Table 5 Evaluation results of well-known & top-performing algorithms for the functions F1 to F15.
From: Learning cooking algorithm for solving global optimization problems
\({\text {Functions}}\) | \({\text {PSO}}\) | \({\text {TSA}}\) | \({\text {SSA}}\) | \({\text {MVO}}\) | \({\text {GWO}}\) | \({\text {WOA}}\) | \({\text {GJO}}\) | \({\text {LSHADE}}\) | \({\text {CMAES}}\) | \({\text {LCA}}\) | |
|---|---|---|---|---|---|---|---|---|---|---|---|
\({\text {F1}}\) | Mean | 1.694E–05 | 3.954E–47 | 1.204E–08 | 3.086E–01 | 1.997E–59 | 6.61E–155 | 4.29E–113 | 2.005E–06 | 1.231E–24 | 0 |
Std | 1.926E–05 | 8.091E–47 | 2.692E–09 | 8.637E–02 | 3.320E–59 | 1.91E–154 | 1.06E–112 | 2.290E–06 | 1.120E–24 | 0 | |
Best | 7.962E–07 | 6.342E–51 | 7.892E–09 | 1.741E–01 | 6.033E–6 | 7.18E–165 | 1.95E–117 | 1.429E–08 | 2.347E–25 | 0 | |
Worst | 6.793E–05 | 2.649E–46 | 1.573E–08 | 4.288E–01 | 1.063E–58 | 6.56E–154 | 3.45E–112 | 7.216E–06 | 4.321E–24 | 0 | |
Median | 1.106E–05 | 1.219E–48 | 1.273E–08 | 2.920E–01 | 3.049E–60 | 1.79E–161 | 2.46E–115 | 1.136E–06 | 8.201E–25 | 0 | |
\({\text {F2}}\) | Mean | 8.188E–03 | 6.762E–29 | 6.591E–01 | 5.155E–01 | 7.543E–35 | 5.75E–103 | 2.362E–66 | 9.163E–04 | 3.573E–12 | 0 |
Std | 4.409E–03 | 1.286E–28 | 8.061E–01 | 1.691E–01 | 5.818E–35 | 1.76E–102 | 3.454E–66 | 1.685E–03 | 1.408E–12 | 0 | |
Best | 3.156E–03 | 3.278E–30 | 1.454E–02 | 3.085E–01 | 1.023E–35 | 2.50E–108 | 3.308E–67 | 5.388E–05 | 1.656E–12 | 0 | |
Worst | 1.477E–02 | 4.296E–28 | 2.245E+00 | 7.696E–01 | 1.991E–34 | 5.72E–102 | 1.117E–65 | 7.189E–03 | 5.666E–12 | 0 | |
Median | 7.437E–03 | 1.350E–29 | 3.143E–01 | 4.565E–01 | 6.116E–35 | 2.91E–107 | 8.758E–67 | 2.315E–04 | 3.678E–12 | 0 | |
\({\text {F3}}\) | Mean | 1.881E+01 | 1.413E–11 | 3.493E+02 | 4.653E+01 | 5.345E–14 | 2.465E+04 | 4.696E–39 | 3.474E+01 | 2.050E+00 | 0 |
Std | 8.849E+00 | 2.883E–11 | 2.755E+02 | 1.994E+01 | 1.613E–13 | 1.254E+04 | 1.398E–38 | 2.717E+01 | 1.389E+00 | 0 | |
Best | 9.030E+00 | 1.878E–16 | 1.086E+02 | 2.501E+01 | 4.204E–20 | 4.527E+03 | 7.583E–46 | 3.729E+00 | 6.423E–01 | 0 | |
Worst | 3.849E+01 | 8.084E–11 | 1.060E+03 | 8.514E+01 | 5.251E–13 | 4.534E+04 | 4.558E–38 | 9.065E+01 | 5.304E+00 | 0 | |
Median | 1.646E+01 | 2.186E–14 | 2.304E+02 | 4.071E+01 | 1.079E–16 | 2.632E+04 | 5.334E–41 | 3.192E+01 | 1.764E+00 | 0 | |
\({\text {F4}}\) | Mean | 7.462E–01 | 5.400E–03 | 8.570E+00 | 9.789E–01 | 8.888E–15 | 4.222E+01 | 1.115E–32 | 8.418E+00 | 7.135E–10 | 0 |
Std | 1.685E–01 | 1.156E–02 | 3.952E+00 | 4.094E–01 | 6.057E–15 | 3.313E+01 | 3.029E–32 | 2.191E+00 | 2.074E–10 | 0 | |
Best | 4.673E–01 | 4.023E–05 | 1.995E+00 | 4.774E–01 | 9.666E–16 | 7.332E–01 | 2.987E–35 | 5.458E+00 | 4.974E–10 | 0 | |
Worst | 1.119E+00 | 3.885E–02 | 1.361E+01 | 1.850E+00 | 1.847E–14 | 8.772E+01 | 9.945E–32 | 1.298E+01 | 1.357E–09 | 0 | |
Median | 7.357E–01 | 1.420E–03 | 8.594E+00 | 9.772E–01 | 1.095E–14 | 4.356E+01 | 6.003E–34 | 8.071E+00 | 6.338E–10 | 0 | |
\({\text {F5}}\) | Mean | 1.567E+02 | 2.815E+01 | 4.130E+02 | 7.026E+02 | 2.673E+01 | 2.750E+01 | 2.773E+01 | 4.638E+01 | 2.705E+00 | 0 |
Std | 1.342E+02 | 8.143E–01 | 7.855E+02 | 9.315E+02 | 6.005E–01 | 7.525E–01 | 7.617E–01 | 2.930E+01 | 6.222E–01 | 0 | |
Best | 2.972E+01 | 2.642E+01 | 2.514E+01 | 3.361E+01 | 2.617E+01 | 2.664E+01 | 2.624E+01 | 3.970E+00 | 1.777E+00 | 0 | |
Worst | 4.328E+02 | 2.886E+01 | 2.671E+03 | 2.481E+03 | 2.793E+01 | 2.875E+01 | 2.887E+01 | 8.412E+01 | 3.812E+00 | 0 | |
Median | 9.772E+01 | 2.833E+01 | 1.404E+02 | 1.578E+02 | 2.667E+01 | 2.715E+01 | 2.80E+01 | 2.916E+01 | 2.748E+00 | 0 | |
\({\text {F6}}\) | Mean | 1.770E–05 | 3.655E+00 | 1.513E–08 | 3.024E–01 | 8.147E–01 | 1.735E–01 | 2.312E+00 | 1.672E–06 | 1.082E–24 | 0 |
Std | 1.063E–05 | 4.294E–01 | 6.384E–09 | 8.260E–02 | 3.183E–01 | 2.382E–01 | 4.422E–01 | 4.948E–06 | 8.075E–25 | 0 | |
Best | 3.187E–06 | 2.576E+00 | 1.008E–08 | 1.885E–01 | 2.516E–01 | 1.111E–02 | 1.749E+00 | 2.501E–08 | 1.832E–25 | 0 | |
Worst | 3.810E–05 | 4.050E+00 | 3.033E–08 | 5.125E–01 | 1.483E+00 | 7.978E–01 | 3.013E+00 | 2.243E–05 | 2.513E–24 | 0 | |
Median | 1.582E–05 | 3.814E+00 | 1.254E–08 | 3.032E–01 | 7.491E–01 | 4.599E–02 | 2.246E+00 | 2.701E–07 | 8.051E–25 | 0 | |
\({\text {F7}}\) | Mean | 8.297E–02 | 5.990E–03 | 9.157E–02 | 2.281E–02 | 8.363E–04 | 9.469E–04 | 2.573E–04 | 5.008E–02 | 3.668E–03 | 2.969E–05 |
Std | 1.844E–02 | 1.790E–03 | 3.812E–02 | 6.110E–03 | 3.756E–04 | 8.758E–04 | 1.034E–04 | 2.134E–02 | 1.629E–03 | 1.651E–05 | |
Best | 4.813E–02 | 3.650E–03 | 3.571E–02 | 1.466E–02 | 1.959E–04 | 1.163E–04 | 1.081E–04 | 2.631E–02 | 7.526E–04 | 1.534E–05 | |
Worst | 1.055E–01 | 9.810E–03 | 1.628E–01 | 3.041E–02 | 1.362E–03 | 2.093E–03 | 4.528E–04 | 1.054E–01 | 6.576E–03 | 6.860E–05 | |
Median | 8.990E–02 | 5.750E–03 | 9.604E–02 | 2.552E–02 | 7.988E–04 | 3.755E–04 | 2.354E–04 | 4.582E–02 | 3.698E–03 | 2.213E–05 | |
\({\text {F8}}\) | Mean | –6.67E+03 | –6.45E+03 | –4.75E+04 | –8.04E+03 | –6.23E+03 | –1.19E+04 | –4.38E+03 | –1.23E+04 | –3.3E+306 | –1.26E+04 |
Std | 9.59E+02 | 6.85E+02 | 8.52E+03 | 3.03E+02 | 4.75E+02 | 9.02E+02 | 1.08E+03 | 1.68E+02 | NA | 1.87E–12 | |
Best | –8.17E+03 | –7.31E+03 | –6.49E+04 | –8.69E+03 | –7.19E+03 | –1.26E+04 | –6.49E+03 | –1.26E+04 | –2.9E+307 | –1.26E+04 | |
Worst | –5.07E+03 | –5.27E+03 | –3.50E+04 | –7.54E+03 | –5.69E+03 | –9.79E+03 | –2.70E+03 | –1.20E+04 | –1.3E+296 | –1.26E+04 | |
Median | –6.68E+03 | –6.73E+03 | –4.63E+04 | –8.07E+03 | –6.08E+03 | –1.22E+04 | –4.32E+03 | –1.22E+04 | –4.7E+303 | –1.26E+04 | |
\({\text {F9}}\) | Mean | 49.85266 | 164.25398 | 52.13577 | 105.04556 | 0.45353 | 0 | 0 | 0.049825 | 157.6098 | 0 |
Std | 9.156932 | 35.025847 | 10.46209 | 33.65920 | 1.395935 | 0 | 0 | 0.222481 | 7.324355 | 0 | |
Best | 33.8776 | 116.1056 | 36.8135 | 51.9801 | 0 | 0 | 0 | 1.275E–06 | 141.9516 | 0 | |
Worst | 64.6898 | 211.1062 | 73.6268 | 164.3799 | 4.5353 | 0 | 0 | 0.995044 | 165.2087 | 0 | |
Median | 49.3953 | 171.94725 | 49.74785 | 98.6025 | 0 | 0 | 0 | 4.593E–05 | 159.2086 | 0 | |
\({\text {F10}}\) | Mean | 9.969E–02 | 1.855E+00 | 1.818E+00 | 1.271E+00 | 1.652E–14 | 3.730E–15 | 4.440E–15 | 2.450E+00 | 2.892E–13 | 4.441E–16 |
Std | 2.847E–01 | 1.572E+00 | 1.026E+00 | 6.649E–01 | 2.915E–15 | 2.187E–15 | 2.428E–30 | 5.409E–01 | 1.621E–13 | 1.012E–31 | |
Best | 1.837E–03 | 1.509E–14 | 3.002E–05 | 2.279E–01 | 1.509E–14 | 8.881E–16 | 4.440E–15 | 1.501E+00 | 1.354E–13 | 4.441E–16 | |
Worst | 9.318E–01 | 3.546E+00 | 2.957E+00 | 2.383E+00 | 2.220E–14 | 7.993E–15 | 4.440E–15 | 3.518E+00 | 7.038E–13 | 4.441E–16 | |
Median | 4.268E–03 | 2.762E+00 | 2.117E+00 | 1.276E+00 | 1.509E–14 | 4.440E–15 | 4.440E–15 | 2.495E+00 | 2.491E–13 | 4.441E–16 | |
\({\text {F11}}\) | Mean | 0.0167412 | 0.016606 | 0.0132815 | 0.593154 | 0.0009793 | 0 | 0 | 0.015958 | 0 | 0 |
Std | 0.0095002 | 0.017481 | 0.0097684 | 0.104295 | 0.0030144 | 0 | 0 | 0.021317 | 0 | 0 | |
Best | 1.229E–07 | 0 | 5.5395E–08 | 0.41554 | 0 | 0 | 0 | 5.590E–08 | 0 | 0 | |
Worst | 0.029553 | 0.061033 | 0.031898 | 0.73028 | 0.0097937 | 0 | 0 | 0.095192 | 0 | 0 | |
Median | 0.0172275 | 0.015464 | 0.013547 | 0.61796 | 0 | 0 | 0 | 0.012328 | 0 | 0 | |
\({\text {F12}}\) | Mean | 4.204E–07 | 7.471E+00 | 5.298E+00 | 1.468E+00 | 4.481E–02 | 7.131E–03 | 2.197E–01 | 5.262E–01 | 8.396E–24 | 1.570E–32 |
Std | 2.873E–07 | 2.605E+00 | 2.743E+00 | 8.326E–01 | 2.331E–02 | 5.741E–03 | 7.453E–02 | 1.281E+00 | 1.968E–23 | 2.808E–48 | |
Best | 4.173E–08 | 3.765E+00 | 2.353E+00 | 4.619E–01 | 6.561E–03 | 1.968E–03 | 1.303E–01 | 4.497E–08 | 3.518E–25 | 1.570E–32 | |
Worst | 9.178E–07 | 1.200E+01 | 1.065E+01 | 3.018E+00 | 7.885E–02 | 1.977E–02 | 3.619E–01 | 5.678E+00 | 9.136E–23 | 1.570E–32 | |
Median | 4.548E–07 | 7.271E+00 | 4.935E+00 | 1.511E+00 | 3.803E–02 | 5.804E–03 | 1.942E–01 | 1.036E–01 | 4.045E–24 | 1.570E–32 | |
\({\text {F13}}\) | Mean | 2.204E–03 | 3.239E+00 | 1.850E–02 | 7.295E–02 | 4.655E–01 | 2.446E–01 | 1.545E+00 | 1.009E–01 | 6.238E–23 | 1.349E–32 |
Std | 4.511E–03 | 7.530E–01 | 3.047E–02 | 3.941E–02 | 1.863E–01 | 1.437E–01 | 1.692E–01 | 3.550E–01 | 7.751E–23 | 5.616E–48 | |
Best | 2.490E–07 | 1.880E+00 | 1.256E–09 | 2.411E–02 | 1.128E–01 | 2.209E–02 | 1.380E+00 | 6.150E–08 | 4.119E–24 | 1.349E–32 | |
Worst | 1.100E–02 | 4.506E+00 | 9.814E–02 | 1.573E–01 | 7.413E–01 | 5.548E–01 | 1.901E+00 | 1.597E+00 | 2.477E–22 | 1.349E–32 | |
Median | 4.661E–06 | 3.030E+00 | 5.493E–03 | 6.252E–02 | 5.004E–01 | 2.251E–01 | 1.495E+00 | 1.109E–02 | 3.125E–23 | 1.349E–32 | |
\({\text {F14}}\) | Mean | 4.53782 | 7.62641 | 1.0974 | 0.998 | 4.3167 | 1.99005 | 7.82613 | 0.998003 | 4.856805 | 0.998 |
Std | 3.24061 | 5.27654 | 0.30594 | 0 | 4.8206 | 1.01782 | 4.98902 | 2.278E–16 | 2.939305 | 0 | |
Best | 0.998 | 0.998 | 0.998 | 0.998 | 0.998 | 0.998 | 0.998 | 0.998003 | 0.99801 | 0.998 | |
Worst | 10.7632 | 15.5038 | 1.992 | 0.998 | 12.6705 | 2.9821 | 12.6705 | 0.998003 | 10.7632 | 0.998 | |
Median | 2.9821 | 8.346 | 0.998 | 0.998 | 0.998 | 1.9900 | 10.7632 | 0.998003 | 4.0102 | 0.998 | |
\({\text {F15}}\) | Mean | 8.699E–04 | 4.604E–03 | 1.005E–03 | 4.715E–03 | 4.501E–03 | 8.040E–04 | 1.579E–03 | 1.356E–03 | 2.491E–03 | 3.109E–04 |
Std | 2.897E–04 | 8.097E–03 | 2.593E–04 | 8.030E–03 | 8.144E–03 | 5.107E–04 | 3.806E–03 | 4.478E–03 | 1.462E–03 | 3.534E–06 | |
Best | 3.145E–04 | 3.079E–04 | 5.634E–04 | 3.256E–04 | 3.074E–04 | 3.088E–04 | 3.075E–04 | 3.074E–04 | 1.135E–03 | 3.087E–04 | |
Worst | 1.085E–03 | 2.036E–02 | 1.479E–03 | 2.036E–02 | 2.036E–02 | 1.503E–03 | 1.270E–02 | 2.036E–02 | 5.810E–03 | 3.185E–04 | |
Median | 9.818E–04 | 4.620E–04 | 1.067E–03 | 7.598E–04 | 3.085E–04 | 5.751E–04 | 3.121E–04 | 3.074E–04 | 1.782E–03 | 3.089E–04 |
