Table 11 Evaluation results of well–known & top–performing algorithms for the CEC 2019 benchmark functions.
From: Learning cooking algorithm for solving global optimization problems
\({\text {Functions}}\) | \({\text {PSO}}\) | \({\text {TSA}}\) | \({\text {SSA}}\) | \({\text {MVO}}\) | \({\text {GWO}}\) | \({\text {WOA}}\) | \({\text {GJO}}\) | \({\text {LSHADE}}\) | \({\text {CMAES}}\) | \({\text {LCA}}\) | |
|---|---|---|---|---|---|---|---|---|---|---|---|
\({\text {CEC19-1}}\) | Mean | 5.736E+11 | 1.291E+08 | 7.488E+09 | 2.351E+09 | 1.441E+08 | 2.685E+10 | 1.503E+07 | 1.445E+07 | 2.552E+08 | 8.214E+04 |
Std | 5.385E+11 | 4.965E+08 | 1.490E+10 | 1.522E+09 | 3.900E+08 | 3.348E+10 | 3.137E+07 | 2.981E+07 | 1.695E+08 | 1.500E+04 | |
Best | 3.562E+10 | 4.417E+04 | 1.480E+08 | 6.789E+08 | 6.207E+04 | 1.177E+06 | 3.941E+04 | 8.727E+05 | 3.449E+07 | 5.556E+04 | |
Worst | 2.678E+12 | 2.232E+09 | 6.778E+10 | 6.630E+09 | 1.363E+09 | 1.039E+11 | 1.237E+08 | 1.264E+08 | 7.858E+08 | 1.139E+05 | |
Median | 5.077E+11 | 4.612E+05 | 3.122E+09 | 1.865E+09 | 6.839E+06 | 5.031E+09 | 6.357E+05 | 2.866E+06 | 2.206E+08 | 8.036E+04 | |
\({\text {CEC19-2}}\) | Mean | 1.040E+04 | 1.824E+01 | 1.734E+01 | 1.798E+01 | 1.734E+01 | 1.734E+01 | 1.741E+01 | 1.734E+01 | 1.098E+02 | 1.751E+01 |
Std | 2.253E+03 | 8.136E–01 | 9.461E–04 | 2.479E–01 | 1.835E–04 | 1.577E–03 | 1.387E–01 | 3.656E–14 | 5.120E+01 | 6.248E–02 | |
Best | 7.586E+03 | 1.735E+01 | 1.734E+01 | 1.756E+01 | 1.734E+01 | 1.734E+01 | 1.734E+01 | 1.734E+01 | 4.401E+01 | 1.744E+01 | |
Worst | 1.321E+04 | 1.956E+01 | 1.735E+01 | 1.826E+01 | 1.734E+01 | 1.735E+01 | 1.768E+01 | 1.734E+01 | 2.683E+02 | 1.759E+01 | |
Median | 9.735E+03 | 1.797E+01 | 1.734E+01 | 1.797E+01 | 1.734E+01 | 1.734E+01 | 1.734E+01 | 1.734E+01 | 9.422E+01 | 1.753E+01 | |
\({\text {CEC19-3}}\) | Mean | 1.270E+01 | 1.270E+01 | 1.270E+01 | 1.270E+01 | 1.270E+01 | 1.270E+01 | 1.270E+01 | 1.270E+01 | 1.270E+01 | 1.270E+01 |
Std | 3.645E–15 | 2.124E–03 | 1.559E–03 | 3.645E–15 | 3.645E–15 | 3.645E–15 | 7.797E–04 | 5.468E–15 | 1.622E–04 | 3.645E–15 | |
Best | 1.270E+01 | 1.270E+01 | 1.270E+01 | 1.270E+01 | 1.270E+01 | 1.270E+01 | 1.270E+01 | 1.270E+01 | 1.270E+01 | 1.270E+01 | |
Worst | 1.270E+01 | 1.271E+01 | 1.271E+01 | 1.270E+01 | 1.270E+01 | 1.270E+01 | 1.270E+01 | 1.270E+01 | 1.270E+01 | 1.270E+01 | |
Median | 1.270E+01 | 1.270E+01 | 1.270E+01 | 1.270E+01 | 1.270E+01 | 1.270E+01 | 1.270E+01 | 1.270E+01 | 1.270E+01 | 1.270E+01 | |
\({\text {CEC19-4}}\) | Mean | 1.393E+01 | 3.084E+03 | 4.895E+01 | 2.731E+01 | 6.104E+01 | 2.852E+02 | 5.413E+02 | 8.897E+00 | 2.365E+01 | 1.468E+04 |
Std | 4.134E+00 | 2.654E+03 | 2.256E+01 | 5.939E+00 | 1.310E+01 | 1.349E+02 | 6.189E+02 | 2.794E+00 | 4.062E+00 | 3.496E+03 | |
Best | 8.955E+00 | 9.851E+01 | 2.985E+01 | 1.838E+01 | 4.738E+01 | 1.230E+02 | 4.559E+01 | 3.214E+00 | 1.319E+01 | 9.195E+03 | |
Worst | 1.990E+01 | 7.697E+03 | 8.955E+01 | 3.501E+01 | 8.216E+01 | 4.492E+02 | 1.496E+03 | 1.393E+01 | 2.941E+01 | 1.948E+04 | |
Median | 1.492E+01 | 2.499E+03 | 3.582E+01 | 2.705E+01 | 5.441E+01 | 3.454E+02 | 8.236E+01 | 8.180E+00 | 2.397E+01 | 1.570E+04 | |
\({\text {CEC19-5}}\) | Mean | 1.119E+00 | 2.412E+00 | 1.281E+00 | 1.262E+00 | 1.447E+00 | 1.737E+00 | 1.513E+00 | 1.033E+00 | 1.015E+00 | 4.441E+00 |
Std | 9.187E–02 | 6.133E–01 | 1.568E–01 | 5.654E–02 | 2.296E–01 | 4.503E–01 | 2.751E–01 | 2.789E–02 | 3.104E–02 | 5.932E–01 | |
Best | 1.027E+00 | 1.773E+00 | 1.153E+00 | 1.193E+00 | 1.184E+00 | 1.368E+00 | 1.191E+00 | 1.000E+00 | 1.000E+00 | 3.312E+00 | |
Worst | 1.268E+00 | 3.504E+00 | 1.580E+00 | 1.358E+00 | 1.794E+00 | 2.546E+00 | 1.819E+00 | 1.108E+00 | 1.076E+00 | 4.893E+00 | |
Median | 1.108E+00 | 2.308E+00 | 1.229E+00 | 1.257E+00 | 1.404E+00 | 1.470E+00 | 1.574E+00 | 1.029E+00 | 1.000E+00 | 4.633E+00 | |
\({\text {CEC19-6}}\) | Mean | 6.249E+00 | 1.092E+01 | 4.311E+00 | 7.065E+00 | 1.042E+01 | 8.131E+00 | 1.029E+01 | 7.493E+00 | 1.040E+01 | 1.008E+01 |
Std | 1.487E+00 | 5.521E–01 | 1.416E+00 | 9.508E–01 | 5.330E–01 | 8.608E–01 | 3.207E–01 | 1.288E+00 | 5.982E–01 | 6.086E–01 | |
Best | 4.540E+00 | 1.037E+01 | 1.709E+00 | 6.090E+00 | 1.000E+01 | 6.715E+00 | 9.879E+00 | 4.781E+00 | 9.467E+00 | 9.146E+00 | |
Worst | 8.356E+00 | 1.186E+01 | 5.361E+00 | 8.620E+00 | 1.130E+01 | 9.189E+00 | 1.067E+01 | 1.141E+01 | 1.167E+01 | 1.091E+01 | |
Median | 6.605E+00 | 1.067E+01 | 5.192E+00 | 6.687E+00 | 1.004E+01 | 8.399E+00 | 1.014E+01 | 7.406E+00 | 1.032E+01 | 1.025E+01 | |
\({\text {CEC19-7}}\) | Mean | 1.447E+02 | 6.204E+02 | 3.097E+02 | 2.353E+02 | 1.666E+02 | 8.144E+02 | 7.109E+02 | –5.339E+01 | 3.170E+02 | 7.229E+02 |
Std | 1.620E+02 | 2.291E+02 | 2.098E+02 | 1.242E+02 | 2.100E+02 | 3.491E+02 | 2.902E+02 | 8.355E+01 | 2.543E+02 | 1.282E+02 | |
Best | –3.788E+01 | 2.955E+02 | 3.335E+01 | 8.290E+01 | –8.679E+01 | 4.574E+02 | 3.776E+02 | –1.695E+02 | 6.247E–01 | 5.753E+02 | |
Worst | 4.154E+02 | 9.176E+02 | 6.048E+02 | 4.319E+02 | 4.484E+02 | 1.290E+03 | 1.068E+03 | 6.334E+01 | 7.868E+02 | 8.552E+02 | |
Median | 1.236E+02 | 5.598E+02 | 2.810E+02 | 2.381E+02 | 1.462E+02 | 7.154E+02 | 7.882E+02 | –6.668E+01 | 3.193E+02 | 7.495E+02 | |
\({\text {CEC19-8}}\) | Mean | 4.831E+00 | 6.588E+00 | 5.091E+00 | 4.381E+00 | 4.926E+00 | 5.817E+00 | 4.802E+00 | 4.642E+00 | 5.129E+00 | 6.144E+00 |
Std | 8.981E–01 | 2.275E–01 | 5.419E–01 | 9.540E–01 | 5.200E–01 | 9.091E–01 | 1.018E+00 | 5.651E–01 | 1.620E+00 | 3.161E–01 | |
Best | 3.671E+00 | 6.273E+00 | 4.427E+00 | 3.161E+00 | 4.233E+00 | 4.200E+00 | 3.663E+00 | 3.247E+00 | 1.700E+00 | 5.722E+00 | |
Worst | 6.197E+00 | 6.921E+00 | 5.726E+00 | 5.842E+00 | 5.586E+00 | 6.642E+00 | 6.155E+00 | 5.535E+00 | 6.968E+00 | 6.486E+00 | |
Median | 4.895E+00 | 6.650E+00 | 5.380E+00 | 4.212E+00 | 4.944E+00 | 6.120E+00 | 4.330E+00 | 4.731E+00 | 5.717E+00 | 6.150E+00 | |
\({\text {CEC19-9}}\) | Mean | 2.357E+00 | 6.082E+01 | 2.450E+00 | 2.383E+00 | 3.967E+00 | 4.379E+00 | 5.036E+00 | 2.451E+00 | 2.393E+00 | 2.310E+03 |
Std | 1.227E–02 | 1.135E+02 | 4.750E–02 | 9.900E–03 | 8.216E–01 | 4.976E–01 | 5.327E–01 | 1.000E–01 | 1.657E–02 | 3.663E+02 | |
Best | 2.344E+00 | 3.780E+00 | 2.376E+00 | 2.372E+00 | 3.038E+00 | 3.877E+00 | 4.386E+00 | 2.356E+00 | 2.365E+00 | 1.758E+03 | |
Worst | 2.372E+00 | 2.821E+02 | 2.506E+00 | 2.401E+00 | 4.958E+00 | 5.224E+00 | 5.576E+00 | 2.807E+00 | 2.439E+00 | 2.694E+03 | |
Median | 2.354E+00 | 6.005E+00 | 2.464E+00 | 2.380E+00 | 3.944E+00 | 4.239E+00 | 5.249E+00 | 2.426E+00 | 2.393E+00 | 2.351E+03 | |
\({\text {CEC19-10}}\) | Mean | 2.006E+01 | 2.047E+01 | 2.000E+01 | 2.005E+01 | 2.047E+01 | 2.018E+01 | 2.046E+01 | 2.009E+01 | 2.042E+01 | 2.048E+01 |
Std | 5.323E–02 | 7.487E–02 | 4.104E–05 | 3.456E–02 | 5.762E–02 | 5.076E–02 | 7.551E–02 | 8.036E–02 | 9.261E–02 | 8.779E–02 | |
Best | 2.001E+01 | 2.038E+01 | 2.000E+01 | 2.001E+01 | 2.035E+01 | 2.014E+01 | 2.034E+01 | 2.000E+01 | 2.025E+01 | 2.037E+01 | |
Worst | 2.014E+01 | 2.060E+01 | 2.000E+01 | 2.011E+01 | 2.050E+01 | 2.027E+01 | 2.054E+01 | 2.040E+01 | 2.057E+01 | 2.060E+01 | |
Median | 2.004E+01 | 2.044E+01 | 2.000E+01 | 2.004E+01 | 2.048E+01 | 2.015E+01 | 2.044E+01 | 2.007E+01 | 2.043E+01 | 2.047E+01 | |
