Table 6 CEC 2021 test function results.
Function | Metric | MSDBO | DBO | AOA | PSO | GWO | WOA | HHO |
|---|---|---|---|---|---|---|---|---|
CEC-1 | Best | 0 | 5.63E-157 | 0 | 2.76E + 07 | 1.20E-32 | 3.00E-87 | 1.71E-80 |
Std | 0 | 9.70E-112 | 5.77E-103 | 1.31E + 08 | 2.80E-29 | 1.61E-82 | 3.59E-68 | |
Average | 0 | 2.13E-112 | 1.05E-103 | 1.66E + 08 | 1.22E-29 | 3.08E-83 | 8.50E-69 | |
p-value | NAN | 1.21E-12 | 1.21E-12 | 1.21E-12 | 1.21E-12 | 1.21E-12 | 1.21E-12 | |
Signed-rank test | + | + | + | + | + | + | ||
CEC-2 | Best | 0 | 0 | 0 | 4.76E + 02 | 3.64E-12 | 0 | 0 |
Std | 0 | 5.86E + 02 | 0 | 6.20E + 02 | 9.39E + 01 | 0 | 6.79E + 02 | |
Average | 0 | 2.08E + 02 | 0 | 1.71E + 03 | 3.60E + 01 | 0 | 1.76E + 02 | |
p-value | NAN | 1.10E-02 | NAN | 1.21E-12 | 1.20E-12 | 6.56E-04 | NAN | |
Signed-rank test | + | = | + | + | + | = | ||
CEC-3 | Best | 0 | 0 | 0 | 5.22E + 01 | 5.72E-30 | 0 | 0 |
Std | 0 | 3.04E + 00 | 0 | 4.42E + 01 | 6.80E + 01 | 0 | 6.02E-32 | |
Average | 0 | 8.84E-01 | 0 | 1.12E + 02 | 7.26E + 01 | 0 | 1.97E-32 | |
p-value | NAN | 1.61E-01 | NAN | 1.21E-12 | 1.21E-12 | 3.34E-01 | NAN | |
Signed-rank test | - | = | + | + | - | = | ||
CEC-4 | Best | 0 | 0 | 0 | 6.13E + 00 | 0 | 0 | 0 |
Std | 0 | 2.18E + 00 | 0 | 1.81E + 01 | 8.23E-01 | 0 | 5.93E-01 | |
Average | 0 | 1.15E + 00 | 0 | 2.16E + 01 | 7.14E-01 | 0 | 1.08E-01 | |
p-value | NAN | 3.13E-04 | NAN | 1.21E-12 | 1.93E-10 | 1.61E-01 | NAN | |
Signed-rank test | + | = | + | + | - | = | ||
CEC-5 | Best | 0 | 1.28E-152 | 0 | 2.17E + 03 | 6.99E-19 | 9.83E-21 | 2.40E-82 |
Std | 0 | 3.64E-01 | 0 | 1.67E + 04 | 3.43E + 00 | 3.25E-19 | 2.92E-16 | |
Average | 0 | 6.64E-02 | 3.89E-217 | 1.45E + 04 | 2.76E + 00 | 3.18E-19 | 9.35E-17 | |
p-value | NAN | 1.21E-12 | 5.58E-03 | 1.21E-12 | 1.21E-12 | 1.21E-12 | 1.21E-12 | |
Signed-rank test | + | + | + | + | + | + | ||
CEC-6 | Best | −2.22E-16 | 4.86E-09 | −1.11E-16 | 1.13E + 01 | 6.13E-02 | 7.88E-04 | 1.44E-05 |
Std | 9.10E-17 | 2.41E + 02 | 3.38E-17 | 1.57E + 02 | 5.53E + 00 | 3.11E-01 | 2.07E + 02 | |
Average | −1.67E-16 | 1.14E + 02 | −1.11E-17 | 2.11E + 02 | 5.43E + 00 | 6.46E-02 | 3.85E + 01 | |
p-value | NAN | 4.95E-11 | 1.84E-09 | 2.80E-11 | 2.80E-11 | 2.80E-11 | 6.53E-11 | |
Signed-rank test | + | + | + | + | + | + | ||
CEC-7 | Best | −2.22E-16 | −2.89E-17 | 0 | 7.02E + 02 | 4.45E-02 | 3.63E-04 | 2.14E-04 |
Std | 1.09E-16 | 2.48E + 00 | 8.31E-119 | 8.78E + 03 | 5.94E + 00 | 7.01E-04 | 1.12E-01 | |
Average | −1.11E-16 | 6.54E-01 | 1.52E-119 | 4.39E + 03 | 2.31E + 00 | 1.41E-03 | 9.96E-02 | |
p-value | NAN | 2.11E-11 | 2.32E-05 | 2.11E-11 | 2.11E-11 | 2.11E-11 | 1.05E-10 | |
Signed-rank test | + | + | + | + | + | + | ||
CEC-8 | Best | 0 | 0 | 0 | 1.25E + 02 | 0 | 0 | 0 |
Std | 0 | 0 | 0 | 2.54E + 02 | 4.09E-16 | 0 | 6.00E + 02 | |
Average | 0 | 0 | 0 | 5.43E + 02 | 8.64E-17 | 0 | 1.10E + 02 | |
p-value | NAN | 3.34E-01 | NAN | 1.21E-12 | 3.34E-01 | 3.34E-01 | NAN | |
Signed-rank test | - | = | + | - | - | = | ||
CEC-9 | Best | 1.41E-315 | 5.74E-163 | 1.08E-312 | 3.24E + 01 | 2.66E-14 | 8.88E-15 | 1.57E-89 |
Std | 0 | 2.19E-67 | 3.95E-110 | 1.67E + 01 | 1.28E-14 | 1.62E-15 | 5.18E-15 | |
Average | 1.67E-314 | 3.99E-68 | 7.21E-111 | 7.63E + 01 | 5.03E-14 | 9.18E-15 | 8.29E-15 | |
p-value | NAN | 3.02E-11 | 3.02E-11 | 3.02E-11 | 2.67E-11 | 1.72E-11 | 3.02E-11 | |
Signed-rank test | + | + | + | + | + | + | ||
CEC-10 | Best | 1.11E-315 | 7.11E-15 | 2.54E-282 | 1.17E + 02 | 1.22E-02 | 1.73E-03 | 6.59E-04 |
Std | 0 | 3.92E + 01 | 7.44E-05 | 2.66E + 01 | 2.05E + 01 | 2.21E + 01 | 4.38E-02 | |
Average | 1.11E-315 | 2.25E + 01 | 2.09E-05 | 1.71E + 02 | 7.66E + 01 | 7.15E + 00 | 8.88E-02 | |
p-value | NAN | 3.02E-11 | 3.02E-11 | 3.02E-11 | 3.02E-11 | 3.02E-11 | 3.02E-11 | |
Signed-rank test | + | + | + | + | + | + | ||
+ /−/ = /gm | 56/6/8/50 | |||||||
