Table 4 Statistical results of the 23 standard benchmark functions.
From: Multi-strategy enhanced sand cat swarm optimization algorithm and its engineering applications
F | dim | Metric | MESCSO | SCSO | AOA | SABO | DBO | SCA | HHO | KOA | BWO | WOA |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
F1 | 30 | mean | 0 | 7.32E-114 | 7.08E-34 | 4.15E-196 | 4.64E-105 | 1.01E+01 | 5.51E-90 | 1.37E+04 | 1.33E-253 | 3.78E-74 |
std | 0 | 3.65E-113 | 3.87E-33 | 0 | 2.53E-104 | 1.71E+01 | 2.74E-89 | 3.45E+03 | 0 | 1.47E-73 | ||
500 | mean | 0 | 5.52E-100 | 6.52E-01 | 3.11E-199 | 1.85E-113 | 1.95E+05 | 5.77E-97 | 4.27E+05 | 2.90E-250 | 1.36E-69 | |
std | 0 | 1.77E-99 | 4.00E-02 | 0 | 7.67E-113 | 6.66E+04 | 1.93E-96 | 6.27E+04 | 0 | 4.98E-69 | ||
F2 | 30 | mean | 0 | 4.32E-60 | 0 | 1.92E-110 | 4.60E-59 | 9.76E-03 | 9.46E-52 | 6.50E+22 | 8.40E-131 | 1.76E-49 |
std | 0 | 2.03E-59 | 0 | 6.95E-110 | 2.48E-58 | 9.89E-03 | 2.14E-51 | 2.98E+03 | 3.28E-130 | 7.83E-49 | ||
500 | mean | 0 | 5.07E-52 | 1.01E-03 | 1.36E+01 | 3.09E-60 | 1.15E+02 | 3.93E-49 | 1.11E+128 | 1.84E-126 | 9.39E-48 | |
std | 0 | 1.47E-51 | 1.64E-03 | 3.10E+01 | 1.56E-59 | 5.48E+01 | 1.73E-48 | 6.10E+128 | 9.57E-126 | 4.83E-47 | ||
F3 | 30 | mean | 0 | 2.83E-98 | 7.12E-03 | 2.23E-36 | 3.31E-49 | 9.11E+03 | 7.76E-75 | 4.71E+04 | 8.66E-244 | 4.27E+04 |
std | 0 | 1.54E-97 | 1.54E-02 | 1.22E-35 | 1.82E-48 | 5.03E+03 | 4.20E-74 | 1.45E+04 | 0 | 1.77E+04 | ||
500 | mean | 0 | 2.02E-84 | 3.04E+01 | 1.12E-03 | 2.62E-07 | 6.84E+06 | 1.17E-29 | 1.17E+07 | 5.53E-229 | 3.14E+07 | |
std | 0 | 1.06E-83 | 1.61E+01 | 6.10E-03 | 1.43E-06 | 1.48E+06 | 6.42E-29 | 3.41E+06 | 0 | 1.24E+07 | ||
F4 | 30 | mean | 0 | 1.31E-50 | 2.81E-02 | 3.53E-77 | 9.10E-49 | 3.77E+01 | 8.63E-50 | 5.33E+01 | 1.39E-126 | 5.59E+01 |
std | 0 | 5.31E-50 | 1.88E-02 | 6.38E-77 | 4.98E-48 | 9.67E+00 | 3.11E-49 | 5.82E+00 | 3.30E-126 | 2.80E+01 | ||
500 | mean | 0 | 8.08E-45 | 1.82E-01 | 2.27E-71 | 3.91E-32 | 9.91E+01 | 1.81E-49 | 8.62E+01 | 2.75E-114 | 8.36E+01 | |
std | 0 | 2.86E-44 | 2.04E-02 | 3.19E-71 | 2.14E-31 | 2.66E-01 | 6.86E-49 | 5.16E+00 | 1.13E-113 | 1.81E+01 | ||
F5 | 30 | mean | 8.91E-04 | 2.82E+01 | 2.84E+01 | 2.83E+01 | 2.58E+01 | 2.23E+04 | 1.01E-02 | 1.75E+07 | 1.30E-05 | 2.80E+01 |
std | 1.16E-03 | 6.98E-01 | 3.72E-01 | 4.66E-01 | 1.75E-01 | 5.08E+04 | 1.15E-02 | 1.15E+07 | 3.48E-05 | 4.64E-01 | ||
500 | mean | 4.61E+02 | 4.98E+02 | 4.99E+02 | 4.98E+02 | 4.98E+02 | 1.85E+09 | 2.14E-01 | 8.40E+08 | 2.60E-04 | 4.96E+02 | |
std | 1.25E+02 | 9.20E-02 | 1.07E-01 | 6.36E-02 | 2.12E-01 | 4.34E+08 | 2.84E-01 | 2.11E+08 | 8.37E-04 | 3.72E-01 | ||
F6 | 30 | mean | 3.44E-08 | 1.89E+00 | 3.21E+00 | 2.53E+00 | 7.28E-03 | 1.67E+01 | 1.36E-04 | 1.34E+04 | 2.43E-14 | 4.59E-01 |
std | 2.37E-08 | 5.42E-01 | 3.22E-01 | 4.37E-01 | 3.51E-02 | 3.58E+01 | 2.09E-04 | 3.02E+03 | 3.53E-14 | 2.83E-01 | ||
500 | mean | 2.26E-05 | 1.06E+02 | 1.16E+02 | 1.11E+02 | 9.02E+01 | 1.89E+05 | 1.56E-03 | 4.26E+05 | 1.33E-12 | 3.30E+01 | |
std | 3.79E-05 | 3.59E+00 | 9.12E-01 | 1.48E+00 | 3.43E+00 | 7.98E+04 | 2.00E-03 | 4.95E+04 | 2.83E-12 | 7.87E+00 | ||
F7 | 30 | mean | 4.41E-05 | 2.17E-04 | 8.16E-05 | 8.66E-05 | 1.19E-03 | 1.47E+01 | 1.48E-04 | 7.42E+00 | 1.45E-04 | 4.14E-03 |
std | 3.76E-05 | 3.17E-04 | 1.07E-04 | 6.62E-05 | 8.34E-04 | 2.36E-01 | 1.33E-04 | 3.45E+00 | 1.03E-04 | 4.19E-03 | ||
500 | mean | 8.28E-05 | 2.24E-04 | 9.13E-05 | 1.10E-04 | 1.72E-03 | 1.48E+04 | 1.87E-04 | 6.90E+03 | 1.12E-04 | 5.49E-03 | |
std | 8.65E-05 | 2.37E-04 | 5.46E-05 | 9.58E-05 | 1.57E-03 | 3.68E+03 | 1.86E-04 | 2.13E+03 | 1.13E-04 | 6.75E-03 | ||
F8 | 30 | mean | -1.26E+04 | -6.64E+03 | -5.29E+03 | -3.08E+03 | -8.82E+03 | -3.72E+03 | -1.26E+04 | -3.77E+03 | -1.26E+04 | -9.36E+03 |
std | 1.64E+00 | 7.54E+02 | 4.39E+02 | 3.66E+02 | 1.96E+03 | 2.52E+02 | 9.62E-01 | 3.78E+02 | 1.21E-06 | 1.45E+03 | ||
500 | mean | -2.09E+05 | -5.99E+04 | -2.31E+04 | -1.21E+04 | -1.35E+05 | -1.55E+04 | -2.09E+05 | -4.40E+04 | -2.09E+05 | -1.61E+05 | |
std | 1.84E+02 | 4.38E+03 | 1.57E+03 | 9.42E+02 | 3.83E+04 | 1.27E+03 | 2.59E+03 | 1.22E+04 | 4.82E-07 | 2.58E+04 | ||
F9 | 30 | mean | 0 | 0 | 0 | 0 | 5.67E-01 | 3.98E+01 | 0 | 2.84E+02 | 0 | 3.38E-02 |
std | 0 | 0 | 0 | 0 | 2.46E+01 | 3.20E+01 | 0 | 2.26E+01 | 0 | 1.85E-01 | ||
500 | mean | 0 | 0 | 8.18E-06 | 0 | 0 | 1.14E+03 | 0 | 6.04E+03 | 0 | 3.03E-14 | |
std | 0 | 0 | 7.75E-06 | 0 | 0 | 4.99E+02 | 0 | 2.03E+02 | 0 | 1.66E-13 | ||
F10 | 30 | mean | 8.88E-16 | 8.88E-16 | 8.88E-16 | 4.00E-15 | 9.63E-16 | 1.47E+01 | 8.89E-16 | 1.88E+01 | 8.88E-16 | 2.93E-15 |
std | 0 | 0 | 0 | 0 | 6.49E-15 | 8.38E+00 | 0 | 1.01E+00 | 0 | 1.90E-15 | ||
500 | mean | 8.88E-16 | 8.88E-16 | 7.96E-03 | 4.00E-15 | 8.88E-16 | 1.91E+01 | 8.88E-16 | 1.99E+01 | 8.88E-16 | 4.94E-15 | |
std | 0 | 0 | 8.30E-04 | 0 | 0 | 3.47E+00 | 0 | 1.85E-01 | 0 | 3.22E-15 | ||
F11 | 30 | mean | 0 | 0 | 2.17E-01 | 0 | 0 | 1.02E+00 | 0 | 1.40E+02 | 0 | 1.97E-02 |
std | 0 | 0 | 1.23E-01 | 0 | 0 | 3.97E-01 | 0 | 3.60E+01 | 0 | 6.40E-02 | ||
500 | mean | 0 | 0 | 9.90E+03 | 0 | 0 | 1.80E+03 | 0 | 3.83E+03 | 0 | 0 | |
std | 0 | 0 | 2.47E+03 | 0 | 0 | 7.34E+02 | 0 | 7.05E+02 | 0 | 0 | ||
F12 | 30 | mean | 1.37E-09 | 1.25E-01 | 5.15E-01 | 2.13E-01 | 2.37E-04 | 2.58E+04 | 1.10E-05 | 1.46E+07 | 3.92E-14 | 2.49E-02 |
std | 9.95E-10 | 6.20E-02 | 4.84E-02 | 1.09E-01 | 8.22E-04 | 1.06E+05 | 1.80E-05 | 9.51E+06 | 7.49E-14 | 2.62E-02 | ||
500 | mean | 2.20E-08 | 7.93E-01 | 1.08E+00 | 9.47E-01 | 6.11E-01 | 5.80E+09 | 2.52E-06 | 1.16E+09 | 6.86E-16 | 1.07E-01 | |
std | 2.79E-08 | 5.97E-02 | 9.44E-03 | 2.34E-02 | 4.16E-02 | 1.60E+09 | 5.49E-06 | 4.79E+08 | 9.82E-16 | 5.08E-02 | ||
F13 | 30 | mean | 2.75E-08 | 2.38E+00 | 2.85E+00 | 2.43E+00 | 6.98E-01 | 1.16E+05 | 7.57E-05 | 4.21E+07 | 3.95E-13 | 5.93E-01 |
std | 2.71E-08 | 4.50E-01 | 1.05E-01 | 6.50E-01 | 5.98E-01 | 3.17E+05 | 1.08E-04 | 2.27E+07 | 1.06E-12 | 2.48E-01 | ||
500 | mean | 1.53E-06 | 4.98E+01 | 5.02E+01 | 4.99E+01 | 4.94E+01 | 9.31E+09 | 5.16E-04 | 2.61E+09 | 4.03E-13 | 1.97E+01 | |
std | 1.27E-06 | 8.56E-02 | 3.99E-02 | 1.15E-02 | 1.53E-01 | 1.79E+09 | 7.74E-04 | 7.45E+08 | 8.04E-13 | 6.13E+00 | ||
F14 | 2 | mean | 9.98E-01 | 4.33E+00 | 1.06E+01 | 3.59E+00 | 1.36E+00 | 1.60E+00 | 1.13E+00 | 5.56E+00 | 1.03E+00 | 2.93E+00 |
std | 8.75E-16 | 4.03E+00 | 3.07E+00 | 2.70E-00 | 7.59E-01 | 9.23E-01 | 3.44E-01 | 3.45E+00 | 1.81E-01 | 2.91E+00 | ||
F15 | 4 | mean | 3.49E-04 | 4.73E-04 | 2.38E-02 | 1.54E-03 | 7.88E-04 | 1.04E-03 | 3.77E-04 | 8.21E-03 | 4.00E-04 | 7.60E-04 |
std | 1.67E-04 | 3.23E-04 | 3.19E-02 | 3.80E-03 | 3.23E-04 | 3.52E-04 | 1.98E-04 | 5.81E-03 | 1.54E-04 | 5.43E-04 | ||
F16 | 2 | mean | -1.03E+00 | -1.03E+00 | -1.03E+00 | -1.03E+00 | -1.03E+00 | -1.03E+00 | -1.03E+00 | -9.74E-01 | -1.03E+00 | -1.03E+00 |
std | 6.12E-16 | 2.92E-10 | 1.23E-07 | 1.60E-02 | 8.29E-12 | 3.98E-05 | 4.41E-09 | 8.94E-02 | 6.61E-04 | 1.74E-09 | ||
F17 | 2 | mean | 3.98E-01 | 3.98E-01 | 4.11E-01 | 4.87E-01 | 3.98E-01 | 4.00E-01 | 3.98E-01 | 5.38E-01 | 3.99E-01 | 3.98E-01 |
std | 2.65E-10 | 1.51E-07 | 1.11E-02 | 2.08E-01 | 2.53E-02 | 2.73E-03 | 1.87E-05 | 1.78E-01 | 1.23E-03 | 5.08E-05 | ||
F18 | 2 | mean | 3.00E+00 | 3.00E+00 | 1.02E+01 | 4.76E+00 | 3.00E+00 | 3.00E+00 | 3.00E+00 | 4.72E+00 | 3.94E+00 | 3.00E+00 |
std | 1.21E-08 | 5.13E-06 | 1.21E+01 | 3.52E+00 | 3.03E-07 | 1.24E-04 | 1.50E-07 | 2.40E+00 | 9.02E-01 | 8.83E-05 | ||
F19 | 3 | mean | -3.86E+00 | -3.86E+00 | -3.85E+00 | -3.62E+00 | -3.86E+00 | -3.85E+00 | -3.86E+00 | -3.84E+00 | -3.86E+00 | -3.86E+00 |
std | 7.38E-06 | 3.43E-03 | 3.92E-03 | 1.77E-01 | 2.73E-03 | 2.56E-03 | 2.22E-02 | 2.54E-03 | 2.54E-03 | 9.68E-03 | ||
F20 | 6 | mean | -3.27E+00 | -3.16E+00 | -3.04E+00 | -3.25E+00 | -3.21E+00 | -2.88E+00 | -3.06E+00 | -3.01E+00 | -3.27E+00 | -3.22E+00 |
std | 4.58E-02 | 1.87E-01 | 9.09E-02 | 1.12E-01 | 7.66E-02 | 3.25E-01 | 1.47E-01 | 1.18E-01 | 5.99E-02 | 1.14E-01 | ||
F21 | 4 | mean | -1.02E+01 | -5.26E+00 | -3.57E+00 | -5.01E+00 | -7.11E+00 | -2.43E+00 | -5.37E+00 | -2.32E+00 | -1.01E+01 | -6.93E+00 |
std | 8.74E-08 | 1.53E+00 | 1.77E+00 | 4.60E-01 | 2.52E+00 | 1.75E+00 | 1.23E+00 | 1.57E+00 | 1.17E-02 | 2.95E+00 | ||
F22 | 4 | mean | -1.04E+01 | -6.06E+00 | -4.46E+00 | -5.12E+00 | -7.93E+00 | -2.89E+00 | -5.42E+00 | -2.56E+00 | -1.04E+01 | -6.81E+00 |
std | 1.78E-07 | 2.23E+00 | 1.82E+00 | 1.21E+00 | 2.69E+00 | 1.69E+00 | 1.28E+00 | 1.68E+00 | 5.49E-03 | 2.80E+00 | ||
F23 | 4 | mean | -1.05E+01 | -5.99E+00 | -3.91E+00 | -5.24E+00 | -8.32E+00 | -3.87E+00 | -5.12E+00 | -3.00E+01 | -1.05E+01 | -6.62E+00 |
std | 1.11E-07 | 2.08E+00 | 1.75E+00 | 1.07E+00 | 2.77E+00 | 1.65E+00 | 1.12E+00 | 1.51E+00 | 6.27E-03 | 3.43E+00 |
