Table 6 Evaluation results of well-known & top-performing algorithms for the functions F16 to F30.
From: Learning cooking algorithm for solving global optimization problems
\({\text {Functions}}\) | \({\text {PSO}}\) | \({\text {TSA}}\) | \({\text {SSA}}\) | \({\text {MVO}}\) | \({\text {GWO}}\) | \({\text {WOA}}\) | \({\text {GJO}}\) | \({\text {LSHADE}}\) | \({\text {CMAES}}\) | \({\text {LCA}}\) | |
|---|---|---|---|---|---|---|---|---|---|---|---|
\({\text {F16}}\) | Mean | \(-1.0316\) | \(-1.0316\) | \(-1.0316\) | \(-1.0316\) | \(-1.0316\) | \(-1.0316\) | \(-1.0316\) | \(-1.0316\) | \(-1.0316\) | \(-1.0316\) |
Std | \(4.5E-16\) | \(4.5E-16\) | \(4.5E-16\) | \(4.5E-16\) | \(4.5E-16\) | \(4.5E-16\) | \(4.5E-16\) | \(4.5E-16\) | \(4.5E-16\) | \(4.5E-16\) | |
Best | \(-1.0316\) | \(-1.0316\) | \(-1.0316\) | \(-1.0316\) | \(-1.0316\) | \(-1.0316\) | \(-1.0316\) | \(-1.0316\) | \(-1.0316\) | \(-1.0316\) | |
Worst | \(-1.0316\) | \(-1.0316\) | \(-1.0316\) | \(-1.0316\) | \(-1.0316\) | \(-1.0316\) | \(-1.0316\) | \(-1.0316\) | \(-1.0316\) | \(-1.0316\) | |
Median | \(-1.0316\) | \(-1.0316\) | \(-1.0316\) | \(-1.0316\) | \(-1.0316\) | \(-1.0316\) | \(-1.0316\) | \(-1.0316\) | \(-1.0316\) | \(-1.0316\) | |
\({\text {F17}}\) | Mean | 0.39789 | 0.397954 | 0.39789 | 0.39789 | 0.397957 | 0.39789 | 0.39796 | 0.397887 | 0.39789 | 0.397931 |
Std | 1.139E–16 | 9.735E–05 | 1.139E–16 | 1.139E–16 | 0.000206 | 1.139E–16 | 0.000195 | 1.139E–16 | 1.139E–16 | 3.596E–05 | |
Best | 0.39789 | 0.39789 | 0.39789 | 0.39789 | 0.39789 | 0.39789 | 0.39789 | 0.397887 | 0.39789 | 0.39789 | |
Worst | 0.39789 | 0.3982 | 0.39789 | 0.39789 | 0.39856 | 0.39789 | 0.39853 | 0.397887 | 0.39789 | 0.39799 | |
Median | 0.39789 | 0.39792 | 0.39789 | 0.39789 | 0.39789 | 0.39789 | 0.39789 | 0.397887 | 0.39789 | 0.39793 | |
\({\text {F18}}\) | Mean | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3.000000001 | 3 |
Std | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | \(1.522E-09\) | 0 | |
Best | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | |
Worst | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3.000000003 | 3 | |
Median | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | |
\({\text {F19}}\) | Mean | –3.8628 | –3.8619 | –3.8628 | –3.8628 | –3.8612 | –3.8593 | –3.8572 | –3.862782 | –3.8628 | –3.8581 |
Std | 1.3E–15 | 0.00237 | 1.3E–15 | 1.3E–15 | 0.003232 | 0.003089 | 0.000365 | 9.112E–16 | 1.3E–15 | 0.00417 | |
Best | –3.8628 | –3.8628 | –3.8628 | –3.8628 | –3.8628 | –3.8627 | –3.8628 | –3.862782 | –3.8628 | –3.8617 | |
Worst | –3.8628 | –3.8550 | –3.8628 | –3.8628 | –3.8549 | –3.8549 | –3.8549 | –3.862782 | –3.8628 | –3.8619 | |
Median | –3.8628 | –3.8627 | –3.8628 | –3.8628 | –3.8628 | –3.8595 | –3.8549 | –3.862782 | –3.8628 | –3.8617 | |
\({\text {F20}}\) | Mean | –3.26255 | –3.22041 | –3.2331 | –3.2623 | –3.24607 | –3.17022 | –3.21823 | –3.3219 | –3.292275 | –2.7719 |
Std | 0.060994 | 0.076133 | 0.060158 | 0.061251 | 0.09606 | 0.263940 | 0.078602 | 4.556E–16 | 0.052822 | 0.18520 | |
Best | –3.322 | –3.3209 | –3.322 | –3.322 | –3.322 | –3.3219 | –3.322 | –3.3219 | –3.322 | –2.9438 | |
Worst | –3.2031 | –3.0861 | –3.1804 | –3.202 | –3.104 | –2.4317 | –3.0867 | –3.3219 | –3.2031 | –2.5042 | |
Median | –3.26255 | –3.20185 | –3.20185 | –3.2625 | –3.322 | –3.2517 | –3.19945 | –3.3219 | –3.322 | –2.821 | |
\({\text {F21}}\) | Mean | –5.64936 | –5.31385 | –8.1441 | –8.1185 | –9.64751 | –9.63652 | –8.12049 | –10.153199 | \(-10.1532\) | \(-10.1532\) |
Std | 3.194666 | 3.251232 | 3.21216 | 2.55663 | 1.555147 | 1.56683 | 2.549866739 | 1.822E–15 | 0 | 0 | |
Best | \(-10.1532\) | –10.349 | \(-10.1532\) | \(-10.1532\) | \(-10.1532\) | \(-10.1532\) | –10.1518 | –10.1531 | \(-10.1532\) | \(-10.1532\) | |
Worst | –2.6829 | –2.6246 | –2.6305 | –5.0552 | –5.1002 | –5.0552 | –5.0551 | –10.1531 | \(-10.1532\) | \(-10.1532\) | |
Median | -5.1008 | –3.8311 | –10.1532 | –10.1531 | –10.1532 | –10.14965 | –10.14685 | –10.1531 | \(-10.1532\) | \(-10.1532\) | |
\({\text {F22}}\) | Mean | –7.29187 | –7.23034 | –8.58438 | –7.75759 | –10.4029 | –8.56993 | –9.86786 | –10.4029 | –10.4029 | –10.4029 |
Std | 3.30111 | 3.760581 | 2.91792 | 2.71400 | 2.190E–04 | 2.67942 | 1.634849 | 5.467E–15 | 3.6E–15 | 3.6E–15 | |
Best | –10.4029 | –10.289 | –10.4029 | –10.4029 | –10.4028 | –10.4029 | –10.4029 | –10.4029 | –10.4029 | –10.4029 | |
Worst | –2.7519 | –2.7241 | –2.7659 | –5.0876 | –10.4022 | –3.7243 | –5.0875 | –10.4029 | –10.4029 | –10.4029 | |
Median | –7.76585 | –10.1615 | –10.4029 | –7.7658 | –10.4026 | –10.3071 | –10.3994 | –10.4029 | –10.4029 | –10.4029 | |
\({\text {F23}}\) | Mean | –8.91403 | –6.44063 | –9.23379 | –7.8418 | –9.72462 | –10.5348 | –9.99744 | \(-10.5364\) | \(-10.5364\) | \(-10.5364\) |
Std | 2.54259 | 3.36187 | 2.72468 | 2.76452 | 2.497545 | 0.001619 | 1.649480 | 5.467E–15 | 5.467E–15 | 5.467E–15 | |
Best | \(-10.5364\) | –10.4249 | –10.5364 | –10.5364 | –10.5363 | –10.5361 | \(-10.5364\) | \(-10.5364\) | –10.5364 | –10.5364 | |
Worst | –5.1285 | –2.4201 | –2.8711 | –5.1284 | –2.4217 | –10.5304 | –5.1743 | –10.5364 | –10.5364 | –10.5364 | |
Median | –10.5364 | –5.12535 | –10.5364 | –7.85585 | –10.5361 | –10.5353 | –10.5364 | –10.5364 | –10.5364 | –10.5364 | |
\({\text {F24}}\) | Mean | –17076.3 | 0.3 | –4830.9 | \(-5\) | \(-5\) | \(-5\) | \(-5\) | \(-5\) | \(-5\) | \(-5\) |
Std | 176.514 | 2.59756 | 78.5908 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
Best | –17384 | \(-5\) | –4941 | \(-5\) | \(-5\) | \(-5\) | \(-5\) | \(-5\) | \(-5\) | \(-5\) | |
Worst | –16810 | 6 | –4703 | \(-5\) | \(-5\) | \(-5\) | \(-5\) | \(-5\) | \(-5\) | \(-5\) | |
Median | –17128.5 | 0 | –4852 | \(-5\) | \(-5\) | \(-5\) | \(-5\) | \(-5\) | \(-5\) | \(-5\) | |
\({\text {F25}}\) | Mean | 5.526E–04 | 1.390E–48 | 1.924E–01 | 2.435E–01 | 2.160E–60 | 2.429E–151 | 3.277E–112 | 2.075E–07 | 1.594E–25 | 0 |
Std | 1.208E–03 | 2.205E–48 | 1.897E–01 | 2.483E–01 | 2.792E–60 | 7.358E–151 | 7.534E–112 | 2.625E–07 | 1.370E–25 | 0 | |
Best | 2.653E–05 | 4.494E–51 | 4.543E–03 | 6.264E–02 | 9.171E–63 | 1.998E–177 | 1.263E–117 | 3.590E–09 | 2.930E–26 | 0 | |
Worst | 4.066E–03 | 7.146E–48 | 7.266E–01 | 7.317E–01 | 9.493E–60 | 2.394E–150 | 2.381E–111 | 8.620E–07 | 6.519E–25 | 0 | |
Median | 9.811E–05 | 2.841E–49 | 1.634E–01 | 1.577E–01 | 7.395E–61 | 1.124E–158 | 5.475E–115 | 8.210E–08 | 1.315E–25 | 0 | |
\({\text {F26}}\) | Mean | 0 | 2.180E–01 | 1.082E–01 | 7.621E–02 | 7.621E–02 | 1.400E–10 | 3.586E–07 | 0 | 2.718E–05 | 2.591E–04 |
Std | 0 | 3.428E–01 | 2.222E–01 | 2.345E–01 | 2.345E–01 | 4.026E–10 | 3.586E–07 | 0 | 6.328E–05 | 8.348E–05 | |
Best | 0 | 1.169E–07 | 4.828E–18 | 8.310E–10 | 1.834E–09 | 3.322E–14 | 1.056E–08 | 0 | 5.314E–08 | 2.271E–04 | |
Worst | 0 | 7.620E–01 | 5.437E–01 | 7.620E–01 | 7.629E–01 | 1.316E–09 | 1.148E–06 | 0 | 0.0002893 | 5.015E–04 | |
Median | 0 | 7.758E–07 | 4.509E–16 | 3.101E–08 | 4.199E–08 | 1.027E–12 | 2.100E–07 | 0 | 0.0000128 | 2.271E–04 | |
\({\text {F27}}\) | Mean | –1 | –0.7499 | –1 | –0.8999 | –1 | –1 | –1 | –1 | –1 | –1 |
Std | 0 | 0 | 0.4442 | 0 | 0.3077 | 0 | 0 | 0 | 0 | 0 | |
Best | –1 | –1 | –1 | –1 | –1 | –1 | –1 | –1 | –1 | –1 | |
Worst | –1 | 0 | –1 | 0 | –1 | –1 | –1 | –1 | –1 | –1 | |
Median | –1 | –0.9999 | –1 | –0.9999 | –1 | –1 | –1 | –1 | –1 | –1 | |
\({\text {F28}}\) | Mean | 8.063E–52 | 2.833E–155 | 6.168E–16 | 7.059E–09 | 1.896E–218 | 0 | 0 | 1.840E–127 | 3.050E–306 | 0 |
Std | 1.595E–51 | 0 | 5.759E–16 | 4.452E–09 | 0 | 0 | 0 | 8.212E–127 | 0 | 0 | |
Best | 1.002E–54 | 1.635E–164 | 7.169E–17 | 2.366E–10 | 1.199E–237 | 0 | 0 | 2.084E–147 | 5.566E–308 | 0 | |
Worst | 5.089E–51 | 2.395E–154 | 1.943E–15 | 1.361E–08 | 1.334E–217 | 0 | 0 | 3.673E–126 | 1.150E–305 | 0 | |
Median | 5.083E–53 | 7.151E–158 | 3.846E–16 | 7.857E–09 | 3.903E–223 | 0 | 0 | 6.004E–135 | 2.598E–307 | 0 | |
\({\text {F29}}\) | Mean | 1.579E–02 | 1.549E+00 | 2.714E–01 | 7.401E–03 | 1.002E+00 | 1.036E+00 | 1.057E+00 | 0 | 1.900E–10 | 0 |
Std | 1.094E–02 | 1.944E+00 | 7.900E–01 | 9.976E–03 | 6.885E–01 | 1.180E+00 | 6.186E–01 | 0 | 4.997E–10 | 0 | |
Best | 1.110E–05 | 3.521E–03 | 2.153E–04 | 2.035E–04 | 9.909E–04 | 7.515E–03 | 1.154E–01 | 0 | 2.271E–21 | 0 | |
Worst | 3.096E–02 | 6.902E+00 | 2.581E+00 | 2.913E–02 | 1.608E+00 | 3.450E+00 | 1.568E+00 | 0 | 1.936E–09 | 0 | |
Median | 1.645E–02 | 1.352E+00 | 1.283E–02 | 1.582E–03 | 1.424E+00 | 7.047E–01 | 1.328E+00 | 0 | 8.872E–12 | 0 | |
\({\text {F30}}\) | Mean | –5.602E+06 | –316.7 | –4.181E+07 | \(-360\) | –324 | –345.6 | –345.6 | \(-360\) | –2.00E+306 | \(-360\) |
Std | 3.186E+04 | 36.274 | 1.397E+06 | 0 | 36.93 | 29.548 | 29.548 | 0 | NA | 0 | |
Best | –5.634E+06 | \(-360\) | –4.373E+07 | \(-360\) | \(-360\) | \(-360\) | \(-360\) | \(-360\) | –4.01E+307 | \(-360\) | |
Worst | –5.536E+06 | –287 | –3.880E+07 | \(-360\) | –288 | –288 | –288 | \(-360\) | –2.53E+150 | \(-360\) | |
Median | –5.614E+06 | –288 | –4.176E+07 | \(-360\) | –324 | \(-360\) | \(-360\) | \(-360\) | –5.35E+226 | \(-360\) |
