Table 2 Multi-strategy effectiveness testing.
From: Multi-strategy collaborative optimization of gravitational search algorithm
Function | Item | GSA | SSAGSA | LeGSA | GbGSA | LoGSA | IMSGSA |
|---|---|---|---|---|---|---|---|
F1 | Mean | 2.91e-17 | 1.81e-17 | 3.64e-37 | 4.10–40 | 3.37e-243 | 0 |
Std | 6.56e-18 | 3.72e-18 | 8.70e-37 | 1.91e-39 | 0 | 0 | |
Rank | 6 | 5 | 4 | 3 | 2 | 1 | |
F2 | Mean | 2.63e-08 | 1.85e-08 | 2.05e-19 | 7.11e-21 | 2.24e-125 | 0 |
Std | 4.21e-09 | 2.54e-09 | 5.38e-19 | 1.40e-20 | 1.22e-124 | 0 | |
Rank | 6 | 4 | 5 | 3 | 2 | 1 | |
F3 | Mean | 1.85e-16 | 1.55e-16 | 3.04e-15 | 5.14e-17 | 9.02e-241 | 0 |
Std | 6.98e-17 | 7.18e-17 | 3.36e-15 | 9.99e-17 | 0 | 0 | |
Rank | 6 | 4 | 5 | 3 | 2 | 1 | |
F4 | Mean | 3.55e-09 | 3.50e-09 | 1.20e-10 | 3.56e-06 | 3.00e-124 | 0 |
Std | 5.24e-10 | 8.62e-10 | 7.17e-11 | 1.31e-05 | 1.64e-123 | 0 | |
Rank | 6 | 4 | 3 | 5 | 2 | 1 | |
F5 | Mean | 388.648 | 1.70e-16 | 1.61e-18 | 1.04e-17 | 5.25e-235 | 0 |
Std | 125.419 | 4.88e-17 | 1.45e-18 | 1.58e-17 | 0 | 0 | |
Rank | 6 | 5 | 3 | 4 | 2 | 1 | |
F6 | Mean | 3.17e-17 | 1.78e-17 | 5.00e-29 | 0 | 3.11e-17 | 0 |
Std | 8.66e-18 | 3.51e-18 | 1.97e-28 | 0 | 8.33e-18 | 0 | |
Rank | 6 | 4 | 3 | 1 | 5 | 1 | |
F7 | Mean | 0.028 | 2.24e-05 | 0.006 | 3.09e-05 | 3.81e-06 | 4.67e-06 |
Std | 0.006 | 1.78e-05 | 0.002 | 5.26e-05 | 4.95e-06 | 3.60e-06 | |
Rank | 6 | 3 | 5 | 4 | 1 | 2 | |
F8 | Mean | 15.376 | 4.69e-05 | 29.735 | 28.430 | 16.759 | 2.36e-29 |
Std | 0.511 | 1.30e-04 | 23.010 | 0.039 | 0.492 | 4.25e-29 | |
Rank | 3 | 2 | 6 | 5 | 4 | 1 | |
F9 | Mean | 20.828 | 6.44e-07 | 36.084 | 1.990 | 0 | 0 |
Std | 4.659 | 3.45e-06 | 8.630 | 7.573 | 0 | 0 | |
Rank | 5 | 3 | 6 | 4 | 1 | 1 | |
F10 | Mean | 4.26e-09 | 3.25e-09 | 3.57e-14 | 3.04e-14 | 4.44e-16 | 4.44e-16 |
Std | 5.72e-10 | 3.75e-10 | 5.43e-15 | 2.64e-14 | 0 | 0 | |
Rank | 6 | 5 | 4 | 3 | 1 | 1 | |
F11 | Mean | 0.003 | 0 | 0.006 | 0 | 0 | 0 |
Std | 0.006 | 0 | 0.009 | 0 | 0 | 0 | |
Rank | 5 | 1 | 6 | 1 | 1 | 1 | |
F12 | Mean | 2.21e-19 | 1.20e-19 | 0.004 | 3.86e-32 | 2.10e-19 | 1.57e-32 |
Std | 7.03e-20 | 3.40e-20 | 0.019 | 1.25e-31 | 4.51e-20 | 5.57e-48 | |
Rank | 5 | 3 | 6 | 2 | 4 | 1 | |
F13 | Mean | 3.22e-18 | 1.91e-18 | 3.66e-04 | 7.33e-32 | 1.396 | 1.35e-32 |
Std | 6.38e-19 | 5.33e-19 | 0.002 | 2.49e-31 | 0.848 | 5.57e-48 | |
Rank | 4 | 3 | 5 | 2 | 6 | 1 | |
F14 | Mean | -2.61e + 03 | -2.61e + 03 | -6.40e + 03 | -1.17e + 04 | -2.69e + 03 | -1.22e + 04 |
Std | 413.060 | 438.576 | 1.27e + 03 | 1.53e + 03 | 365.770 | 1.08e + 03 | |
Rank | 5 | 6 | 3 | 2 | 4 | 1 | |
F15 | Mean | 0.403 | 1.03e-06 | 0.398 | 0.109 | 6.24e-247 | 0 |
Std | 0.014 | 4.12e-06 | 2.26e-16 | 0.055 | 0 | 0 | |
Rank | 6 | 3 | 5 | 4 | 2 | 1 | |
F16 | Mean | 2.60e-09 | 1.72e-09 | 5.27e-15 | 2.44e-22 | 4.69e-127 | 0 |
Std | 2.87e-10 | 2.30e-10 | 9.38e-15 | 5.91e-22 | 1.84e-126 | 0 | |
Rank | 6 | 5 | 4 | 3 | 2 | 1 | |
F17 | Mean | 0.001 | 0.003 | 0.274 | 0.013 | 6.54e-65 | 0 |
Std | 0.002 | 0.002 | 0.113 | 0.025 | 2.54e-64 | 0 | |
Rank | 3 | 4 | 6 | 5 | 2 | 1 | |
F18 | Mean | 0.020 | 0.054 | 7.490 | 0.236 | 1.23e-61 | 0 |
Std | 0.019 | 0.030 | 2.643 | 0.602 | 4.81e-61 | 0 | |
Rank | 3 | 4 | 6 | 5 | 2 | 1 | |
F19 | Mean | 1.28e-17 | 8.87e-18 | 8.35e-29 | 1.22e-31 | 1.41e-17 | 1.50e-32 |
Std | 3.41e-18 | 2.37e-18 | 2.92e-28 | 5.85e-31 | 4.14e-18 | 1.11e-47 | |
Rank | 5 | 4 | 3 | 2 | 6 | 1 | |
F20 | Mean | 1.37e-05 | 7.57e-06 | 2.54e-04 | 4.18e-17 | 2.21e-157 | 0 |
Std | 5.55e-06 | 6.51e-06 | 3.99e-05 | 1.44e-16 | 1.21e-156 | 0 | |
Rank | 5 | 4 | 6 | 3 | 2 | 1 | |
F21 | Mean | 1.37e-15 | 9.07e-16 | 3.05e-26 | 0.683 | 1.35e-15 | 0 |
Std | 5.38e-16 | 3.73e-16 | 8.82e-26 | 0.846 | 5.15e-16 | 0 | |
Rank | 5 | 3 | 2 | 6 | 4 | 1 | |
F22 | Mean | 3.10e-04 | 2.35e-04 | 1.881 | 1.06e-14 | 0 | 0 |
Std | 3.37e-05 | 3.79e-05 | 1.856 | 1.80e-14 | 0 | 0 | |
Rank | 5 | 4 | 6 | 3 | 1 | 1 | |
F23 | Mean | 0.058 | 4.40e-10 | 0.046 | 0.012 | 0 | 0 |
Std | 0.007 | 1.97e-09 | 0.007 | 0.008 | 0 | 0 | |
Rank | 6 | 3 | 4 | 5 | 1 | 1 | |
F24 | Mean | 9.438 | 0 | 8.078 | 5.237 | 0 | 0 |
Std | 1.335 | 0 | 1.320 | 3.802 | 0 | 0 | |
Rank | 6 | 1 | 5 | 4 | 1 | 1 | |
Count | 0 | 2 | 0 | 2 | 7 | 23 | |
Avg rank | 5.2 | 3.63 | 4.63 | 3.25 | 2.5 | 1.04 | |
Total rank | 6 | 4 | 5 | 3 | 2 | 1 |
