Research Article
A Chaotic Multi-Objective Runge–Kutta Optimization Algorithm for Optimized Circuit Design
Table 4
Comparison results of the 10 chaotic maps using 15 benchmark test functions.
| FUNCTION | Chebyshev | Circle | Gauss | Iterative | Logistic | Piecewise | Sine | Singer | Sinuisodal | Tent |
| F1 | 2.14E-03 | 2.70E-04 | 1.14E-03 | 2.00E-05 | 7.16E-03 | 4.20E-04 | 5.00E-04 | 4.03E-03 | 4.03E-03 | 8.10E-04 | F2 | −4.00E + 07 | −4.00E + 07 | −4.00E + 07 | 4.00E + 07 | 4.00E + 07 | 4.00E + 07 | −4.00E + 07 | −4.00E + 07 | −4.00E + 07 | −4.00E + 07 | F3 | −1.40E + 01 | −1.40E + 01 | −1.40E + 01 | −1.40E + 01 | −1.40E + 01 | −1.40E + 01 | −1.40E + 01 | −1.40E + 01 | −1.40E + 01 | −1.39E + 01 | F4 | 1.52E + 01 | 1.50E + 01 | 1.50E + 01 | 1.51E + 01 | 1.52E + 01 | 1.51E + 01 | 1.52E + 01 | 1.52E + 01 | 1.51E + 01 | 1.52E + 01 | F5 | 0.00E + 00 | 0.00E + 00 | 0.00E + 00 | 0.00E + 00 | 0.00E + 00 | 0.00E + 00 | 0.00E + 00 | 0.00E + 00 | 0.00E + 00 | 0.00E + 00 | F6 | −7.89E + 03 | −6.41E + 03 | −4.39E + 03 | −2.79E + 03 | −2.84E + 03 | −4.14E + 03 | −3.27E + 03 | −2.58E + 03 | −4.28E + 03 | −6.13E + 03 | F7 | −1.55E + 02 | −1.39E + 02 | −1.59E + 02 | −1.37E + 02 | −1.12E + 02 | −9.79E + 01 | −1.28E + 02 | −1.11E + 02 | −1.32E + 02 | −1.02E + 02 | F8 | 1.85E + 02 | 2.01E + 02 | 1.68E + 02 | 2.06E + 02 | 2.03E + 02 | 2.06E + 02 | 2.06E + 02 | 2.03E + 02 | 1.90E + 02 | 2.02E + 02 | F9 | 7.15E-01 | 6.36E-01 | 8.48E-01 | 7.24E-01 | 6.81E-01 | 8.07E-01 | 6.05E-01 | 7.67E-01 | 6.55E-01 | 6.79E-01 | F10 | 8.26E + 00 | 8.25E + 00 | 8.22E + 00 | 8.27E + 00 | 8.21E + 00 | 8.25E + 00 | 8.17E + 00 | 8.29E + 00 | 8.25E + 00 | 8.36E + 00 | F11 | −1.06E + 07 | −1.04E + 07 | −1.06E + 07 | −1.05E + 07 | −1.08E + 06 | −1.09E + 06 | −1.03E + 06 | −1.03E + 06 | −1.05E + 06 | −1.09E + 06 | F12 | −5.03E + 05 | −4.98E + 05 | −4.72E + 05 | −4.82E + 05 | −4.95E + 05 | −4.84E + 05 | −4.86E + 05 | −5.01E + 05 | −5.02E + 05 | −4.93E + 05 | F13 | −4.96E + 05 | −4.80E + 05 | −4.82E + 05 | −4.73E + 05 | −4.81E + 05 | −4.80E + 05 | −4.81E + 05 | −4.90E + 05 | −5.01E + 05 | −4.87E + 05 | F14 | −3.70E + 01 | −3.71E + 01 | −3.70E + 01 | −3.68E + 01 | −3.65E + 01 | −3.65E + 01 | −3.59E + 01 | 3.64E + 01 | −3.60E + 01 | 3.68E + 01 | F15 | −6.10E-04 | −6.10E-04 | −1.47E-03 | −5.00E-04 | −7.00E-04 | −2.50E-04 | −4.70E-04 | −1.07E-03 | 1.00E-02 | −5.80E-04 |
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Bold values are the best results obtained for each function.
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