Table 3 The values of average and average Rank on nine algorithms.
From: Enhancing grasshopper optimization algorithm (GOA) with levy flight for engineering applications
F | Index | AHA | AO | DA | DMOA | GBO | HGS | HHO | LFGOA | MVO |
|---|---|---|---|---|---|---|---|---|---|---|
F1 | Average | 2.65E+00 | 1.46E+02 | 1.36E+03 | 6.97E+02 | 7.83E+07 | 6.45E+02 | 9.34E+02 | 3.06E-09 | 7.17E+02 |
Rank | 2 | 3 | 8 | 5 | 9 | 4 | 7 | 1 | 6 | |
F2 | Average | 3.93E−02 | 5.57E-01 | 9.15E+00 | 4.21E+00 | 3.43E+35 | 9.42E+07 | 1.88E+08 | 9.21E-29 | 6.37E+00 |
Rank | 2 | 3 | 6 | 4 | 9 | 7 | 8 | 1 | 5 | |
F3 | Average | 2.38E+02 | 1.02E+02 | 3.76E+03 | 2.28E+03 | 9.40E+01 | 2.30E+03 | 1.51E+03 | 7.95E-10 | 9.03E+02 |
Rank | 4 | 3 | 9 | 7 | 2 | 8 | 6 | 1 | 5 | |
F4 | Average | 1.41E−01 | 7.46E-01 | 2.77E+01 | 1.63E+01 | 4.17E+06 | 1.57E+00 | 1.61E+00 | 6.59E-06 | 8.98E+00 |
Rank | 2 | 3 | 8 | 7 | 9 | 4 | 5 | 1 | 6 | |
F5 | Average | 7.12E+01 | 8.44E+04 | 1.61E+06 | 4.63E+05 | 2.57E+03 | 2.14E+06 | 2.02E+06 | 4.00E+00 | 8.94E+05 |
Rank | 2 | 4 | 7 | 5 | 3 | 9 | 8 | 1 | 6 | |
F6 | Average | 1.13E+02 | 1.41E+02 | 2.45E+03 | 8.13E+02 | 6.81E+05 | 2.11E+03 | 8.03E+02 | 1.25E+00 | 5.66E+02 |
Rank | 2 | 3 | 8 | 6 | 9 | 7 | 5 | 1 | 4 | |
F7 | Average | 6.74E−02 | 5.60E-02 | 7.09E-01 | 1.53E-01 | 1.03E+01 | 3.38E+00 | 1.48E+00 | 5.55E-01 | 2.46E-01 |
Rank | 2 | 3 | 8 | 6 | 9 | 7 | 5 | 1 | 4 | |
F8 | Average | -5.94E+03 | -2.39E+03 | -2.26E+03 | -7.12E+12 | 5.11E+01 | -1.20E+04 | -1.20E+04 | -1.34E+00 | -2.20E+03 |
Rank | 6 | 5 | 4 | 9 | 2 | 7 | 8 | 1 | 3 | |
F9 | Average | 4.13E+00 | 1.60E+00 | 5.73E+01 | 5.01E+01 | 1.56E+01 | 1.11E+01 | 9.63E+00 | 0.00E+00 | 4.75E+01 |
Rank | 3 | 2 | 9 | 8 | 6 | 5 | 4 | 1 | 7 | |
F10 | Average | 2.90E−01 | 2.77E-01 | 1.09E+01 | 6.54E+00 | 3.24E-01 | 1.15E+00 | 6.42E-01 | 9.81E-09 | 6.25E+00 |
Rank | 3 | 2 | 9 | 8 | 4 | 6 | 5 | 1 | 7 | |
F11 | Average | 2.86E−01 | 1.37E+00 | 2.48E+01 | 7.30E+00 | 4.95E-03 | 5.31E+00 | 5.76E+00 | 1.51E-07 | 7.25E+00 |
Rank | 3 | 4 | 9 | 8 | 2 | 5 | 6 | 1 | 7 | |
F12 | Average | 8.05E−01 | 3.27E+05 | 4.29E+06 | 6.53E+05 | 2.31E+00 | 4.66E+06 | 4.26E+06 | 4.11E+00 | 1.63E+06 |
Rank | 1 | 4 | 8 | 5 | 2 | 9 | 7 | 3 | 6 | |
F13 | Average | 4.41E+00 | 3.38E+05 | 3.73E+06 | 2.33E+06 | 6.65E+01 | 1.21E+07 | 1.00E+07 | 5.02E-01 | 3.40E+06 |
Rank | 2 | 4 | 7 | 5 | 3 | 9 | 8 | 1 | 6 | |
F14 | Average | 1.97E+00 | 3.50E+00 | 1.22E+00 | 1.63E+00 | 4.54E-01 | 1.57E+00 | 2.16E+00 | 2.11E+01 | 1.62E+00 |
Rank | 6 | 8 | 2 | 5 | 1 | 3 | 7 | 9 | 4 | |
F15 | Average | 2.92E−03 | 2.42E-03 | 6.09E-03 | 1.58E-03 | 7.85E-04 | 1.71E-03 | 4.71E-03 | 1.48E-01 | 2.91E-03 |
Rank | 6 | 4 | 8 | 2 | 1 | 3 | 7 | 9 | 5 | |
F16 | Average | -1.03E+00 | -1.01E+00 | -1.00E+00 | -1.03E+00 | -1.03E+00 | -1.03E+00 | -1.02E+00 | -9.94E-04 | -1.01E+00 |
Rank | 6 | 3 | 2 | 7 | 8 | 9 | 5 | 1 | 4 | |
F17 | Average | 4.10E−01 | 5.22E-01 | 4.17E-01 | 4.13E-01 | 4.04E-01 | 4.16E-01 | 4.09E-01 | 5.55E+01 | 4.37E-01 |
Rank | 3 | 8 | 6 | 4 | 1 | 5 | 2 | 9 | 1 | |
F18 | Average | 3.11E+00 | 3.55E+00 | 4.09E+00 | 3.16E+00 | 3.59E+00 | 3.13E+00 | 3.20E+00 | 6.00E+02 | 3.71E+00 |
Rank | 1 | 5 | 8 | 3 | 6 | 2 | 4 | 9 | 7 | |
F19 | Average | -3.86E+00 | -3.75E+00 | -3.85E+00 | -3.86E+00 | -3.86E+00 | -3.86E+00 | -3.83E+00 | -6.81E-02 | -3.84E+00 |
Rank | 6 | 2 | 5 | 7 | 8 | 9 | 3 | 1 | 4 | |
F20 | Average | -3.26E+00 | -2.67E+00 | -3.06E+00 | -3.25E+00 | -3.29E+00 | -3.26E+00 | -2.98E+00 | -5.15E-03 | -3.09E+00 |
Rank | 7 | 2 | 4 | 6 | 9 | 8 | 3 | 1 | 5 | |
F21 | Average | -7.79E+00 | -9.99E+00 | -6.84E+00 | -9.09E+00 | -4.98E+00 | -7.51E+00 | -4.87E+00 | -2.74E-01 | -6.15E+00 |
Rank | 7 | 9 | 5 | 8 | 3 | 6 | 2 | 1 | 4 | |
F22 | Average | -7.96E+00 | -1.03E+01 | -7.43E+00 | -9.24E+00 | -9.94E+00 | -9.18E+00 | -4.93E+00 | -2.94E-01 | -2.42E+00 |
Rank | 5 | 9 | 4 | 7 | 8 | 6 | 3 | 1 | 2 | |
F23 | Average | -8.32E+00 | -1.04E+01 | -7.14E+00 | -8.72E+00 | -4.85E+00 | -9.98E+00 | -4.94E+00 | -3.23E-01 | -6.08E+00 |
Rank | 6 | 9 | 5 | 7 | 2 | 8 | 3 | 1 | 4 | |
Friedmans test | 3.7826 | 4.4348 | 6.4783 | 6.0435 | 5.0435 | 6.3478 | 5.2609 | 2.4783 | 4.8696 | |
