Table 3 Statistical results for CEC 2019 problems.
From: A hybrid swarm intelligent optimization algorithm for antenna design problems
Problem | jDE10037 | DE | SSA | SOA | NMRA | SSNMRA | |
|---|---|---|---|---|---|---|---|
\(p_{1}\) | Best | 3.378E+04 | 3.224E+09 | 8.423E+07 | 4.060E+04 | 8.442E+04 | 4.378E+04 |
Mean | 1.590E+05 | 3.418E+11 | 7.216E+09 | 2.326E+08 | 4.079E+05 | 7.537E+04 | |
Median | 9.530E+04 | 2.393E+11 | 4.165E+09 | 2.591E+06 | 3.649E+05 | 5.232E+04 | |
Std | 1.597E+05 | 3.391E+11 | 7.857E+09 | 5.630E+08 | 2.777E+05 | 1.203E+05 | |
Worst | 6.237E+05 | 1.401E+12 | 3.675E+10 | 3.446E+09 | 1.380E+06 | 8.635E+05 | |
p-rank | − | − | − | − | − | ||
f-rank | 2 | 6 | 5 | 4 | 3 | 1 | |
\(p_{2}\) | Best | 2.331E+06 | 1.734E+01 | 1.734E+01 | 1.734E+01 | 1.783E+01 | 1.734E+01 |
Mean | 2.385E+06 | 4.829E+01 | 1.735E+01 | 1.739E+01 | 1.878E+01 | 1.735E+01 | |
Median | 2.388E+06 | 1.734E+01 | 1.734E+01 | 1.735E+01 | 1.878E+01 | 1.734E+01 | |
Std | 2.719E+04 | 9.286E+01 | 4.940E-02 | 1.047E-01 | 5.396E-01 | 2.730E-02 | |
Worst | 2.431E+06 | 4.564E+02 | 1.769E+01 | 1.768E+01 | 1.984E+01 | 1.765E+01 | |
p-rank | − | − | − | − | − | ||
f-rank | 6 | 5 | 2 | 3 | 4 | 1 | |
\(p_{3}\) | Best | 1.377E+05 | 1.269E+01 | 1.270E+01 | 1.270E+01 | 1.270E+01 | 1.270E+01 |
Mean | 1.310E+06 | 1.271E+01 | 1.270E+01 | 1.270E+01 | 1.270E+01 | 1.270E+01 | |
Median | 1.129E+06 | 1.270E+01 | 1.270E+01 | 1.270E+01 | 1.270E+01 | 1.270E+01 | |
Std | 8.519E+05 | 1.600E-03 | 4.045E-04 | 2.712E-06 | 4.155E-06 | 1.915E-06 | |
Worst | 2.814E+06 | 1.271E+01 | 1.270E+01 | 1.270E+01 | 1.270E+01 | 1.270E+01 | |
p-rank | − | − | − | − | − | ||
f-rank | 6 | 5 | 4 | 2 | 3 | 1 | |
\(p_{4}\) | Best | 1.250E+05 | 7.889E+01 | 1.669E+02 | 6.129E+01 | 8.965E+01 | 1.492E+01 |
Mean | 3.475E+05 | 1.554E+03 | 2.468E+03 | 5.064E+02 | 4.244E+02 | 3.995E+01 | |
Median | 3.718E+05 | 8.652E+02 | 2.064E+03 | 1.846E+02 | 3.037E+02 | 3.382E+01 | |
Std | 1.149E+05 | 1.631E+03 | 1.580E+03 | 5.393E+02 | 3.517E+02 | 2.085E+01 | |
Worst | 5.099E+05 | 7.336E+03 | 6.888E+03 | 2.442E+03 | 1.722E+03 | 1.144E+02 | |
p-rank | − | − | − | − | − | ||
f-rank | 6 | 4 | 5 | 3 | 2 | 1 | |
\(p_{5}\) | Best | 5.520E+04 | 1.546E+00 | 1.238E+00 | 1.370E+00 | 1.467E+00 | 1.051E+00 |
Mean | 1.673E+05 | 2.157E+00 | 2.525E+00 | 1.711E+00 | 2.253E+00 | 1.248E+00 | |
Median | 1.473E+05 | 2.110E+00 | 2.328E+00 | 1.700E+00 | 2.206E+00 | 1.223E+00 | |
Std | 8.426E+04 | 3.059E-01 | 9.193E-01 | 2.017E-01 | 4.546E-01 | 1.472E-01 | |
Worst | 3.771E+05 | 3.472E+00 | 6.515E+00 | 2.242E+00 | 3.557E+00 | 1.497E+00 | |
p-rank | − | − | − | − | − | ||
f-rank | 6 | 3 | 4 | 2 | 5 | 1 | |
\(p_{6}\) | Best | 3.501E+04 | 5.664E+00 | 9.203E+00 | 7.715E+00 | 1.006E+01 | 1.174E+00 |
Mean | 3.841E+04 | 9.773E+00 | 9.370E+00 | 1.106E+01 | 1.144E+01 | 4.789E+00 | |
Median | 3.789E+04 | 1.029E+01 | 9.287E+00 | 1.111E+01 | 1.134E+01 | 4.838E+00 | |
Std | 2.063E+03 | 1.490E+00 | 1.794E+00 | 7.126E-01 | 6.668E-01 | 7.400E-01 | |
Worst | 4.155E+04 | 1.205E+01 | 1.080E+01 | 1.230E+01 | 1.271E+01 | 8.402E+00 | |
p-rank | − | − | − | − | − | ||
f-rank | 6 | 3 | 2 | 4 | 5 | 1 | |
\(p_{7}\) | Best | 2.482E+06 | 3.143E+02 | −8.991E+01 | −7.308E+01 | −5.988E+01 | −9.837E+01 |
Mean | 9.105E+06 | 1.257E+03 | 3.497E+02 | 3.274E+02 | 2.315E+02 | 2.018E+02 | |
Median | 9.185E+06 | 2.309E+03 | 3.334E+02 | 3.496E+02 | 1.924E+02 | 2.199E+02 | |
Std | 4.528E+06 | 4.121E+02 | 2.244E+02 | 1.847E+02 | 1.600E+02 | 1.361E+02 | |
Worst | 1.589E+07 | 1.860E+03 | 9.112E+02 | 6.905E+02 | 6.562E+02 | 6.099E+02 | |
p-rank | − | − | − | − | − | ||
f-rank | 6 | 5 | 4 | 3 | 2 | 1 | |
\(p_{8}\) | Best | 1.591E+08 | 6.491E+00 | 3.371E+00 | 4.843E+00 | 5.006E+00 | 3.912E+00 |
Mean | 1.219E+09 | 7.010E+00 | 5.253E+00 | 6.455E+00 | 6.032E+00 | 5.230E+00 | |
Median | 1.372E+09 | 7.055E+00 | 5.318E+00 | 6.526E+00 | 6.061E+00 | 5.347E+00 | |
Std | 4.388E+08 | 2.152E-01 | 7.189E-01 | 4.392E-01 | 3.355E-01 | 5.572E-01 | |
Worst | 1.779E+09 | 7.336E+00 | 6.494E+00 | 7.174E+00 | 6.704E+00 | 6.315E+00 | |
p-rank | − | − | − | − | − | ||
f-rank | 6 | 5 | 2 | 4 | 3 | 1 | |
\(p_{9}\) | Best | 6.086E+08 | 3.762E+00 | 2.940E+00 | 4.276E+00 | 2.748E+00 | 2.371E+00 |
Mean | 9.207E+08 | 2.714E+02 | 8.338E+01 | 6.668E+01 | 1.156E+01 | 2.653E+00 | |
Median | 9.494E+08 | 1.287E+02 | 5.584E+00 | 6.226E+00 | 4.384E+00 | 2.602E+00 | |
Std | 1.131E+08 | 3.517E+02 | 1.342E+02 | 1.222E+02 | 3.411E+01 | 1.895E-01 | |
Worst | 1.056E+09 | 1.958E+03 | 5.684E+02 | 3.636E+02 | 2.229E+02 | 3.165E+00 | |
p-rank | − | − | − | − | − | ||
f-rank | 6 | 5 | 4 | 3 | 2 | 1 | |
\(p_{10}\) | Best | 1.796E+05 | 2.023E+01 | 2.011E+01 | 2.036E+01 | 2.012E+01 | 1.998E+01 |
Mean | 1.541E+06 | 2.045E+01 | 2.031E+01 | 2.051E+01 | 2.051E+01 | 2.003E+01 | |
Median | 1.761E+06 | 2.046E+01 | 2.030E+01 | 2.052E+01 | 2.054E+01 | 2.000E+01 | |
Std | 7.460E+05 | 1.115E-01 | 1.007E-01 | 7.190E-02 | 1.053E-01 | 7.550E-02 | |
Worst | 2.533E+06 | 2.067E+01 | 2.053E+01 | 2.070E+01 | 2.066E+01 | 2.039E+01 | |
p-rank | − | − | − | − | − | ||
f-rank | 6 | 3 | 2 | 4 | 5 | 1 | |
w/l/t | 0/10/0 | 0/10/0 | 0/10/0 | 0/10/0 | 0/10/0 | NA | |
Average f-rank | 5.60 | 4.40 | 3.40 | 3.20 | 3.40 | 1.00 | |
Overall f-rank | 6 | 5 | 3 | 2 | 3 | 1 |
