Table 9 Comparison with other advanced intelligent algorithms in 100-dimensional benchmark test function.
From: Multi-strategy collaborative optimization of gravitational search algorithm
Function | Item | KOA | HHO | SO | ROA | WSO | CSA | JS | SMA | GJO | IMSGSA |
|---|---|---|---|---|---|---|---|---|---|---|---|
F1 | Mean | 3.47e-66 | 0 | 0 | 2.84e-205 | 1.35e-24 | 1.29e-50 | 0 | 0 | 0 | 0 |
Std | 5.84e-66 | 0 | 0 | 0 | 1.44e-24 | 6.49e-51 | 0 | 0 | 0 | 0 | |
h | + | = | = | + | + | + | = | = | = | ||
F2 | Mean | 1.49e-27 | 0 | 0 | 7.43e-101 | 2.23e-16 | 9.060 | 0 | 0 | 0 | 0 |
Std | 7.68e-27 | 0 | 0 | 2.52e-100 | 1.25e-16 | 2.061 | 0 | 0 | 0 | 0 | |
h | + | = | = | + | + | + | = | = | = | ||
F3 | Mean | 0.129 | 0 | 0 | 1.29e-189 | 1.648 | 165.566 | 7.23e-72 | 0 | 0 | 0 |
Std | 0.104 | 0 | 0 | 0 | 0.987 | 75.725 | 3.95e-71 | 0 | 0 | 0 | |
h | + | = | = | + | + | + | + | = | = | ||
F4 | Mean | 4.723 | 0 | 0 | 3.44e-99 | 0.011 | 12.753 | 1.33e-303 | 0 | 1.14e-187 | 0 |
Std | 1.396 | 0 | 0 | 1.88e-98 | 0.005 | 1.455 | 0 | 0 | 0 | 0 | |
h | + | = | = | + | + | + | + | = | + | ||
F5 | Mean | 14.657 | 0 | 0 | 9.51e-164 | 2.084 | 2.030 | 6.30e-24 | 0 | 0 | 0 |
Std | 11.267 | 0 | 0 | 0 | 1.106 | 2.303 | 1.95e-23 | 0 | 0 | 0 | |
h | + | = | = | + | + | + | + | = | = | ||
F6 | Mean | 2.35e-30 | 1.01e-07 | 0.028 | 5.01e-07 | 0.354 | 0 | 9.14e-10 | 1.79e-04 | 15.872 | 0 |
Std | 8.40e-31 | 1.62e-07 | 0.074 | 6.78e-07 | 0.355 | 0 | 5.01e-09 | 1.34e-04 | 0.971 | 0 | |
h | + | + | + | + | + | = | + | + | + | ||
F7 | Mean | 0.021 | 2.58e-06 | 4.32e-06 | 2.65e-06 | 0.041 | 0.645 | 4.91e-05 | 6.23e-06 | 7.32e-06 | 1. 76e-06 |
Std | 0.008 | 1.83e-06 | 3.33e-06 | 2.83e-06 | 0.009 | 0.268 | 1.45e-05 | 4.89e-06 | 5.00e-06 | 1.81e-06 | |
h | + | + | + | + | + | + | + | + | + | ||
F8 | Mean | 40.228 | 5.93e-06 | 0.266 | 2.69e-04 | 113.861 | 104.034 | 0.002 | 0.011 | 98.038 | 2.44e-28 |
Std | 34.330 | 8.70e-06 | 0.594 | 7.91e-04 | 32.146 | 20.968 | 0.007 | 0.015 | 0.688 | 1.72e-28 | |
h | + | + | + | + | + | + | + | + | + | ||
F9 | Mean | 0.796 | 0 | 0 | 0 | 1.04e-12 | 83.112 | 0 | 0 | 0 | 0 |
Std | 2.721 | 0 | 0 | 0 | 4.16e-13 | 23.594 | 0 | 0 | 0 | 0 | |
h | + | = | = | = | + | + | = | = | = | ||
F10 | Mean | 0.7530 | 4.44e-16 | 2.58e-15 | 4.44e-16 | 2.08e-12 | 19.967 | 7.31e-15 | 4.44e-16 | 5.42e-15 | 4.44E-16 |
Std | 3.6479 | 0 | 1.77e-15 | 0 | 1.47e-12 | 1.11e-14 | 9.01e-16 | 0 | 1.77e-15 | 0 | |
h | + | = | + | = | + | + | + | = | + | ||
F11 | Mean | 0.011 | 0 | 0.006 | 0 | 0.013 | 0.002 | 0 | 0 | 0 | 0 |
Std | 0.034 | 0 | 0.015 | 0 | 0.020 | 0.005 | 0 | 0 | 0 | 0 | |
h | + | = | = | = | + | + | = | = | = | ||
F12 | Mean | 0.022 | 6.05e-10 | 1.52e-05 | 4.51e-09 | 0.012 | 4.861 | 3.76e-16 | 1.35e-06 | 0.597 | 4.71e-33 |
Std | 0.035 | 8.41e-10 | 2.29e-05 | 7.88e-09 | 0.015 | 0.796 | 1.91e-15 | 3.17e-06 | 0.092 | 1.39e-48 | |
h | + | + | + | + | + | + | + | + | + | ||
F13 | Mean | 0.057 | 2.87e-08 | 0.001 | 4.33e-07 | 0.787 | 135.891 | 0.023 | 4.41e-05 | 8.322 | 1.35e-32 |
Std | 0.176 | 3.57e-08 | 0.002 | 5.56e-07 | 0.295 | 34.321 | 0.029 | 4.12e-05 | 0.256 | 5.57e-48 | |
h | + | + | + | + | + | + | + | + | + | ||
F14 | Mean | -3.61e + 04 | -4.19e + 04 | -4.19e + 04 | -4.19e + 04 | -2.86e + 04 | -3.15e + 04 | -2.51e + 04 | -4.19e + 04 | -9.68e + 03 | -4.15e + 04 |
Std | 1.77e + 03 | 2.136e-04 | 0.129 | 6.50e-06 | 1.53e + 03 | 6.65e + 03 | 1.59e + 03 | 0.003 | 3.64e + 03 | 2.16e + 03 | |
h | + | - | - | - | + | + | + | - | + | ||
F15 | Mean | 2.033 | 0 | 0.074 | 2.63e-182 | 15.070 | 9.710 | 0.269 | 0 | 0.100 | 0 |
Std | 0.813 | 0 | 0.042 | 0 | 2.504 | 0.991 | 0.150 | 0 | 3.09e-13 | 0 | |
h | + | = | + | + | + | + | + | = | + | ||
F16 | Mean | 5.84e-04 | 0 | 0 | 1.43e-95 | 1.13e-06 | 3.600 | 0 | 0 | 0 | 0 |
Std | 0.003 | 0 | 0 | 7.86e-95 | 6.81e-07 | 2.189 | 0 | 0 | 0 | 0 | |
h | + | = | = | + | + | + | = | = | = | ||
F17 | Mean | 2.18e-09 | 0 | 0 | 1.20e-44 | 0.081 | 2.636 | 0 | 0 | 0 | 0 |
Std | 6.23e-09 | 0 | 0 | 6.55e-44 | 0.053 | 0.202 | 0 | 0 | 0 | 0 | |
h | + | = | = | + | + | + | = | = | = | ||
F18 | Mean | 6.57e-08 | 0 | 0 | 1.93e-46 | 18.917 | 336.366 | 0 | 0 | 0 | 0 |
Std | 1.37e-07 | 0 | 0 | 7.14e-46 | 9.484 | 17.805 | 0 | 0 | 0 | 0 | |
h | + | = | = | + | + | + | = | = | = | ||
F19 | Mean | 3.932 | 2.87e-08 | 2.37e-04 | 1.37e-07 | 3.707 | 7.305 | 0.015 | 8.98e-06 | 7.727 | 1.50e-32 |
Std | 1.580 | 3.34e-08 | 3.53e-04 | 1.95e-07 | 0.480 | 2.487 | 0.041 | 1.23e-05 | 0.296 | 1.11e-47 | |
h | + | + | + | + | + | + | + | + | + | ||
F20 | Mean | 2.34e-04 | 0 | 6.48e-05 | 1.04e-195 | 0.004 | 0.569 | 8.24e-222 | 0 | 4.83e-50 | 0 |
Std | 1.18e-04 | 0 | 2.51e-04 | 0 | 0.002 | 0.166 | 0 | 0 | 2.65e-49 | 0 | |
h | + | = | + | + | + | + | + | = | + | ||
F21 | Mean | 1.94e-27 | 1.77e-05 | 0.128 | 3.35e-04 | 3.705 | 2.020 | 7.45e-10 | 0.002 | 3.13e + 03 | 0 |
Std | 1.14e-27 | 2.34e-05 | 0.274 | 5.47e-04 | 13.086 | 1.902 | 3.29e-09 | 0.002 | 254.636 | 0 | |
h | + | + | + | + | + | + | + | + | + | ||
F22 | Mean | 0.331 | 0 | 0 | 0 | 1.45e-13 | 64.288 | 0 | 0 | 0 | 0 |
Std | 0.289 | 0 | 0 | 0 | 6.90e-14 | 5.185 | 0 | 0 | 0 | 0 | |
h | + | = | = | = | + | + | = | = | = | ||
F23 | Mean | 0.038 | 0 | 0.003 | 0 | 0.078 | 0.075 | 0.006 | 0 | 0.003 | 0 |
Std | 0.007 | 0 | 0.001 | 0 | 0.006 | 0.007 | 5.39e-10 | 0 | 2.26e-13 | 0 | |
h | + | = | + | = | + | + | + | = | + | ||
F24 | Mean | 49.410 | 0 | 0 | 0 | 10.819 | 51.558 | 35.543 | 0 | 0 | 0 |
Std | 4.381 | 0 | 0 | 0 | 5.651 | 10.508 | 3.972 | 0 | 0 | 0 | |
h | + | = | = | = | + | + | + | = | = | ||
w/t/l | 24/0/0 | 7/16/1 | 10/13/1 | 17/6/1 | 24/0/0 | 23/1/0 | 16/8/0 | 7/16/1 | 13/11/0 | -/-/- |
