Table 8 The p-Values of the Wilcoxon rank-sum test over 23 benchmark functions.
From: Enhancing grasshopper optimization algorithm (GOA) with levy flight for engineering applications
F | AHA | AO | DA | DMOA | GBO | HGS | HHO | MVO |
|---|---|---|---|---|---|---|---|---|
F1 | 1.33E-29 | 1.12E-30 | 1.10E-03 | 1.36E-04 | 4.92E-04 | 1.66E-27 | 3.81E-29 | 1.07E-02 |
F2 | 9.55E-05 | 2.89E-01 | 1.72E-34 | 2.39E-31 | 3.18E-01 | 1.65E-01 | 5.83E-04 | 5.94E-34 |
F3 | 3.71E-26 | 2.20E-29 | 9.50E-09 | 1.83E-34 | 1.52E-14 | 1.24E-23 | 4.49E-19 | 3.11E-07 |
F4 | 2.00E-30 | 5.28E-31 | 9.68E-01 | 4.04E-11 | 2.07E-34 | 8.90E-30 | 8.74E-27 | 1.83E-01 |
F5 | 5.63E-15 | 1.06E-28 | 6.79E-29 | 2.17E-34 | 4.57E-09 | 8.19E-15 | 6.66E-21 | 5.05E-31 |
F6 | 3.07E-34 | 1.76E-32 | 3.17E-12 | 6.34E-01 | 3.17E-08 | 1.93E-26 | 1.01E-28 | 8.20E-03 |
F7 | 1.14E-02 | 1.30E-03 | 9.41E-35 | 8.51E-35 | 4.41E-23 | 3.21E-31 | 7.59E-30 | 2.60E-34 |
F8 | 7.48E-39 | 1.34E-36 | 7.30E-39 | 8.07E-39 | 8.08E-39 | 7.95E-39 | 8.06E-39 | 4.71E-39 |
F9 | 2.15E-05 | 9.75E-01 | 1.01E-36 | 2.79E-38 | 4.14E-31 | 4.55E-01 | 2.44E-05 | 1.15E-36 |
F10 | 2.62E-23 | 9.46E-27 | 6.68E-09 | 9.96E-18 | 3.73E-11 | 4.66E-23 | 7.46E-24 | 1.71E-28 |
F11 | 1.53E-29 | 7.68E-33 | 9.95E-04 | 1.68E-01 | 2.57E-34 | 7.94E-28 | 3.83E-27 | 2.63E-01 |
F12 | 1.85E-04 | 7.78E-35 | 3.61E-13 | 3.93E-16 | 3.70E-03 | 5.03E-32 | 5.03E-32 | 5.71E-16 |
F13 | 1.76E-34 | 2.18E-33 | 2.72E-13 | 2.11E-23 | 4.80E-09 | 3.18E-24 | 1.97E-27 | 9.16E-15 |
F14 | 1.56E-16 | 2.73E-01 | 1.34E-01 | 1.29E-05 | 5.18E-26 | 4.46E-32 | 8.75E-29 | 2.08E-28 |
F15 | 1.27E-24 | 2.31E-04 | 9.33E-10 | 7.59E-14 | 9.82E-04 | 2.00E-19 | 7.58E-29 | 7.45E-12 |
F16 | 3.80E-19 | 7.14E-33 | 4.09E-27 | 3.11E-29 | 2.82E-33 | 2.05E-30 | 5.70E-28 | 8.30E-08 |
F17 | 5.99E-12 | 6.12E-08 | 9.03E-01 | 1.05E-24 | 1.52E-20 | 9.27E-26 | 2.03E-21 | 7.26E-01 |
F18 | 3.38E-11 | 3.17E-41 | 3.94E-02 | 1.19E-25 | 7.84E-36 | 4.45E-26 | 1.09E-26 | 2.20E-03 |
F19 | 7.38E-39 | 1.21E-40 | 4.98E-39 | 7.74E-39 | 8.06E-39 | 8.09E-39 | 8.10E-39 | 7.54E-39 |
F20 | 1.77E-35 | 5.95E-37 | 1.26E-35 | 1.82E-35 | 1.88E-35 | 1.89E-35 | 1.89E-35 | 1.78E-35 |
F21 | 3.67E-22 | 3.59E-36 | 4.94E-06 | 3.29E-17 | 2.56E-31 | 1.25E-25 | 3.58E-20 | 6.52E-23 |
F22 | 6.72E-26 | 3.38E-38 | 6.45E-16 | 2.06E-29 | 9.21E-25 | 6.63E-34 | 6.22E-26 | 7.86E-16 |
F23 | 1.59E-22 | 2.73E-38 | 1.48E-12 | 8.93E-33 | 9.58E-25 | 6.51E-33 | 2.71E-28 | 4.35E-14 |