Table 5 Comparison with other GSA improved algorithms in 100 dimensions of benchmark function.
From: Multi-strategy collaborative optimization of gravitational search algorithm
Function | Item | GSA | HGSA | HSSOGSA | LCGSA | MACGSA | GPSOGSA | SCGSA | IMSGSA |
|---|---|---|---|---|---|---|---|---|---|
F1 | Mean | 6.73e-17 | 3.16e-34 | 6.83e-18 | 2.99e-05 | 6.90e-155 | 2.14e-19 | 2.46e-19 | 0 |
Std | 1.34e-17 | 8.64e-34 | 7.49e-19 | 1.33e-05 | 1.73e-154 | 2.53e-20 | 2.05e-19 | 0 | |
h | + | + | + | + | + | + | + | ||
F2 | Mean | 7.15e-08 | 1.61e-16 | 2.11e-08 | 0.035 | 2.33e-92 | 5.57e-09 | 1.85e-09 | 0 |
Std | 6.39e-09 | 9.69e-17 | 1.22e-09 | 0.006 | 9.52e-92 | 4.05e-10 | 3.55e-10 | 0 | |
h | + | + | + | + | + | + | + | ||
F3 | Mean | 191.336 | 1.03e + 03 | 8.50e-08 | 0.012 | 1.60e-149 | 1.15e-13 | 703.195 | 0 |
Std | 58.635 | 207.024 | 2.41e-07 | 0.005 | 8.49e-149 | 2.58e-13 | 194.648 | 0 | |
h | + | + | + | + | + | + | + | ||
F4 | Mean | 1.05e-08 | 2.30e-05 | 10.345 | 0.013 | 1.27e-91 | 0.068 | 1.57e-08 | 0 |
Std | 1.86e-09 | 8.51e-05 | 3.757 | 0.002 | 5.04e-91 | 0.119 | 6.28e-09 | 0 | |
h | + | + | + | + | + | + | + | ||
F5 | Mean | 870.452 | 748.829 | 4.58e-17 | 69.663 | 2.54e-122 | 2.68e-18 | 1.66e + 03 | 0 |
Std | 147.143 | 97.385 | 8.06e-18 | 23.101 | 7.79e-122 | 4.37e-19 | 231.878 | 0 | |
h | + | + | + | + | + | + | + | ||
F6 | Mean | 6.71e-17 | 1.54e-32 | 9.46e-13 | 3.38e-05 | 3.13e-04 | 1.26e-15 | 2.88e-19 | 0 |
Std | 1.21e-17 | 9.30e-33 | 4.75e-12 | 2.39e-05 | 3.72e-05 | 4.24e-15 | 3.14e-19 | 0 | |
h | + | + | + | + | + | + | + | ||
F7 | Mean | 0.068 | 0.160 | 0.027 | 0.272 | 1.43e-06 | 0.027 | 0.042 | 1.76e-06 |
Std | 0.019 | 0.042 | 0.006 | 0.029 | 1.28e-06 | 0.005 | 0.009 | 1.81e-06 | |
h | + | + | + | + | = | + | + | ||
F8 | Mean | 81.958 | 101.753 | 96.123 | 89.885 | 93.542 | 75.907 | 88.249 | 2.44e-28 |
Std | 10.070 | 47.489 | 17.488 | 1.267 | 0.188 | 20.585 | 0.335 | 1.72e-28 | |
h | + | + | + | + | + | + | + | ||
F9 | Mean | 55.817 | 113.823 | 276.996 | 70.183 | 0 | 265.255 | 44.408 | 0 |
Std | 8.293 | 13.847 | 40.924 | 10.068 | 0 | 34.230 | 6.424 | 0 | |
h | + | + | + | + | = | + | + | ||
F10 | Mean | 3.44e-09 | 1.45e-14 | 1.04e-09 | 0.002 | 1.87e-15 | 1.94e-10 | 1.70e-10 | 4.44E-16 |
Std | 3.96e-10 | 2.72e-15 | 4.27e-11 | 6.03e-04 | 1.77e-15 | 1.04e-11 | 5.47e-11 | 0 | |
h | + | + | + | + | + | + | + | ||
F11 | Mean | 0.100 | 3.70e-18 | 0.003 | 0.066 | 0 | 0.003 | 9.04e-04 | 0 |
Std | 0.189 | 2.03e-17 | 0.006 | 0.085 | 0 | 0.006 | 0.003 | 0 | |
h | + | + | + | + | = | + | + | ||
F12 | Mean | 0.002 | 0.001 | 0.093 | 0.056 | 0.007 | 0.029 | 0.003 | 4.71e-33 |
Std | 0.008 | 0.006 | 0.133 | 0.080 | 0.013 | 0.052 | 0.010 | 1.39e-48 | |
h | + | + | + | + | + | + | + | ||
F13 | Mean | 7.08e-18 | 0.003 | 2.79e-14 | 7.36e-04 | 6.13e-05 | 8.25e-16 | 3.66e-04 | 1.35e-32 |
Std | 1.31e-18 | 0.005 | 9.19e-14 | 0.003 | 8.18e-06 | 1.84e-15 | 0.002 | 5.57e-48 | |
h | + | + | + | + | + | + | + | ||
F14 | Mean | -4.97e + 03 | -9.86e + 03 | -2.29e + 04 | -4.93e + 03 | -4.95e + 03 | -2.29e + 04 | -4.90e + 03 | -4.15e + 04 |
Std | 548.950 | 2.75e + 03 | 869.335 | 519.684 | 513.188 | 1.18e + 03 | 438.581 | 2.16e + 03 | |
h | + | + | + | + | + | + | + | ||
F15 | Mean | 1.415 | 2.192 | 5.854 | 0.942 | 5.34e-156 | 6.059 | 1.271 | 0 |
Std | 0.243 | 0.402 | 1.151 | 0.154 | 1.91e-155 | 1.196 | 0.260 | 0 | |
h | + | + | + | + | + | + | + | ||
F16 | Mean | 7.10e-09 | 1.23e-04 | 0.740 | 0.004 | 6.32e-94 | 0.143 | 1.86e-10 | 0 |
Std | 7.65e-10 | 4.89e-04 | 0.221 | 6.37e-04 | 1.74e-93 | 0.127 | 4.96e-11 | 0 | |
h | + | + | + | + | + | + | + | ||
F17 | Mean | 6.38e-04 | 0.092 | 4.448 | 0.529 | 5.02e-49 | 3.553 | 3.77e-04 | 0 |
Std | 8.77e-04 | 0.025 | 0.252 | 0.164 | 1.54e-48 | 0.356 | 3.18e-04 | 0 | |
h | + | + | + | + | + | + | + | ||
F18 | Mean | 4.045 | 8.910 | 644.328 | 221.295 | 9.87e-48 | 572.795 | 0.038 | 0 |
Std | 5.752 | 2.759 | 32.030 | 27.805 | 2.67e-47 | 50.981 | 0.042 | 0 | |
h | + | + | + | + | + | + | + | ||
F19 | Mean | 3.41e-17 | 0.381 | 15.629 | 0.058 | 2.75e-04 | 15.276 | 1.25e-19 | 1.50e-32 |
Std | 4.79e-18 | 0.397 | 7.473 | 0.315 | 4.59e-05 | 8.488 | 1.12e-19 | 1.11e-47 | |
h | + | + | + | + | + | + | + | ||
F20 | Mean | 1.91e-04 | 0.029 | 0.004 | 0.004 | 1.35e-151 | 6.27e-04 | 1.24e-04 | 0 |
Std | 4.08e-05 | 0.007 | 3.63e-04 | 0.001 | 6.28e-151 | 9.43e-05 | 1.93e-05 | 0 | |
h | + | + | + | + | + | + | + | ||
F21 | Mean | 1.29e-14 | 0.007 | 3.89e-10 | 0.007 | 1.522 | 2.30e-11 | 4.60e-17 | 0 |
Std | 3.61e-15 | 0.039 | 1.02e-09 | 0.003 | 1.243 | 6.92e-11 | 4.24e-17 | 0 | |
h | + | + | + | + | + | + | + | ||
F22 | Mean | 9.57e-04 | 1.982 | 26.069 | 5.067 | 0 | 20.673 | 2.28e-05 | 0 |
Std | 8.94e-05 | 1.109 | 4.753 | 0.916 | 0 | 4.043 | 8.56e-06 | 0 | |
h | + | + | + | + | = | + | + | ||
F23 | Mean | 0.077 | 0.078 | 0.177 | 0.074 | 3.70e-17 | 0.066 | 0.093 | 0 |
Std | 0.005 | 0.004 | 0.011 | 0.004 | 8.42e-17 | 0.006 | 0.006 | 0 | |
h | + | + | + | + | + | + | + | ||
F24 | Mean | 22.283 | 35.638 | 44.860 | 20.666 | 0 | 44.215 | 22.564 | 0 |
Std | 2.332 | 2.545 | 3.282 | 1.693 | 0 | 3.358 | 1.772 | 0 | |
h | + | + | + | + | = | + | + | ||
w/t/l | 24/0/0 | 24/0/0 | 24/0/0 | 24/0/0 | 19/5/0 | 24/0/0 | 24/0/0 | -/-/- |
