Research Article
From Determinism and Probability to Chaos: Chaotic Evolution towards Philosophy and Methodology of Chaotic Optimization
Table 7
Algorithms’ rank without DE by Friedman test for F1–F25 of 10D and 30D, respectively. The abbreviation meanings are in Table
2.
| Function | Logistic | Tent | Gauss | Hénon-rand | Hénon-attrac. |
| | 10-dimensional function | F1 | 3.07 | 4.93 | 2.33 | 2.47 | 2.20 | F2 | 3.17 | 4.87 | 1.73 | 2.73 | 2.50 | F3 | 2.40 | 4.90 | 1.77 | 3.33 | 2.60 | F4 | 3.30 | 4.60 | 2.03 | 2.50 | 2.57 | F5 | 2.63 | 4.83 | 2.83 | 3.00 | 1.70 | F6 | 3.20 | 4.77 | 2.50 | 3.03 | 1.50 | F7 | 3.17 | 4.77 | 1.83 | 3.03 | 2.20 | F8 | 2.33 | 4.73 | 2.57 | 2.97 | 2.40 | F9 | 2.40 | 4.70 | 2.77 | 2.37 | 2.77 | F10 | 3.13 | 4.83 | 2.20 | 2.57 | 2.27 | F11 | 2.90 | 4.73 | 1.53 | 3.97 | 1.87 | F12 | 1.93 | 4.83 | 3.63 | 3.10 | 1.50 | F13 | 3.00 | 4.70 | 1.50 | 4.03 | 1.77 | F14 | 2.67 | 5.00 | 1.73 | 3.27 | 2.33 | F15 | 2.27 | 4.90 | 2.77 | 3.13 | 1.93 | F16 | 2.67 | 4.90 | 2.47 | 3.23 | 1.73 | F17 | 2.73 | 4.87 | 2.33 | 3.30 | 1.77 | F18 | 2.47 | 4.02 | 2.47 | 3.58 | 2.47 | F19 | 2.48 | 4.10 | 2.42 | 3.52 | 2.48 | F20 | 2.50 | 4.03 | 2.43 | 3.53 | 2.50 | F21 | 3.07 | 4.57 | 1.53 | 3.57 | 2.27 | F22 | 3.00 | 4.97 | 2.43 | 2.43 | 2.17 | F23 | 3.17 | 4.67 | 1.97 | 3.07 | 2.13 | F24 | 3.43 | 4.17 | 2.70 | 2.77 | 1.93 | F25 | 2.27 | 2.10 | 3.73 | 4.03 | 2.87 | Ave. | 2.77 | 4.58 | 2.33 | 3.14 | 2.18 |
| | 30-dimensional function | F1 | 3.20 | 4.93 | 1.10 | 3.77 | 2.00 | F2 | 2.87 | 4.97 | 1.20 | 3.83 | 2.13 | F3 | 2.67 | 4.93 | 1.33 | 3.80 | 2.27 | F4 | 2.37 | 4.87 | 1.17 | 3.87 | 2.73 | F5 | 2.07 | 4.90 | 2.33 | 3.67 | 2.03 | F6 | 3.47 | 4.90 | 1.50 | 3.43 | 1.70 | F7 | 2.63 | 4.93 | 1.60 | 3.33 | 2.50 | F8 | 2.73 | 4.80 | 2.70 | 2.17 | 2.60 | F9 | 3.37 | 4.60 | 1.73 | 2.77 | 2.53 | F10 | 3.23 | 4.87 | 2.90 | 1.90 | 2.10 | F11 | 2.70 | 4.67 | 1.50 | 4.33 | 1.80 | F12 | 1.73 | 4.47 | 4.33 | 3.03 | 1.43 | F13 | 3.03 | 4.23 | 1.07 | 4.73 | 1.93 | F14 | 2.50 | 4.77 | 2.23 | 3.87 | 1.63 | F15 | 2.73 | 4.70 | 1.50 | 3.43 | 2.63 | F16 | 2.43 | 4.80 | 2.43 | 3.33 | 2.00 | F17 | 2.43 | 4.77 | 3.03 | 2.80 | 1.97 | F18 | 2.02 | 3.95 | 2.02 | 5.00 | 2.02 | F19 | 2.02 | 3.95 | 2.02 | 5.00 | 2.02 | F20 | 2.02 | 3.95 | 2.02 | 5.00 | 2.02 | F21 | 3.23 | 4.87 | 1.47 | 2.70 | 2.73 | F22 | 2.30 | 4.97 | 2.27 | 2.87 | 2.60 | F23 | 3.27 | 4.63 | 1.40 | 2.83 | 2.87 | F24 | 3.10 | 4.30 | 2.67 | 1.77 | 3.17 | F25 | 2.27 | 1.60 | 4.00 | 5.00 | 2.13 | Ave. | 2.66 | 4.53 | 2.06 | 3.53 | 2.22 |
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