Table 5 Experimental outcomes for various algorithms on CEC2005 test suite.
Functions | Fun01 | Fun02 | Fun03 | Fun04 | Fun05 | |||||
|---|---|---|---|---|---|---|---|---|---|---|
| Â | AVG | STD | AVG | STD | AVG | STD | AVG | STD | AVG | STD |
PSO | 1.851E+02 | 2.987E+01 | 4.062E+00 | 1.106E+00 | 1.890E+02 | 6.882E+01 | 1.311E+01 | 1.381E+00 | 1.251E+03 | 7.537E+02 |
GWO | 1.605E-12 | 9.735E-13 | 9.938E-17 | 9.470E-17 | 1.267E-05 | 3.805E-05 | 7.714E-01 | 6.381E-01 | 2.690E+01 | 7.417E-01 |
GJO | 1.914E-27 | 3.523E-27 | 2.008E-32 | 2.899E-32 | 2.623E-17 | 8.792E-17 | 9.296E+00 | 1.222E+01 | 2.779E+01 | 7.210E-01 |
SO | 7.266E-82 | 1.991E-81 | 4.383E-43 | 1.645E-42 | 7.566E-57 | 2.313E-56 | 1.818E-36 | 2.998E-36 | 2.034E+01 | 1.437E+01 |
SCSO | 1.824E-120 | 7.157E-120 | 1.592E-75 | 6.730E-75 | 5.275E-101 | 2.883E-100 | 3.086E-49 | 9.025E-49 | 2.799E+01 | 6.575E-01 |
AVOA | 1.979E-286 | 0.000E+00 | 1.148E-142 | 6.286E-142 | 7.838E-222 | 0.000E+00 | 1.727E-144 | 6.681E-144 | 6.049E-05 | 5.016E-05 |
CMAES | 1.547E+01 | 2.761E+00 | 4.174E-03 | 1.018E-03 | 2.171E+00 | 2.942E+00 | 2.877E+01 | 3.950E+00 | 3.202E+01 | 2.195E+01 |
SHADE | 1.039E+02 | 3.586E+01 | 6.024E-04 | 1.359E-04 | 2.242E+04 | 4.028E+03 | 6.983E+01 | 2.611E+00 | 1.125E+02 | 4.310E+01 |
BKA | 9.991E-74 | 5.472E-73 | 2.643E-38 | 1.448E-37 | 5.021E-88 | 2.268E-87 | 4.565E-44 | 2.284E-43 | 2.788E+01 | 8.927E-01 |
CBKA | 7.589E-92 | 3.914E-91 | 1.007E-48 | 4.587E-48 | 3.088E-93 | 9.441E-93 | 1.482E-48 | 3.609E-48 | 2.798E+01 | 8.564E-01 |
IBKA | 3.677E-157 | 2.014E-156 | 1.856E-82 | 1.014E-81 | 1.456E-154 | 7.952E-154 | 7.207E-82 | 3.162E-81 | 2.821E+01 | 7.308E-01 |
QOBLBKA | 3.532E-156 | 1.935E-155 | 4.435E-83 | 2.380E-82 | 1.147E-150 | 6.285E-150 | 4.568E-75 | 2.502E-74 | 2.822E+01 | 7.890E-01 |
AMOMM-BKA | 0.000E+00 | 0.000E+00 | 2.899E-276 | 0.000E+00 | 0.000E+00 | 0.000E+00 | 9.399E-274 | 0.000E+00 | 2.464E+01 | 1.077E-01 |
| Â | Fun06 | Fun07 | Fun08 | Fun09 | Fun10 | |||||
|---|---|---|---|---|---|---|---|---|---|---|
AVG | STD | AVG | STD | AVG | STD | AVG | STD | AVG | STD | |
PSO | 2.558E+00 | 1.217E+00 | 1.526E+03 | 2.196E+02 | -6.629E+03 | 1.200E+03 | 1.624E+02 | 2.868E+01 | 2.539E+00 | 4.597E-01 |
GWO | 7.572E-01 | 3.147E-01 | 6.528E-03 | 2.107E-03 | -6.044E+03 | 9.671E+02 | 2.108E+00 | 4.237E+00 | 1.025E-13 | 1.932E-14 |
GJO | 2.641E+00 | 4.910E-01 | 1.420E-03 | 9.305E-04 | -4.366E+03 | 1.015E+03 | 0.000E+00 | 0.000E+00 | 6.484E-15 | 1.656E-15 |
SO | 7.023E-01 | 6.342E-01 | 2.283E-04 | 2.364E-04 | -1.251E+04 | 9.966E+01 | 6.008E+00 | 1.138E+01 | 1.059E-01 | 5.800E-01 |
SCSO | 1.776E+00 | 5.534E-01 | 1.250E-04 | 1.364E-04 | -6.603E+03 | 8.131E+02 | 0.000E+00 | 0.000E+00 | 4.441E-16 | 0.000E+00 |
AVOA | 4.283E-07 | 3.569E-07 | 1.377E-04 | 1.559E-04 | -1.227E+04 | 5.537E+02 | 0.000E+00 | 0.000E+00 | 4.441E-16 | 0.000E+00 |
CMAES | 9.214E-06 | 2.962E-06 | 1.599E-01 | 2.267E-02 | -5.429E+03 | 4.607E+01 | 1.271E+02 | 6.809E+01 | 9.096E-04 | 1.401E-04 |
SHADE | 2.988E-05 | 1.588E-05 | 9.341E-01 | 2.361E-01 | -1.231E+04 | 1.643E+02 | 7.243E-01 | 8.663E-01 | 2.178E-02 | 1.111E-01 |
BKA | 1.969E+00 | 1.083E+00 | 2.704E-04 | 1.772E-04 | -8.903E+03 | 1.189E+03 | 0.000E+00 | 0.000E+00 | 4.441E-16 | 0.000E+00 |
CBKA | 1.766E+00 | 4.694E-01 | 2.638E-04 | 1.686E-04 | -8.903E+03 | 9.643E+02 | 0.000E+00 | 0.000E+00 | 4.441E-16 | 0.000E+00 |
IBKA | 2.076E+00 | 1.341E+00 | 2.569E-05 | 2.645E-05 | -9.977E+03 | 1.355E+03 | 0.000E+00 | 0.000E+00 | 4.441E-16 | 0.000E+00 |
QOBLBKA | 2.263E+00 | 1.578E+00 | 2.585E-04 | 2.278E-04 | -7.887E+03 | 1.673E+03 | 0.000E+00 | 0.000E+00 | 4.441E-16 | 0.000E+00 |
AMOMM-BKA | 1.223E-05 | 3.089E-05 | 2.428E-05 | 2.388E-05 | -1.034E+04 | 5.998E+02 | 0.000E+00 | 0.000E+00 | 4.441E-16 | 0.000E+00 |
| Â | Fun11 | Fun12 | Fun13 | Fun14 | Fun15 | |||||
|---|---|---|---|---|---|---|---|---|---|---|
AVG | STD | AVG | STD | AVG | STD | AVG | STD | AVG | STD | |
PSO | 1.142E-01 | 5.645E-02 | 5.286E-02 | 5.185E-02 | 5.157E-01 | 1.931E-01 | 3.496E+00 | 2.548E+00 | 9.280E-04 | 1.368E-04 |
GWO | 6.797E-03 | 8.944E-03 | 5.676E-02 | 3.246E-02 | 5.943E-01 | 2.878E-01 | 4.690E+00 | 4.027E+00 | 4.433E-03 | 8.104E-03 |
GJO | 0.000E+00 | 0.000E+00 | 2.138E-01 | 1.200E-01 | 1.668E+00 | 2.513E-01 | 3.803E+00 | 4.144E+00 | 2.477E-03 | 6.066E-03 |
SO | 6.653E-02 | 1.693E-01 | 1.669E-01 | 3.289E-01 | 4.641E-01 | 8.096E-01 | 1.064E+00 | 2.522E-01 | 5.547E-04 | 2.668E-04 |
SCSO | 0.000E+00 | 0.000E+00 | 9.805E-02 | 4.812E-02 | 2.404E+00 | 3.510E-01 | 5.237E+00 | 4.489E+00 | 3.747E-04 | 2.315E-04 |
AVOA | 0.000E+00 | 0.000E+00 | 2.556E-08 | 1.725E-08 | 5.442E-08 | 6.246E-08 | 1.687E+00 | 1.855E+00 | 4.242E-04 | 1.841E-04 |
CMAES | 3.665E-04 | 1.374E-03 | 9.734E-07 | 4.217E-07 | 1.376E-05 | 6.276E-06 | 5.166E+00 | 3.608E+00 | 6.399E-03 | 5.751E-03 |
SHADE | 7.136E-04 | 1.944E-03 | 7.923E-03 | 2.655E-02 | 7.361E-04 | 2.779E-03 | 1.031E+00 | 1.815E-01 | 1.198E-03 | 1.335E-03 |
BKA | 0.000E+00 | 0.000E+00 | 7.668E-02 | 1.136E-01 | 1.866E+00 | 5.379E-01 | 1.295E+00 | 9.054E-01 | 1.835E-03 | 5.064E-03 |
CBKA | 0.000E+00 | 0.000E+00 | 5.886E-02 | 2.459E-02 | 1.746E+00 | 3.167E-01 | 9.980E-01 | 2.182E-16 | 2.982E-03 | 6.934E-03 |
IBKA | 0.000E+00 | 0.000E+00 | 1.078E-01 | 1.548E-01 | 1.679E+00 | 5.131E-01 | 1.262E+00 | 8.591E-01 | 1.158E-03 | 3.647E-03 |
QOBLBKA | 0.000E+00 | 0.000E+00 | 1.025E-01 | 1.741E-01 | 1.731E+00 | 3.625E-01 | 1.624E+00 | 1.384E+00 | 1.163E-03 | 3.645E-03 |
AMOMM-BKA | 0.000E+00 | 0.000E+00 | 4.157E-07 | 7.149E-07 | 5.854E-02 | 6.678E-02 | 9.980E-01 | 1.623E-16 | 3.321E-04 | 5.994E-05 |
| Â | Fun16 | Fun17 | Fun18 | Fun19 | Fun20 | |||||
|---|---|---|---|---|---|---|---|---|---|---|
AVG | STD | AVG | STD | AVG | STD | AVG | STD | AVG | STD | |
PSO | -1.032E+00 | 4.701E-16 | 3.979E-01 | 0.000E+00 | 3.000E+00 | 6.311E-15 | -3.863E+00 | 2.067E-15 | -3.251E+00 | 5.924E-02 |
GWO | -1.032E+00 | 2.618E-08 | 3.979E-01 | 2.874E-06 | 3.000E+00 | 4.231E-05 | -3.862E+00 | 2.152E-03 | -3.275E+00 | 7.160E-02 |
GJO | -1.032E+00 | 2.266E-07 | 3.979E-01 | 4.992E-05 | 3.000E+00 | 3.551E-06 | -3.859E+00 | 3.846E-03 | -3.125E+00 | 1.496E-01 |
SO | -1.032E+00 | 5.532E-16 | 3.979E-01 | 2.932E-08 | 3.900E+00 | 4.930E+00 | -3.837E+00 | 1.411E-01 | -3.322E+00 | 2.603E-10 |
SCSO | -1.032E+00 | 5.812E-10 | 3.979E-01 | 2.865E-08 | 3.000E+00 | 7.252E-08 | -3.861E+00 | 3.212E-03 | -3.177E+00 | 2.100E-01 |
AVOA | -1.032E+00 | 4.103E-16 | 3.979E-01 | 0.000E+00 | 3.000E+00 | 4.736E-06 | -3.863E+00 | 9.864E-11 | -3.266E+00 | 6.037E-02 |
CMAES | -1.032E+00 | 6.775E-16 | 4.040E-01 | 2.137E-02 | 3.000E+00 | 6.226E-16 | -3.863E+00 | 2.390E-15 | -3.168E+00 | 2.033E-01 |
SHADE | -1.032E+00 | 6.584E-16 | 3.979E-01 | 0.000E+00 | 3.000E+00 | 1.296E-15 | -3.863E+00 | 2.710E-15 | -3.308E+00 | 3.653E-02 |
BKA | -1.032E+00 | 5.684E-16 | 3.979E-01 | 0.000E+00 | 3.000E+00 | 2.267E-15 | -3.863E+00 | 2.445E-15 | -3.293E+00 | 5.328E-02 |
CBKA | -1.032E+00 | 5.532E-16 | 3.979E-01 | 3.243E-16 | 3.000E+00 | 2.389E-15 | -3.863E+00 | 2.316E-15 | -3.294E+00 | 5.150E-02 |
IBKA | -1.032E+00 | 4.215E-11 | 3.979E-01 | 3.729E-12 | 3.000E+00 | 9.590E-15 | -3.863E+00 | 5.088E-08 | -3.294E+00 | 5.102E-02 |
QOBLBKA | -1.032E+00 | 4.503E-07 | 3.979E-01 | 1.310E-11 | 3.000E+00 | 2.903E-15 | -3.863E+00 | 2.613E-12 | -3.282E+00 | 5.858E-02 |
AMOMM-BKA | -1.032E+00 | 6.046E-16 | 3.979E-01 | 0.000E+00 | 3.000E+00 | 1.365E-15 | -3.863E+00 | 2.354E-15 | -3.322E+00 | 5.827E-03 |
Functions | Fun21 | Fun22 | Fun23 | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
AVG | STD | AVG | STD | AVG | STD | |||||
PSO | -7.385E+00 | 3.112E+00 | -8.956E+00 | 2.447E+00 | -8.845E+00 | 2.904E+00 | ||||
GWO | -9.138E+00 | 2.061E+00 | -1.023E+01 | 9.628E-01 | -1.053E+01 | 1.023E-03 | ||||
GJO | -8.708E+00 | 2.447E+00 | -9.606E+00 | 2.065E+00 | -9.895E+00 | 1.959E+00 | ||||
SO | -1.003E+01 | 4.339E-01 | -1.028E+01 | 4.340E-01 | -1.034E+01 | 5.660E-01 | ||||
SCSO | -6.076E+00 | 2.073E+00 | -6.961E+00 | 2.697E+00 | -6.406E+00 | 2.942E+00 | ||||
AVOA | -1.015E+01 | 2.178E-13 | -1.040E+01 | 2.160E-13 | -1.054E+01 | 1.948E-13 | ||||
CMAES | -7.429E+00 | 3.553E+00 | -9.894E+00 | 1.938E+00 | -1.004E+01 | 1.888E+00 | ||||
SHADE | -9.632E+00 | 1.544E+00 | -1.015E+01 | 1.394E+00 | -1.052E+01 | 7.242E-02 | ||||
BKA | -9.902E+00 | 1.373E+00 | -1.040E+01 | 2.697E-05 | -1.002E+01 | 1.961E+00 | ||||
CBKA | -1.015E+01 | 2.448E-06 | -1.040E+01 | 2.348E-05 | -1.054E+01 | 7.920E-06 | ||||
IBKA | -1.015E+01 | 2.265E-07 | -1.040E+01 | 2.069E-04 | -1.054E+01 | 4.931E-06 | ||||
QOBLBKA | -1.015E+01 | 3.230E-03 | -1.015E+01 | 1.394E+00 | -1.054E+01 | 2.430E-06 | ||||
AMOMM-BKA | -1.015E+01 | 5.278E-15 | -1.040E+01 | 1.682E-15 | -1.054E+01 | 1.714E-15 | ||||
