Table 8 Comparison with other advanced intelligent algorithms in 50-dimensional benchmark test function.
From: Multi-strategy collaborative optimization of gravitational search algorithm
Func-tion | Item | KOA | HHO | SO | ROA | WSO | CSA | JS | SMA | GJO | IMSGSA |
|---|---|---|---|---|---|---|---|---|---|---|---|
F1 | Mean | 1.49e-71 | 0 | 0 | 2.00e-91 | 4.02e-18 | 1.65e-51 | 0 | 0 | 0 | 0 |
Std | 2.84e-71 | 0 | 0 | 1.09e-90 | 6.96e-18 | 1.20e-51 | 0 | 0 | 0 | 0 | |
h | + | = | = | + | + | + | = | = | = | ||
F2 | Mean | 2.11e-38 | 0 | 0 | 1.71e-51 | 1.03e-12 | 3.431 | 5.43e-204 | 0 | 0 | 0 |
Std | 2.88e-38 | 0 | 0 | 9.37e-51 | 7.16e-13 | 1.579 | 0 | 0 | 0 | 0 | |
h | + | = | = | + | + | + | + | = | = | ||
F3 | Mean | 3.92e-06 | 0 | 0 | 3.24e-94 | 0.995 | 0.927 | 4.80e-63 | 0 | 0 | 0 |
Std | 3.25e-06 | 0 | 0 | 1.62e-93 | 0.593 | 0.796 | 2.56e-62 | 0 | 0 | 0 | |
h | + | = | = | + | + | + | + | = | = | ||
F4 | Mean | 0.205 | 0 | 0 | 3.74e-46 | 0.105 | 5.759 | 1.64e-158 | 0 | 2.35e-265 | 0 |
Std | 0.218 | 0 | 0 | 2.05e-45 | 0.080 | 1.556 | 4.68e-158 | 0 | 0 | 0 | |
h | + | = | = | + | + | + | + | = | + | ||
F5 | Mean | 3.68e-05 | 0 | 0 | 7.56e-92 | 1.229 | 1.95e-08 | 2.49e-32 | 0 | 0 | 0 |
Std | 5.57e-05 | 0 | 0 | 3.58e-91 | 0.665 | 5.32e-08 | 6.11e-32 | 0 | 0 | 0 | |
h | + | = | = | + | + | + | + | = | = | ||
F6 | Mean | 6.40e-32 | 2.42e-07 | 9.51e-04 | 1.64e-06 | 0.017 | 0 | 1.31e-23 | 5.96e-05 | 5.539 | 0 |
Std | 6.47e-32 | 3.27e-07 | 0.003 | 2.90e-06 | 0.063 | 0 | 7.19e-23 | 3.01e-05 | 0.635 | 0 | |
h | + | + | + | + | + | = | + | + | + | ||
F7 | Mean | 0.009 | 4.40e-06 | 1.03e-05 | 8.10e-06 | 0.033 | 0.527 | 7.91e-05 | 1.02e-05 | 1.28e-05 | 1.97e-06 |
Std | 0.003 | 4.61e-06 | 7.96e-06 | 1.38e-05 | 0.009 | 0.250 | 2.56e-05 | 6.16e-06 | 9.34e-06 | 1.68e-06 | |
h | + | + | + | + | + | + | + | + | + | ||
F8 | Mean | 0.628 | 2.30e-05 | 0.610 | 4.27e-04 | 61.615 | 58.066 | 0.003 | 0.007 | 47.382 | 1.21e-28 |
Std | 1.434 | 2.36e-05 | 0.840 | 8.94e-04 | 28.201 | 32.776 | 0.011 | 0.008 | 0.957 | 8.02e-29 | |
h | + | + | + | + | + | + | + | + | + | ||
F9 | Mean | 1.508 | 0 | 0 | 0 | 8.88e-06 | 40.263 | 5.607 | 0 | 0 | 0 |
Std | 2.658 | 0 | 0 | 0 | 4.86e-05 | 12.517 | 10.218 | 0 | 0 | 0 | |
h | + | = | = | = | + | + | + | = | = | ||
F10 | Mean | 4.36e-09 | 4.44e-16 | 1.15e-15 | 4.44e-16 | 1.23e-09 | 19.967 | 6.01e-15 | 4.44e-16 | 4.11e-15 | 4.44e-16 |
Std | 2.39e-08 | 0 | 1.45e-15 | 0 | 8.45e-10 | 3.55e-15 | 1.79e-15 | 0 | 6.49e-16 | 0 | |
h | + | = | + | = | + | + | + | = | + | ||
F11 | Mean | 0.007 | 0 | 0.004 | 0 | 0.027 | 0.006 | 0 | 0 | 0 | 0 |
Std | 0.009 | 0 | 0.007 | 0 | 0.037 | 0.008 | 0 | 0 | 0 | 0 | |
h | + | = | = | = | + | + | = | = | = | ||
F12 | Mean | 0.073 | 5.51e-09 | 1.29e-06 | 2.49e-08 | 0.012 | 4.011 | 0.002 | 8.18e-06 | 0.388 | 9.42e-33 |
Std | 0.191 | 7.45e-09 | 5.78e-06 | 4.15e-08 | 0.030 | 1.493 | 0.011 | 1.38e-05 | 0.128 | 2.78e-48 | |
h | + | + | + | + | + | + | + | + | + | ||
F13 | Mean | 0.022 | 1.43e-07 | 0.002 | 1.11e-06 | 0.152 | 4.449 | 0.015 | 2.22e-05 | 3.305 | 1.35e-32 |
Std | 0.054 | 2.31e-07 | 0.004 | 2.04e-06 | 0.142 | 13.021 | 0.029 | 1.51e-05 | 0.317 | 5.57e-48 | |
h | + | + | + | + | + | + | + | + | + | ||
F14 | Mean | -1.98e + 04 | -2.09e + 04 | -2.09e + 04 | -2.09e + 04 | -1.44e + 04 | -1.41e + 04 | -1.33e + 04 | -2.09e + 04 | -6.86e + 03 | 2.08e + 04 |
Std | 690.846 | 0.001 | 0.316 | 3.22e-06 | 929.596 | 3.48e + 03 | 780.584 | 0.001 | 1.82e + 03 | 1.08e + 03 | |
h | + | - | - | - | + | + | + | - | + | ||
F15 | Mean | 0.882 | 0 | 0.070 | 1.99e-114 | 7.853 | 3.492 | 0.100 | 0 | 0.100 | 0 |
Std | 0.304 | 0 | 0.043 | 1.08e-113 | 2.382 | 0.642 | 1.16e-10 | 0 | 2.90e-12 | 0 | |
h | + | = | + | + | + | + | + | = | + | ||
F16 | Mean | 4.21e-15 | 0 | 0.003 | 1.29e-47 | 9.37e-08 | 0.694 | 7.42e-206 | 0 | 0 | 0 |
Std | 2.36e-15 | 0 | 0.005 | 7.09e-47 | 6.26e-08 | 0.924 | 0 | 0 | 0 | 0 | |
h | + | = | + | + | + | + | + | = | = | ||
F17 | Mean | 4.00e-11 | 0 | 0 | 2.32e-26 | 0.023 | 2.288 | 0 | 0 | 0 | 0 |
Std | 8.58e-11 | 0 | 0 | 8.49e-26 | 0.015 | 0.278 | 0 | 0 | 0 | 0 | |
h | + | = | = | + | + | + | = | = | = | ||
F18 | Mean | 1.81e-09 | 0 | 0 | 7.88e-24 | 2.371 | 140.776 | 0 | 0 | 0 | 0 |
Std | 4.48e-09 | 0 | 0 | 3.71e-23 | 2.674 | 13.032 | 0 | 0 | 0 | 0 | |
h | + | = | = | + | + | + | = | = | = | - | |
F19 | Mean | 1.282 | 1.12e-07 | 4.38e-04 | 1.88e-07 | 1.564 | 4.063 | 0.093 | 6.42e-06 | 3.374 | 1.50e-32 |
Std | 0.724 | 2.34e-07 | 9.06e-04 | 2.72e-07 | 0.313 | 1.266 | 0.123 | 9.52e-06 | 0.291 | 1.11e-47 | |
h | + | + | + | + | + | + | + | + | + | ||
F20 | Mean | 5.60e-05 | 0 | 2.38e-04 | 3.05e-109 | 0.003 | 0.143 | 8.47e-17 | 0 | 2.96e-11 | 0 |
Std | 4.26e-05 | 0 | 3.10e-04 | 1.64e-108 | 0.002 | 0.060 | 4.61e-16 | 0 | 1.62e-10 | 0 | |
h | + | = | + | + | + | + | + | = | + | ||
F21 | Mean | 5.25e-29 | 2.77e-05 | 0.067 | 5.01e-04 | 1.56e-09 | 1.308 | 7.65e-15 | 0.002 | 568.831 | 0 |
Std | 4.39e-29 | 3.87e-05 | 0.191 | 9.25e-04 | 3.75e-09 | 1.612 | 4.19e-14 | 0.001 | 81.644 | 0 | |
h | + | + | + | + | + | + | + | + | + | ||
F22 | Mean | 0.117 | 0 | 0 | 0 | 7.16e-11 | 26.859 | 0 | 0 | 0 | 0 |
Std | 0.150 | 0 | 0 | 0 | 7.15e-11 | 3.288 | 0 | 0 | 0 | 0 | |
h | + | = | = | = | + | + | = | = | = | ||
F23 | Mean | 0.018 | 0 | 0.003 | 0 | 0.048 | 0.045 | 0.005 | 0 | 0.003 | 0 |
Std | 0.003 | 0 | 0.001 | 0 | 0.006 | 0.005 | 0.002 | 0 | 7.38e-12 | 0 | |
h | + | = | + | = | + | + | + | = | + | ||
F24 | Mean | 15.591 | 0 | 0 | 0 | 4.051 | 24.032 | 14.755 | 0 | 0 | 0 |
Std | 2.994 | 0 | 0 | 0 | 3.035 | 5.069 | 1.764 | 0 | 0 | 0 | |
h | + | = | = | = | + | + | + | = | = | ||
w/t/l | 24/0/0 | 7/16/1 | 12/11/1 | 17/6/1 | 24/0/0 | 23/1/0 | 19/5/0 | 7/16/1 | 13/11/0 | -/-/- |
