 0 | |
Worst | 1.080E–05 | 2.690E–01 | 1.085E–09 | 1.273E–05 | 6.916E–27 | 2.335E–04 | 4.504E–14 | 2.771E+00 | 0 | |
Median | 4.191E–06 | 3.477E–02 | 2.511E–12 | 5.278E–10 | 1.169E–28 | 1.194E–05 | 8.987E–17 | 1.898E+00 | 0 | |
\({\text {F7}}\) | Mean | 1.415E–03 | 1.040E–03 | 5.429E–04 | 5.460E–02 | 7.321E–05 | 1.016E–04 | 2.255E–04 | 1.041E–04 | 2.969E–05 |
Std | 4.332E–04 | 1.185E–03 | 2.086E–04 | 2.505E–02 | 5.329E–05 | 1.985E–04 | 1.330E–04 | 1.573E–04 | 1.651E–05 | |
Best | 7.231E–04 | 2.755E–05 | 1.847E–04 | 1.888E–02 | 5.563E–06 | 3.240E–06 | 1.935E–05 | 2.874E–06 | 1.534E–05 | |
Worst | 2.576E–03 | 4.881E–03 | 8.562E–04 | 1.015E–01 | 1.673E–04 | 9.265E–04 | 4.618E–04 | 6.886E–04 | 6.860E–05 | |
Median | 1.389E–03 | 8.353E–04 | 5.748E–04 | 5.118E–02 | 6.474E–05 | 4.619E–05 | 2.215E–04 | 4.609E–05 | 2.213E–05 | |
\({\text {F8}}\) | Mean | –9.748E+03 | –9.080E+03 | –8.154E+03 | –7.601E+03 | –1.257E+04 | –1.257E+04 | –1.257E+04 | –6.920E+03 | –1.26E+04 |
Std | 1.085E+03 | 1.220E+03 | 5.918E+02 | 1.025E+03 | 3.732E–12 | 3.002E–01 | 1.430E–10 | 5.515E+02 | 1.87E–12 | |
Best | –1.095E+04 | –1.257E+04 | –9.175E+03 | –8.789E+03 | –1.257E+04 | –1.257E+04 | –1.257E+04 | –7.872E+03 | –1.26E+04 | |
Worst | –7.319E+03 | –7.725E+03 | –7.268E+03 | –4.414E+03 | –1.257E+04 | –1.257E+04 | –1.257E+04 | –5.906E+03 | –1.26E+04 | |
Median | –1.007E+04 | –8.874E+03 | –8.127E+03 | –7.804E+03 | –1.257E+04 | –1.257E+04 | –1.257E+04 | –6.923E+03 | –1.26E+04 | |
\({\text {F9}}\) | Mean | 1.814E+01 | 0 | 1.380E+01 | 3.661E+01 | 0 | 0 | 0 | 0 | 0 |
Std | 7.141E+00 | 0 | 6.331E+00 | 8.832E+00 | 0 | 0 | 0 | 0 | 0 | |
Best | 3.227E+00 | 0 | 0 | 1.990E+01 | 0 | 0 | 0 | 0 | 0 | |
Worst | 3.060E+01 | 0 | 2.687E+01 | 5.472E+01 | 0 | 0 | 0 | 0 | 0 | |
Median | 1.908E+01 | 0 | 1.492E+01 | 3.681E+01 | 0 | 0 | 0 | 0 | 0 | |
\({\text {F10}}\) | Mean | 1.341E–14 | 2.931E–15 | 6.128E–15 | 9.046E+00 | 4.441E–16 | 4.441E–16 | 1.155E–15 | 4.441E–16 | 4.441E–16 |
Std | 2.383E–15 | 2.334E–15 | 1.786E–15 | 1.807E+00 | 2.023E–31 | 2.023E–31 | 1.458E–15 | 2.023E–31 | 1.012E–31 | |
Best | 7.550E–15 | 4.441E–16 | 3.997E–15 | 4.383E+00 | 4.441E–16 | 4.441E–16 | 4.441E–16 | 4.441E–16 | 4.441E–16 | |
Worst | 1.465E–14 | 7.550E–15 | 7.550E–15 | 1.173E+01 | 4.441E–16 | 4.441E–16 | 3.997E–15 | 4.441E–16 | 4.441E–16 | |
Median | 1.465E–14 | 3.997E–15 | 7.550E–15 | 9.123E+00 | 4.441E–16 | 4.441E–16 | 4.441E–16 | 4.441E–16 | 4.441E–16 | |
\({\text {F11}}\) | Mean | 1.180E–02 | 3.307E–03 | 0 | 1.032E–01 | 0 | 0 | 0 | 0 | 0 |
Std | 1.467E–02 | 1.479E–02 | 0 | 1.283E–01 | 0 | 0 | 0 | 0 | 0 | |
Best | 0 | 0 | 0 | 7.396E–03 | 0 | 0 | 0 | 0 | 0 | |
Worst | 5.880E–02 | 6.614E–02 | 0 | 5.940E–01 | 0 | 0 | 0 | 0 | 0 | |
Median | 8.627E–03 | 0 | 0 | 6.851E–02 | 0 | 0 | 0 | 0 | 0 | |
\({\text {F12}}\) | Mean | 2.283E–07 | 1.130E–02 | 1.037E–02 | 1.770E+00 | 1.892E–25 | 1.149E–06 | 1.571E–32 | 6.675E–02 | 1.570E–32 |
Std | 7.663E–08 | 1.370E–02 | 3.191E–02 | 1.828E+00 | 2.749E–25 | 1.161E–06 | 5.616E–48 | 2.410E–02 | 2.808E–48 | |
Best | 7.831E–08 | 7.591E–04 | 4.222E–15 | 2.516E–04 | 8.837E–28 | 1.159E–08 | 1.571E–32 | 2.695E–02 | 1.570E–32 | |
Worst | 3.967E–07 | 6.256E–02 | 1.037E–01 | 7.249E+00 | 9.150E–25 | 3.925E–06 | 1.571E–32 | 1.147E–01 | 1.570E–32 | |
Median | 2.256E–07 | 8.073E–03 | 3.779E–13 | 1.242E+00 | 3.747E–26 | 7.914E–07 | 1.571E–32 | 6.303E–02 | 1.570E–32 | |
\({\text {F13}}\) | Mean | 1.469E–02 | 2.273E–01 | 6.869E–02 | 1.035E+01 | 1.333E–24 | 2.155E–05 | 1.350E–32 | 2.392E+00 | 1.349E–32 |
Std | 3.586E–02 | 1.625E–01 | 6.716E–02 | 7.885E+00 | 2.261E–24 | 3.914E–05 | 2.808E–48 | 2.809E–01 | 5.616E–48 | |
Best | 1.902E–06 | 1.967E–02 | 8.994E–12 | 1.099E–02 | 2.506E–28 | 2.016E–07 | 1.350E–32 | 1.752E+00 | 1.349E–32 | |
Worst | 9.889E–02 | 6.187E–01 | 1.956E–01 | 2.573E+01 | 8.684E–24 | 1.604E–04 | 1.350E–32 | 2.789E+00 | 1.349E–32 | |
Median | 7.286E–06 | 2.092E–01 | 4.224E–02 | 8.715E+00 | 5.157E–25 | 8.669E–06 | 1.350E–32 | 2.495E+00 | 1.349E–32 | |
\({\text {F14}}\) | Mean | 0.9980038 | 2.5697519 | 0.9980038 | 0.9980038 | 0.9980038 | 1.2445459 | 0.9980038 | 3.6494023 | 0.998 |
Std | 2.278E–16 | 2.9462685 | 2.278E–16 | 2.278E–16 | 1.161E–12 | 1.102569 | 2.278E–16 | 3.476762 | 0 | |
Best | 0.9980038 | 0.9980038 | 0.9980038 | 0.9980038 | 0.9980038 | 0.9980038 | 0.9980038 | 0.9980038 | 0.998 | |
Worst | 0.9980038 | 10.763180 | 0.9980038 | 0.9980038 | 0.9980038 | 5.9288451 | 0.9980038 | 12.670505 | 0.998 | |
Median | 0.9980038 | 0.9980038 | 0.9980038 | 0.9980038 | 0.9980038 | 0.9980038 | 0.9980038 | 2.9821051 | 0.998 | |
\({\text {F15}}\) | Mean | 3.533E–04 | 6.378E–04 | 1.312E–03 | 1.579E–03 | 3.448E–04 | 3.298E–04 | 4.448E–04 | 3.784E–04 | 3.109E–04 |
Std | 2.048E–04 | 4.774E–04 | 4.484E–03 | 4.430E–03 | 3.730E–05 | 1.879E–05 | 3.355E–04 | 2.083E–04 | 3.534E–06 | |
Best | 3.075E–04 | 3.085E–04 | 3.075E–04 | 3.075E–04 | 3.079E–04 | 3.090E–04 | 3.075E–04 | 3.075E–04 | 3.087E–04 | |
Worst | 1.223E–03 | 2.180E–03 | 2.036E–02 | 2.036E–02 | 4.228E–04 | 3.773E–04 | 1.223E–03 | 1.223E–03 | 3.185E–04 | |
Median | 3.075E–04 | 4.489E–04 | 3.075E–04 | 6.100E–04 | 3.306E–04 | 3.292E–04 | 3.075E–04 | 3.075E–04 | 3.089E–04 |
