Table 4 Comparison with other GSA improved algorithms in 50 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 | 2.17e-17 | 2.97e-37 | 1.59e-18 | 5.10e-06 | 3.19e-105 | 4.41e-20 | 2.28e-20 | 0 |
Std | 4.31e-18 | 2.06e-37 | 1.72e-19 | 2.42e-06 | 1.73e-104 | 5.49e-21 | 1.69e-20 | 0 | |
h | + | + | + | + | + | + | + | ||
F2 | Mean | 2.90e-08 | 1.26e-17 | 7.00e-09 | 0.0127 | 3.71e-55 | 1.70e-09 | 4.34e-10 | 0 |
Std | 3.55e-09 | 7.77e-18 | 5.78e-10 | 0.0045 | 7.11e-55 | 1.28e-10 | 1.33e-10 | 0 | |
h | + | + | + | + | + | + | + | ||
F3 | Mean | 5.976 | 19.848 | 3.20e-17 | 4.60e-04 | 1.32e-104 | 1.53e-18 | 50.629 | 0 |
Std | 3.023 | 7.736 | 6.42e-18 | 1.83e-04 | 6.46e-104 | 4.65e-19 | 26.097 | 0 | |
h | + | + | + | + | + | + | + | ||
F4 | Mean | 3.00e-09 | 2.47e-17 | 0.018 | 0.004 | 5.43e-54 | 1.13e-10 | 8.37e-10 | 0 |
Std | 4.14e-10 | 6.33e-18 | 0.097 | 7.23e-04 | 1.56e-53 | 1.28e-11 | 2.09e-10 | 0 | |
h | + | + | + | + | + | + | + | ||
F5 | Mean | 483.347 | 228.571 | 6.52e-18 | 7.05e-04 | 1.76e-81 | 2.55e-19 | 803.020 | 0 |
Std | 79.069 | 42.335 | 1.06e-18 | 7.23e-04 | 7.72e-81 | 5.05e-20 | 106.004 | 0 | |
h | + | + | + | + | + | + | + | ||
F6 | Mean | 2.22e-17 | 1.23e-33 | 5.74e-15 | 6.19e-06 | 3.53e-05 | 9.34e-16 | 2.38e-20 | 0 |
Std | 5.56e-18 | 1.74e-33 | 1.91e-14 | 4.27e-06 | 5.57e-06 | 2.59e-15 | 2.60e-20 | 0 | |
h | + | + | + | + | + | + | + | ||
F7 | Mean | 0.025 | 0.042 | 0.012 | 0.078 | 2.56e-06 | 0.013 | 0.015 | 1.97e-06 |
Std | 0.006 | 0.010 | 0.003 | 0.014 | 2.17e-06 | 0.004 | 0.004 | 1.68e-06 | |
h | + | + | + | + | + | + | + | ||
F8 | Mean | 36.2216 | 42.4815 | 54.1770 | 40.0788 | 43.5437 | 24.9404 | 40.4356 | 1.21e-28 |
Std | 0.3384 | 0.2338 | 27.9076 | 0.9242 | 0.1905 | 24.6476 | 0.2018 | 8.02e-29 | |
h | + | + | + | + | + | + | + | ||
F9 | Mean | 25.173 | 45.072 | 122.745 | 31.475 | 0 | 125.298 | 21.060 | 0 |
Std | 4.609 | 10.566 | 19.617 | 6.246 | 0 | 19.086 | 4.586 | 0 | |
h | + | + | + | + | = | + | + | ||
F10 | Mean | 2.68e-09 | 7.31e-15 | 7.02e-10 | 0.001 | 1.87e-15 | 1.31e-10 | 8.82e-11 | 4.44e-16 |
Std | 2.87e-10 | 9.01e-16 | 5.34e-11 | 2.65e-04 | 1.77e-15 | 1.07e-11 | 5.39e-11 | 0 | |
h | + | + | + | + | + | + | + | ||
F11 | Mean | 4.93e-04 | 0 | 0.005 | 0.029 | 0 | 0.010 | 3.29e-04 | 0 |
Std | 0.003 | 0 | 0.008 | 0.038 | 0 | 0.012 | 0.002 | 0 | |
h | + | = | + | + | = | + | + | ||
F12 | Mean | 0.003 | 9.46e-33 | 0.073 | 0.129 | 0.008 | 0.025 | 8.52e-23 | 9.42e-33 |
Std | 0.013 | 6.37e-35 | 0.127 | 0.179 | 0.027 | 0.067 | 9.23e-23 | 2.78e-48 | |
h | + | + | + | + | + | + | + | ||
F13 | Mean | 2.09e-18 | 7.32e-04 | 2.09e-14 | 3.67e-04 | 8.61e-06 | 3.46e-17 | 1.91e-21 | 1.35e-32 |
Std | 5.21e-19 | 0.003 | 9.76e-14 | 0.002 | 1.10e-06 | 9.02e-17 | 2.34e-21 | 5.57e-48 | |
h | + | + | + | + | + | + | + | ||
F14 | Mean | -3.75e + 03 | -6.90e + 03 | -1.21e + 04 | -3.69e + 03 | -3.69e + 03 | -1.21e + 04 | -3.58e + 03 | 2.08e + 04 |
Std | 446.779 | 993.467 | 881.243 | 423.605 | 494.487 | 951.148 | 506.087 | 1.08e + 03 | |
h | + | + | + | + | + | + | + | ||
F15 | Mean | 0.557 | 0.862 | 2.016 | 0.398 | 3.64e-106 | 2.381 | 0.503 | 0 |
Std | 0.178 | 0.126 | 0.495 | 4.93e-06 | 1.96e-105 | 0.487 | 0.145 | 0 | |
h | + | + | + | + | + | + | + | ||
F16 | Mean | 2.92e-09 | 1.37e-16 | 0.173 | 0.001 | 7.48e-55 | 0.029 | 4.31e-11 | 0 |
Std | 4.16e-10 | 2.31e-16 | 0.092 | 3.95e-04 | 2.70e-54 | 0.030 | 1.19e-11 | 0 | |
h | + | + | + | + | + | + | + | ||
F17 | Mean | 4.06e-04 | 0.007 | 3.833 | 0.313 | 1.30e-29 | 2.714 | 4.20e-04 | 0 |
Std | 3.93e-04 | 0.005 | 0.550 | 0.170 | 2.47e-29 | 0.581 | 3.13e-04 | 0 | |
h | + | + | + | + | + | + | + | ||
F18 | Mean | 0.016 | 0.357 | 287.654 | 94.918 | 4.51e-28 | 244.953 | 0.014 | 0 |
Std | 0.015 | 0.447 | 26.952 | 20.775 | 5.39e-28 | 35.463 | 0.014 | 0 | |
h | + | + | + | + | + | + | + | - | |
F19 | Mean | 9.72e-18 | 0.018 | 2.222 | 2.66e-06 | 3.41e-05 | 1.312 | 7.26e-21 | 1.50e-32 |
Std | 2.44e-18 | 0.084 | 2.550 | 1.44e-06 | 5.76e-06 | 1.384 | 5.11e-21 | 1.11e-47 | |
h | + | + | + | + | + | + | + | ||
F20 | Mean | 5.72e-05 | 8.38e-04 | 0.001 | 9.63e-04 | 1.08e-105 | 9.86e-05 | 5.64e-05 | 0 |
Std | 1.64e-05 | 2.47e-04 | 1.87e-04 | 3.66e-04 | 5.30e-105 | 1.90e-05 | 1.85e-05 | 0 | |
h | + | + | + | + | + | + | + | ||
F21 | Mean | 1.95e-15 | 2.97e-31 | 7.72e-12 | 6.78e-04 | 0.161 | 2.04e-10 | 1.21e-18 | 0 |
Std | 7.39e-16 | 9.25e-31 | 2.92e-11 | 4.56e-04 | 0.136 | 9.36e-10 | 1.51e-18 | 0 | |
h | + | + | + | + | + | + | + | ||
F22 | Mean | 4.15e-04 | 0 | 7.152 | 1.873 | 0 | 5.537 | 5.18e-06 | 0 |
Std | 5.76e-05 | 0 | 3.361 | 0.355 | 0 | 2.727 | 2.89e-06 | 0 | |
h | + | = | + | + | = | + | + | ||
F23 | Mean | 0.057 | 0.056 | 0.138 | 0.052 | 2.96e-17 | 0.039 | 0.073 | 0 |
Std | 0.006 | 0.005 | 0.016 | 0.004 | 7.68e-17 | 0.005 | 0.006 | 0 | |
h | + | + | + | + | + | + | + | ||
F24 | Mean | 12.489 | 17.836 | 20.229 | 11.837 | 0 | 19.101 | 13.592 | 0 |
Std | 1.171 | 1.962 | 2.559 | 0.936 | 0 | 2.062 | 1.425 | 0 | |
h | + | + | + | + | = | + | + | ||
w/t/l | 24/0/0 | 22/2/0 | 24/0/0 | 24/0/0 | 20/4/0 | 24/0/0 | 24/0/0 | -/-/- |
