Table 3 Statistical outcomes for the 100-digit challenge (CEC 2019) numerical problems.
Challenges | BWOA65 | CDO58 | COA59 | FPA66 | HHO60 | YDSE55 | ZOA51 | ARNMRA67 | FROBL-GJO68 | jDE-10069 | GPC | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(GPC_{1}\) | Mean | 1.5294E+05 | 9.5879E+04 | 1.6522E+05 | 5.3014E+08 | 5.0159E+04 | 3.8512E+06 | 7.1435E+04 | 1.350E+05 | 4.520E+04 | 1.59E+05 | 1.0000E+10 |
Std | 2.1936E+05 | 2.6979E+00 | 1.26407E+05 | 2.4666E+08 | 4.4810E+03 | 1.8195E+06 | 1.4253E+05 | 7.839E+04 | 4.204E+03 | 1.597E+05 | 0.0000E+00 | |
p-rank | + | + | + | + | + | + | + | + | + | + | ||
f-rank | 6 | 4 | 8 | 10 | 2 | 9 | 3 | 5 | 1 | 7 | 11 | |
\(GPC_{2}\) | Mean | 1.7532E+01 | 1.9847E+01 | 1.7916E+01 | 2.2660E+01 | 1.7357E+01 | 1.7355E+01 | 1.7389E+01 | 1.784E+01 | 1.734E+01 | 2.385E+06 | 1.7343E+01 |
Std | 3.8690E–01 | 0.0000E+00 | 3.0206E–01 | 3.5269E+00 | 7.9998E–03 | 4.9060E–03 | 9.7529E–01 | 3.432E–01 | 8.392E–02 | 2.719E+04 | 9.5955E–05 | |
p-rank | − | − | − | − | − | − | − | − | − | − | ||
f-rank | 2 | 9 | 8 | 10 | 5 | 4 | 6 | 7 | 3 | 11 | 1 | |
\(GPC_{3}\) | Mean | 1.2702E+01 | 1.2702E+01 | 1.2702E+01 | 1.2702E+01 | 1.2702E+01 | 1.2702E+01 | 1.2702E+01 | 1.270E+01 | 1.270E+01 | 1.31E+06 | 1.2702E+01 |
Std | 6.1579E–04 | 3.3028E–06 | 1.4773E–04 | 9.9446E–08 | 8.4058E–06 | 6.9331E–10 | 8.9366E–06 | 3.245E–08 | 3.102E–04 | 8.519E+05 | 1.3500E–14 | |
p-rank | − | − | − | − | − | − | − | − | − | − | ||
f-rank | 10 | 5 | 8 | 4 | 6 | 2 | 7 | 3 | 9 | 11 | 1 | |
\(GPC_{4}\) | Mean | 4.5309E+03 | 5.4836E+03 | 1.0194E+04 | 1.3845E+02 | 1.6806E+02 | 5.7472E+01 | 7.3522E+02 | 3.528E+02 | 9.776E+02 | 3.475E+05 | 4.1084E+01 |
Std | 3.3190E+03 | 8.8105E+01 | 2.361E+02 | 3.0541E+03 | 2.6490E+01 | 6.6113E+01 | 7.9702E+00 | 8.5208E+02 | 1.644E+03 | 1.149E+05 | 7.7348E+00 | |
p-rank | − | − | − | − | − | − | − | − | − | − | ||
f-rank | 8 | 9 | 10 | 3 | 4 | 2 | 6 | 5 | 7 | 11 | 1 | |
\(GPC_{5}\) | Mean | 2.6193E+00 | 3.8556E+00 | 3.7507E+00 | 1.5793E+00 | 2.3368E+00 | 1.3300E+00 | 1.6316E+00 | 1.939E+00 | 1.698E+00 | 1.673e+05 | 1.1549E+00 |
Std | 7.0345E–01 | 8.9450E–02 | 7.1965E–01 | 8.0326E–02 | 4.9634E–01 | 8.1574E–02 | 3.2080E–01 | 3.127E–01 | 4.527E–01 | 8.426e+04 | 3.1311E–02 | |
p-rank | − | − | − | − | − | − | − | − | − | − | ||
f-rank | 8 | 10 | 9 | 3 | 7 | 2 | 4 | 6 | 5 | 11 | 1 | |
\(GPC_{6}\) | Mean | 1.0063E+01 | 1.0667E+01 | 9.9332E+00 | 1.0333E+01 | 9.3245E+00 | 9.8942E+00 | 7.7901E+00 | 1.036E+01 | 1.013E+01 | 3.841E+04 | 9.3846E+00 |
Std | 1.3329E+00 | 5.6535E–01 | 8.7596E–01 | 7.0873E–01 | 1.1888E+00 | 4.6791E–01 | 9.4376E–01 | 6.533E–01 | 1.732E+00 | 2.063E+03 | 7.3711E–01 | |
p-rank | − | − | − | − | + | − | + | − | − | − | ||
f-rank | 6 | 10 | 5 | 8 | 2 | 4 | 1 | 9 | 7 | 11 | 3 | |
\(GPC_{7}\) | Mean | 5.9318E+02 | 8.0019E+02 | 2.4750E+02 | 5.0637E+01 | 3.6530E+02 | 2.2852E+02 | 7.7402E+01 | -2.860E+00 | 5.522E+02 | 9.105E+06 | 5.0637E+01 |
Std | 2.9809E+02 | 1.1585E+02 | 2.3388E+02 | 7.5341E+01 | 1.8888E+02 | 1.0203E+02 | 6.1565E+01 | 1.192E+02 | 3.044E+02 | 4.528E+06 | 7.0755E+01 | |
p-rank | − | − | − | − | − | − | − | − | − | − | ||
f-rank | 9 | 10 | 6 | 2 | 7 | 5 | 3 | 4 | 8 | 11 | 1 | |
\(GPC_{8}\) | Mean | 5.7614E+00 | 6.1826E+00 | 6.0490E+00 | 5.6594E+00 | 5.7615E+00 | 5.8395E+00 | 4.2537E+00 | 5.594E+00 | 5.343E+00 | 1.219E+09 | 5.3032E+00 |
Std | 5.3632E–01 | 3.6138E–01 | 3.9446E–01 | 3.4696E–01 | 5.2577E–01 | 3.9440E–01 | 5.2491E–01 | 7.893E–01 | 3.227E–01 | 4.388E+08 | 4.3006E–01 | |
p-rank | − | − | − | − | − | − | + | − | − | − | ||
f-rank | 6 | 10 | 9 | 5 | 7 | 8 | 1 | 4 | 3 | 11 | 2 | |
\(GPC_{9}\) | Mean | 6.2079E+02 | 3.0304E+03 | 1.2186E+03 | 5.3861E+00 | 2.9154E+00 | 3.1351E+00 | 6.2241E+00 | 1.126E+01 | 6.544E+01 | 9.207E+08 | 2.6235E+00 |
Std | 4.2195E+02 | 1.4339E+03 | 5.0662E+02 | 1.8055E+00 | 3.07977E–01 | 2.1050E–01 | 2.9711E+00 | 1.932E+01 | 1.743E+02 | 1.131E+08 | 8.1972E–02 | |
p-rank | − | − | − | − | − | − | − | − | − | − | ||
f-rank | 8 | 10 | 9 | 4 | 2 | 3 | 5 | 6 | 7 | 11 | 1 | |
\(GPC_{10}\) | Mean | 2.0280E+01 | 2.0451E+01 | 2.0361E+01 | 2.0371E+01 | 2.0143E+01 | 2.0402E+01 | 1.8951E+01 | 2.037E+01 | 1.993E+01 | 1.541E+06 | 1.9678E+01 |
Std | 3.3555E–01 | 9.8487E–02 | 1.1034E–01 | 8.9158-02 | 1.0614E–01 | 6.9634E–01 | 3.0286E+00 | 7.670E–02 | 2.424E+00 | 7.46E+05 | 3.0152E+00 | |
p-rank | − | − | − | − | − | − | + | − | − | − | ||
f-rank | 5 | 10 | 6 | 8 | 4 | 9 | 1 | 7 | 3 | 11 | 2 | |
w/l/t | 01/09/00 | 01/09/00 | 01/09/00 | 01/09/00 | 02/08/00 | 01/09/00 | 04/06/00 | 01/09/00 | 01/09/00 | 01/09/00 | NA | |
Average f-rank | 6.80 | 8.70 | 7.80 | 5.70 | 4.60 | 4.80 | 3.70 | 5.60 | 5.30 | 10.60 | 2.04 | |
Overall f-rank | 8 | 10 | 9 | 7 | 3 | 4 | 2 | 6 | 5 | 11 | 1 |
