Research Article
Multipopulation Particle Swarm Optimization Algorithm with Neighborhood Learning
Table 6
Results of comparison algorithms on benchmark functions (50 dimensions).
| | | BLPSO | CLPSO | SLPSO | ACPSO | SWPSO-I | SFAPSO | RTPSO | SWNWPSO |
| | f1 | Min | 4.96 E − 76 | 3.59 E + 02 | 5.00 E − 168 | 2.94 E − 08 | 7.66 E − 04 | 0.00 E + 00 | 9.60 E + 00 | 0.00 E + 00 | | Mean | 3.20 E − 75 | 1.51 E + 03 | 8.04 E − 166 | 2.03 E − 07 | 4.89 E − 01 | 0.00 E + 00 | 3.38 E + 02 | 2.90 E − 30 | | Std. | 3.18 E − 75 | 1.42 E + 03 | 0.00 E + 00 | 1.30 E − 07 | 1.25 E + 00 | 0.00 E + 00 | 6.39 E + 02 | 2.41 E − 30 |
| | f2 | Min | 1.00 E + 00 | 1.00 E + 00 | 1.00 E + 00 | 1.00 E + 00 | 1.00 E + 00 | 1.00 E + 00 | 1.00 E + 00 | 1.00 E + 00 | | Mean | 1.00 E + 00 | 1.00 E + 00 | 1.00 E + 00 | 1.00 E + 00 | 1.00 E + 00 | 1.00 E + 00 | 1.00 E + 00 | 1.00 E + 00 | | Std. | 0.00 E + 00 | 7.42 E − 08 | 4.34 E − 16 | 0.00 E + 00 | 2.26 E − 16 | 2.26 E − 16 | 8.21 E − 10 | 0.00 E + 00 |
| | f3 | Min | 0.00 E + 00 | 7.77 E + 00 | 0.00 E + 00 | 3.98 E − 08 | 1.21 E − 04 | 9.07 E − 06 | 9.38 E − 02 | 0.00 E + 00 | | Mean | 0.00 E + 00 | 9.07 E + 00 | 2.47 E − 04 | 9.93 E − 03 | 5.85 E − 03 | 7.46 E − 03 | 9.80 E − 01 | 0.00 E + 00 | | Std. | 0.00 E + 00 | 8.63 E − 01 | 1.35 E − 03 | 1.35 E − 02 | 7.66 E − 03 | 8.06 E − 03 | 5.48 E − 01 | 0.00 E + 00 |
| | f4 | Min | 1.13 E − 138 | 4.67 E − 04 | 0.00 E + 00 | 4.99 E − 45 | 0.00 E + 00 | 0.00 E + 00 | 8.35 E − 17 | 3.08 E − 33 | | Mean | 8.88 E − 131 | 2.22 E − 03 | 0.00 E + 00 | 2.53 E − 39 | 8.14 E − 14 | 0.00 E + 00 | 2.25 E − 08 | 3.08 E − 33 | | Std. | 4.83 E − 130 | 1.50 E − 03 | 0.00 E + 00 | 6.87 E − 39 | 3.43 E − 13 | 0.00 E + 00 | 8.96 E − 08 | 0.00 E + 00 |
| | f5 | Min | 3.99 E − 09 | 4.20 E + 00 | 1.27 E − 08 | 0.00 E + 00 | 0.00 E + 00 | 0.00 E + 00 | 0.00 E + 00 | 0.00 E + 00 | | Mean | 1.01 E − 06 | 5.05 E + 00 | 1.16 E − 06 | 0.00 E + 00 | 1.39 E − 06 | 0.00 E + 00 | 3.36 E − 02 | 0.00 E + 00 | | Std. | 1.24 E − 06 | 4.40 E − 01 | 1.08 E − 06 | 0.00 E + 00 | 3.26 E − 06 | 0.00 E + 00 | 1.08 E − 01 | 0.00 E + 00 |
| | f6 | Min | 5.85 E − 27 | 8.53 E + 02 | 1.62 E − 85 | 9.10 E − 04 | 3.51 E − 01 | 1.71 E − 01 | 3.17 E + 00 | 0.00 E + 00 | | Mean | 1.14 E − 26 | 9.97 E + 02 | 5.22 E − 84 | 3.76 E − 03 | 8.22 E − 01 | 9.52 E − 01 | 6.39 E + 01 | 0.00 E + 00 | | Std. | 3.98 E − 27 | 6.29 E + 01 | 5.06 E − 84 | 1.15 E − 03 | 7.90 E − 01 | 1.59 E + 00 | 6.43 E + 01 | 0.00 E + 00 |
| | f7 | Min | 6.86 E − 03 | 4.76 E + 01 | 1.04 E − 30 | 2.16 E − 01 | 9.00 E − 02 | 5.44 E − 01 | 6.88 E − 01 | 0.00 E + 00 | | Mean | 1.90 E − 02 | 5.41 E + 01 | 2.45 E − 06 | 4.15 E − 01 | 1.77 E − 01 | 2.12 E + 00 | 3.71 E + 00 | 0.00 E + 00 | | Std. | 1.08 E − 02 | 2.91 E + 00 | 1.34 E − 05 | 8.41 E − 02 | 5.35 E − 02 | 1.00 E + 00 | 1.98 E + 00 | 0.00 E + 00 |
| | f8 | Min | 6.23 E − 30 | 1.35 E + 45 | 7.43 E − 84 | 1.50 E − 03 | 3.07 E − 01 | 3.18 E − 01 | 2.43 E + 02 | 0.00 E + 00 | | Mean | 5.52 E − 29 | 2.63 E + 51 | 1.54 E − 82 | 3.45 E − 03 | 1.59 E + 00 | 9.28 E + 01 | 4.10 E + 63 | 0.00 E + 00 | | Std. | 4.43 E − 29 | 5.77 E + 51 | 1.59 E − 82 | 1.71 E − 03 | 2.64 E + 00 | 1.54 E + 02 | 2.25 E + 64 | 0.00 E + 00 |
| | f9 | Min | 2.04 E − 96 | 2.49 E + 07 | 0.00 E + 00 | 2.97 E − 25 | 1.03 E − 14 | 3.97 E − 16 | 3.54 E − 04 | 0.00 E + 00 | | Mean | 1.53 E − 90 | 9.24 E + 07 | 0.00 E + 00 | 2.15 E − 19 | 2.22 E − 10 | 1.68 E − 12 | 3.69 E + 01 | 0.00 E + 00 | | Std. | 3.79 E − 90 | 4.01 E + 07 | 0.00 E + 00 | 5.76 E − 19 | 5.66 E − 10 | 3.82 E − 12 | 1.24 E + 02 | 0.00 E + 00 |
| | f10 | Min | 2.41 E − 81 | 6.50 E + 02 | 0.00 E + 00 | 5.60 E − 08 | 0.00 E + 00 | 0.00 E + 00 | 0.00 E + 00 | 0.00 E + 00 | | Mean | 2.51 E − 10 | 7.66 E + 02 | 0.00 E + 00 | 3.57 E − 07 | 0.00 E + 00 | 0.00 E + 00 | 3.72 E + 02 | 0.00 E + 00 | | Std. | 3.89 E − 10 | 5.71 E + 01 | 0.00 E + 00 | 2.52 E − 07 | 0.00 E + 00 | 0.00 E + 00 | 3.51 E + 02 | 0.00 E + 00 |
| | f11 | Min | 2.66 E − 15 | 1.76 E + 01 | 2.66 E − 15 | 6.90 E − 04 | 3.64 E − 02 | 3.11 E − 02 | 2.11 E + 00 | 8.88 E − 16 | | Mean | 5.98 E − 15 | 1.83 E + 01 | 6.69 E − 15 | 1.72 E − 03 | 1.26 E + 00 | 2.19 E + 00 | 4.75 E + 00 | 8.88 E − 16 | | Std. | 9.01 E − 16 | 3.12 E − 01 | 2.03 E − 15 | 5.13 E − 04 | 8.96 E − 01 | 6.62 E − 01 | 1.65 E + 00 | 0.00 E + 00 |
| | f12 | Min | 3.50 E − 03 | 4.92 E + 01 | 2.11 E − 133 | 8.19 E − 04 | 1.51 E − 02 | 7.09 E − 02 | 1.51 E + 00 | 0.00 E + 00 | | Mean | 4.96 E − 03 | 5.84 E + 01 | 1.28 E − 16 | 4.05 E − 03 | 3.11 E − 02 | 2.46 E − 01 | 1.83 E + 01 | 0.00 E + 00 | | Std. | 5.94 E − 04 | 4.84 E + 00 | 2.01 E − 16 | 2.05 E − 03 | 1.46 E − 02 | 1.24 E − 01 | 1.60 E + 01 | 0.00 E + 00 |
| | f13 | Min | 9.46 E − 03 | 5.22 E − 01 | 9.17 E − 02 | 3.91 E − 03 | 4.14 E − 02 | 2.13 E − 02 | 5.46 E − 01 | 8.00 E − 01 | | Mean | 1.19 E − 02 | 6.44 E − 01 | 1.22 E − 01 | 6.01 E − 03 | 6.27 E − 02 | 7.28 E − 02 | 7.14 E − 01 | 9.97 E − 01 | | Std. | 1.47 E − 03 | 6.95 E − 02 | 2.09 E − 02 | 1.22 E − 03 | 1.14 E − 02 | 2.45 E − 02 | 7.31 E − 02 | 1.19 E − 01 |
| | f14 | Min | 3.76 E − 01 | 9.42 E + 00 | 1.00 E − 01 | 1.02 E − 01 | 1.01 E − 01 | 1.00 E − 01 | 9.64 E + 00 | 0.00 E + 00 | | Mean | 5.12 E − 01 | 1.18 E + 01 | 1.00 E − 01 | 1.77 E − 01 | 1.40 E − 01 | 1.03 E − 01 | 1.50 E + 01 | 0.00 E + 00 | | Std. | 6.70 E − 02 | 8.65 E − 01 | 7.06 E − 17 | 7.01 E − 02 | 1.22 E − 01 | 6.07 E − 03 | 2.19 E + 00 | 0.00 E + 00 |
| | f15 | Min | 4.64 E − 03 | 2.30 E + 01 | 2.08 E − 02 | 2.12 E − 01 | 7.04 E − 03 | 5.77 E − 05 | 1.54 E − 01 | 1.26 E − 06 | | Mean | 7.28 E − 03 | 3.31 E + 01 | 3.32 E − 02 | 6.27 E − 01 | 2.17 E − 02 | 9.77 E − 04 | 5.84 E − 01 | 1.67 E − 04 | | Std. | 1.50 E − 03 | 5.93 E + 00 | 4.35 E − 03 | 2.90 E − 01 | 1.11 E − 02 | 7.33 E − 04 | 5.14 E − 01 | 1.92 E − 04 |
| | f16 | Min | 1.57 E + 01 | 4.08 E + 02 | 1.79 E + 01 | 3.29 E − 01 | 1.31 E + 01 | 2.49 E + 01 | 9.27 E + 01 | 0.00 E + 00 | | Mean | 2.42 E + 01 | 4.53 E + 02 | 2.96 E + 01 | 4.26 E + 00 | 3.07 E + 01 | 4.93 E + 01 | 2.73 E + 02 | 0.00 E + 00 | | Std. | 3.06 E + 00 | 1.79 E + 01 | 6.11 E + 00 | 2.21 E + 00 | 7.33 E + 00 | 1.27 E + 01 | 8.12 E + 01 | 0.00 E + 00 | | f17 | Min | 2.00 E − 01 | 1.59 E + 01 | 5.01 E − 01 | 6.00 E − 01 | 2.00 E − 01 | 5.00 E − 01 | 2.30 E + 00 | 0.00 E + 00 | | Mean | 2.00 E − 01 | 1.88 E + 01 | 6.00 E − 01 | 8.03 E − 01 | 2.83 E − 01 | 9.73 E − 01 | 6.71 E + 00 | 0.00 E + 00 | | Std. | 3.07 E − 08 | 1.18 E + 00 | 5.22 E − 02 | 1.10 E − 01 | 5.92 E − 02 | 2.35 E − 01 | 2.45 E + 00 | 0.00 E + 00 |
| | f18 | Min | 4.40 E − 52 | 7.52 E + 08 | 2.94 E − 219 | 3.16 E − 09 | 4.10 E − 11 | 1.50 E − 05 | 4.62 E − 04 | 0.00 E + 00 | | Mean | 1.36 E − 47 | 3.93 E + 11 | 1.36 E − 207 | 5.77 E − 05 | 6.64 E − 08 | 2.74 E − 01 | 3.18 E − 01 | 0.00 E + 00 | | Std. | 3.55 E − 47 | 5.41 E + 11 | 0.00 E + 00 | 3.03 E − 04 | 1.54 E − 07 | 9.65 E − 01 | 1.47 E + 00 | 0.00 E + 00 |
| | f19 | Min | 1.65 E − 20 | 4.80 E − 12 | 2.72 E − 20 | 1.23 E − 20 | 1.21 E − 20 | 1.24 E − 20 | 8.42 E − 15 | 0.00 E + 00 | | Mean | 1.83 E − 20 | 7.25 E − 11 | 3.34 E − 20 | 1.86 E − 20 | 1.29 E − 20 | 2.06 E − 20 | 2.44 E − 08 | 0.00 E + 00 | | Std. | 1.38 E − 21 | 7.97 E − 11 | 3.46 E − 21 | 4.09 E − 21 | 8.62 E − 22 | 3.07 E − 20 | 7.49 E − 08 | 0.00 E + 00 |
| | f20 | Min | 1.00 E + 00 | 1.00 E + 00 | 1.00 E + 00 | 1.00 E + 00 | 1.00 E + 00 | 1.00 E + 00 | 1.00 E + 00 | 0.00 E + 00 | | Mean | 1.00 E + 00 | 1.00 E + 00 | 1.00 E + 00 | 1.00 E + 00 | 1.00 E + 00 | 1.00 E + 00 | 1.00 E + 00 | 0.00 E + 00 | | Std. | 0.00 E + 00 | 7.14 E − 17 | 0.00 E + 00 | 0.00 E + 00 | 0.00 E + 00 | 0.00 E + 00 | 0.00 E + 00 | 0.00 E + 00 |
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