Research Article
Nonlinear Inertia Weighted Teaching-Learning-Based Optimization for Solving Global Optimization Problem
Table 2
Performance comparisons of PSO, ABC, DE, TLBO, and NIWTLBO in terms of fitness value. Population size: 40;
: 30 (except
~
:
); max. eval.: 80,000FEs.
| Number | Function | | | PSO | ABC | DE | TLBO | NIWTLBO |
| | Sphere | 0 | Mean | 8.99E − 12 | 9.91E − 16 | 7.15E − 27 | 1.85E − 286 | 0 | Std. | 5.92E − 12 | 5.36E − 16 | 1.06E − 26 | 0 | 0 |
| | SumSquares | 0 | Mean | 1.11E − 10 | 7.81E − 16 | 9.06E − 26 | 1.57E − 286 | 0 | Std. | 2.49E − 10 | 1.32E − 16 | 3.07E − 26 | 0 | 0 |
| | Tablet | 0 | Mean | 3.68E − 08 | 9.54E − 16 | 2.40E − 26 | 7.66E − 285 | 0 | Std. | 1.64E − 08 | 1.78E − 16 | 1.87E − 26 | 0 | 0 |
| | Quartic | 0 | Mean | 5.84E − 02 | 1.52E − 01 | 4.03E − 01 | 2.07E − 02 | 2.03E − 02 | Std. | 3.83E − 02 | 4.18E − 02 | 1.29E − 01 | 5.26E − 02 | 3.52E − 02 |
| | Schwefel 1.2 | 0 | Mean | 2.47E + 05 | 8.82E + 03 | 2.21E + 04 | 1.52E − 84 | 0 | Std. | 1.48E + 05 | 1.28E + 03 | 5.21E + 03 | 2.97E − 84 | 0 |
| | Schwefel 2.22 | 0 | Mean | 5.16E − 03 | 2.01E − 14 | 4.31E − 16 | 1.79E − 143 |
4.45E – 323 | Std. | 6.94E − 03 | 1.08E − 14 | 1.04E − 16 | 1.21E − 143 | 0 |
| | Schwefel 2.21 | 0 | Mean | 1.21E + 00 | 5.49E + 01 | 1.21E − 02 | 8.31E − 120 | 2.40E − 315 | Std. | 6.02E − 01 | 1.38E + 01 | 2.81E − 03 | 4.05E − 120 | 0 |
| | Zakharov | 0 | Mean | 1.62E + 02 | 2.59E + 02 | 5.84E + 01 | 5.95E − 51 | 1.06E − 319 | Std. | 6.33E + 01 | 2.84E + 01 | 7.01E + 00 | 5.22E − 51 | 0 |
| | Rosenbrock | 0 | Mean | 3.01E + 01 | 1.04E + 01 | 2.43E + 01 | 1.29E + 01 | 1.83E + 01 | Std. | 2.57E + 01 | 2.57E + 00 | 4.61E + 00 | 5.28E + 00 | 6.91E + 00 |
| | Schaffer | −1 | Mean | −1 | −1 | −1 | −1 | −1 | Std. | 0 | 0 | 0 | 0 | 0 |
| | Dropwave | −1 | Mean | −1 | −1 | −1 | −1 | −1 | Std. | 0 | 0 | 0 | 0 | 0 |
| | Bohachevsky1 | 0 | Mean | 0 | 0 | 0 | 0 | 0 | Std. | 0 | 0 | 0 | 0 | 0 |
| | Bohachevsky2 | 0 | Mean | 0 | 0 | 0 | 0 | 0 | Std. | 0 | 0 | 0 | 0 | 0 |
| | Bohachevsky3 | 0 | Mean | 0 | 8.46E − 16 | 0 | 0 | 0 | Std. | 0 | 2.95E − 16 | 0 | 0 | 0 |
| | Six-Hump Camel Back | −1.03163 | Mean | −1.03163 | −1.03163 | −1.03163 | −1.03163 | −1.03163 | Std. | 0 | 0 | 0 | 0 | 0 |
| | Branin | 0.398 | Mean | 0.3979 | 0.3979 | 0.3979 | 0.3979 | 0.3979 | Std. | 0 | 0 | 0 | 0 | 0 |
| | Goldstein-Price | 3 | Mean | 3 | 3 | 3 | 3 | 3 | Std. | 8.11E − 15 | 4.32E − 15 | 1.36E − 15 | 6.78E − 16 | 6.56E − 16 |
| | Ackley | 0 | Mean | 1.18E + 00 | 2.82E − 13 | 2.49E − 14 | 4.44E − 15 | 8.66E − 16 | Std. | 3.85E − 01 | 3.06E − 14 | 6.07E − 15 | 0 | 0 |
| | Rastrigin | 0 | Mean | 1.08E + 02 | 1.29E − 13 | 9.33E + 01 | 6.93E + 00 | 0 | Std. | 2.80E + 01 | 2.57E − 13 | 9.43E + 00 | 5.92E + 00 | 0 |
| | Griewank | 0 | Mean | 6.77E − 03 | 7.10E − 03 | 0 | 0 | 0 | Std. | 9.29E − 03 | 9.56E − 03 | 0 | 0 | 0 |
| | Schwefel 2.26 | −837.9658 | Mean | −8789.43 | −12561.79 | −11312.51 | −9178.59 | −8324.302 | Std. | 4.63E + 02 | 1.96E + 02 | 1.58E + 03 | 7.97E + 02 | 1.71E + 02 |
| | Multimod | 0 | Mean | 8.69E − 67 | 8.52E − 19 | 4.66E − 311 | 0 | 0 | Std. | 1.74E − 66 | 8.34E − 19 | 0 | 0 | 0 |
| | Noncontinuous Rastrigin | 0 | Mean | 1.83E + 02 | 1.99E − 14 | 6.94E + 01 | 1.55E + 01 | 0 | Std. | 3.15E + 01 | 1.83E − 14 | 9.13E + 00 | 2.65E + 00 | 0 |
| | Weierstrass | 0 | Mean | 6.27E + 01 | 1.12E − 02 | 1.38E + 01 | 0 | 0 | Std. | 2.03E + 01 | 7.73E − 03 | 6.07E − 01 | 0 | 0 |
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