Research Article
An Effective Hybrid Firefly Algorithm with Harmony Search for Global Numerical Optimization
Table 2
Mean normalized optimization results.
| | | ACO | BBO | DE | ES | FA | GA | HS | HSFA | PSO | SGA |
| | F01 | 1.01 | 1.01 | 1.00 | 1.02 | 1.08 | 1.04 | 1.07 | 1.00 | 1.01 | 1.25 | | F02 | 1.43 | 2.71 | 1.00 | 2.55 | 1.00 | 1.39 | 16.66 | 1.00 | 3.13 | 1.22 | | F03 | 1.25 | 1.84 | 1.00 | 2.28 | 1.00 | 1.17 | 11.77 | 1.01 | 3.50 | 1.26 | | F04 | | | 49.66 | | 1.00 | | | | | | | F05 | 1.01 | 1.02 | 1.00 | 1.11 | 1.00 | 1.01 | 1.15 | 1.00 | 1.05 | 1.19 | | F06 | 1.03 | 1.02 | 1.00 | 1.09 | 1.00 | 1.02 | 1.03 | 1.00 | 1.03 | 3.01 | | F07 | 2.40 | 2.48 | 2.27 | 2.35 | 2.23 | 1.83 | 1.88 | 1.00 | 1.71 | 2.99 | | F08 | 1.72 | 1.72 | 1.72 | 1.72 | 1.72 | 1.72 | 1.72 | 1.72 | 1.72 | 1.00 | | F09 | 1.03 | 1.01 | 1.00 | 2.05 | 17.29 | 1.00 | 6.55 | 1.00 | 1.04 | 1.24 | | F10 | 2.40 | 2.40 | 2.40 | 3.06 | 2.40 | 2.40 | 3.09 | 2.40 | 2.70 | 1.00 | | F11 | 1.00 | 1.00 | 1.00 | 1.03 | 1.00 | 1.00 | 1.03 | 1.00 | 1.02 | 1.25 | | F12 | 1.00 | 1.00 | 1.00 | 1.01 | 1.00 | 1.00 | 1.02 | 1.00 | 1.00 | 1.14 | | F13 | 4.32 | 2.56 | 3.68 | 5.56 | 1.39 | 4.98 | 5.70 | 1.00 | 4.83 | 2.63 | | F14 | 36.17 | 7.98 | 43.16 | 73.74 | 11.68 | 33.13 | 70.32 | 1.00 | 53.62 | 8.48 | | F15 | 570.98 | 14.02 | 27.90 | | 141.86 | 99.02 | 652.65 | 1.00 | 485.92 | 12.10 | | F16 | | 75.20 | 317.08 | | 7.35 | 942.08 | | 1.00 | | 26.84 | | F17 | 21.98 | 2.35 | 7.67 | 21.63 | 5.30 | 7.33 | 19.01 | 1.00 | 15.46 | 2.26 | | F18 | 8.49 | 5.40 | 14.18 | 66.70 | 2.31 | 28.49 | 139.02 | 1.00 | 52.77 | 5.69 | | F19 | | 167.15 | 544.18 | | 25.71 | | | 1.00 | | 39.88 | | F20 | 93.79 | 13.59 | 68.16 | 276.60 | 20.05 | 92.42 | 282.65 | 1.00 | 173.17 | 9.33 | | F21 | 3.20 | 2.49 | 1.74 | 1.00 | 3.69 | 2.65 | 3.88 | 1.78 | 2.55 | 2.42 | | F22 | | | | | 6.64 | | | | | 9.81 | | F23 | | | | | 7.36 | | | | | | | F24 | 112.59 | 8.00 | 48.08 | 188.98 | 1.04 | 25.76 | 133.99 | 1.00 | 52.91 | 2.92 | | F25 | | 103.34 | 637.38 | | 17.91 | | | 1.00 | | 62.77 | | F26 | 24.37 | 4.58 | 21.06 | 32.51 | 7.75 | 20.84 | 29.89 | 1.00 | 23.03 | 7.29 | | F27 | 37.23 | 2.38 | 5.34 | 49.70 | 1.00 | 10.38 | 34.12 | 1.04 | 12.06 | 2.00 | | F28 | 37.76 | 18.45 | 73.51 | 92.92 | 93.82 | 31.93 | 109.20 | 1.00 | 112.28 | 21.21 | | F29 | 4.79 | 2.52 | 6.72 | 7.41 | 1.00 | 5.40 | 7.13 | 1.93 | 4.81 | 4.31 | | F30 | 42.08 | 6.33 | 16.76 | 63.65 | 9.36 | 30.16 | 53.57 | 1.00 | 35.27 | 8.32 | | F31 | 2.98 | 3.13 | 3.87 | 4.56 | 1.00 | 3.93 | 4.78 | 1.15 | 3.97 | 2.79 | | F32 | 205.80 | 13.56 | 37.41 | 382.80 | 1.87 | 131.27 | 361.49 | 1.00 | 151.62 | 14.65 | | F33 | 40.44 | 20.26 | 53.05 | 312.01 | 5.14 | 111.20 | 471.25 | 1.00 | 194.10 | 15.72 | | F34 | 274.21 | 27.02 | 46.57 | 546.26 | 6.17 | 138.85 | 550.25 | 1.00 | 188.96 | 25.75 | | F35 | | 1.46 | 3.32 | 3.57 | 1.18 | 3.12 | 3.34 | 1.00 | 3.12 | 2.64 | | F36 | 9.82 | 5.26 | 14.12 | 29.95 | 10.67 | 16.90 | 35.57 | 1.00 | 23.95 | 5.37 |
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The bold data are the best function value among different methods for the specified function.
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