# A Cyclical Non-Linear Inertia-Weighted Teaching-Learning-Based Optimization Algorithm
## 4 Benchmark Tests
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**No.**} & **PSO** & **ABC** & **DE** & **TLBO** & **CNIWTLBO** \\  & **(Mean \(\pm\) SD)** & **(Mean \(\pm\) SD)** & **(Mean \(\pm\) SD)** & **(Mean \(\pm\) SD)** & **(Mean \(\pm\) SD)** \\ \hline _f1_ & 8.68E-12 \(\pm\) 6.15E-12 & 9.53E-16 \(\pm\) 5.13E-16 & 7.28E-27 \(\pm\) 2.35E-26 & 3.42E-287 \(\pm\) 0.00 & **0.00E+00 \(\pm\) 0.00E+00** \\ \hline _f2_ & 2.14E-10 \(\pm\) 1.26E-10 & 7.38E-16 \(\pm\) 1.32E-16 & 8.52E-26 \(\pm\) 2.66E-26 & 8.74E-286 \(\pm\) 0.00 & **0.00E+00 \(\pm\) 0.00E+00** \\ \hline _f3_ & 3.26E-08 \(\pm\) 1.52E-08 & 8.62E-16 \(\pm\) 1.29E-16 & 3.02E-26 \(\pm\) 1.38E-26 & 6.28E-285 \(\pm\) 0.00 & **0.00E+00 \(\pm\) 0.00E+00** \\ \hline _f4_ & 2.25E+05 \(\pm\) 1.16E+05 & 7.52E+03 \(\pm\) 1.46E+03 & 2.32E+04 \(\pm\) 2.34E+03 & 2.48E-84 \(\pm\) 1.29E-84 & **0.00E+00 \(\pm\) 0.00E+00** \\ \hline _f5_ & 5.02E-03 \(\pm\) 3.26E-03 & 2.36E-14 \(\pm\) 1.22E-14 & 4.57E-16 \(\pm\) 1.16E-16 & 1.65E-143 \(\pm\) 1.32E-143 & **4.62e-323 \(\pm\) 0.00E+0** \\ \hline _f6_ & 1.23E+00 \(\pm\) 5.24E-01 & 3.67E+01 \(\pm\) 1.05 E+01 & 1.19E-02 \(\pm\) 2.15E-03 & 7.68E-120 \(\pm\) 3.82E-120 & **2.64E-315 \(\pm\) 0.00E+00** \\ \hline _f7_ & 1.58E+02 \(\pm\) 4.72E+01 & 2.45E+02 \(\pm\) 2.16E+01 & 5.63E+01 \(\pm\) 6.74E+00 & 6.04E-51 \(\pm\) 4.62E-51 & **1.82E-319 \(\pm\) 0.00E+00** \\ \hline _f8_ & 3.05E+01 \(\pm\) 2.26E+01 & **1.12E+01 \(\pm\) 2.43E+00** & 2.51E+01 \(\pm\) 3.47E+00 & 1.32E+01 \(\pm\) 4.36E+00 & 1.78E+01 \(\pm\) 5.13E+00 \\ \hline _f9_ & \(-\)1.00E+00 \(\pm\) 0.00E+00 & \(-\)1.00E+00 \(\pm\) 0.00E+00 & \(-\)1.00E+00 \(\pm\) 0.00E+00 & \(-\)1.00E+00 \(\pm\) 0.00E+00 & **-1.00E+00 \(\pm\) 0.00E+00** \\ \hline _f10_ & -1.00E+00 \(\pm\) 0.00E+00 & -1.00E+00 \(\pm\) 0.00E+00 & -1.00E+00 \(\pm\) 0.00E+00 & -1.00E+00 \(\pm\) 0.00E+00 & **-1.00E+00 \(\pm\) 0.00E+00** \\ \hline _f11_ & 0.00E+00 \(\pm\) 0.00E+00 & 0.00E+00 \(\pm\) 0.00E+00 & 0.00E+00 \(\pm\) 0.00E+00 & 0.00E+00 \(\pm\) 0.00E+00 & **0.00E+00 \(\pm\) 0.00E+00** \\ \hline _f12_ & 0.00E+00 \(\pm\) 0.00E+00 & 0.00E+00 \(\pm\) 0.00E+00 & 0.00E+00 \(\pm\) 0.00E+00 & 0.00E+00 \(\pm\) 0.00E+00 & **0.00E+00 \(\pm\) 0.00E+00** \\ \hline _f13_ & \(-\)1.03E+00 \(\pm\) 0.00 & \(-\)1.03E+0 \(\pm\) 0.00 & \(-\)1.03E+03 \(\pm\) 0.00 & \(-\)1.03E+03 \(\pm\) 0.00 & \(-\)1.03E+03 \(\pm\) 0.00 \\ \hline _f14_ & 3.00 E \(\pm\) 8.23E-15 & 3.00 E \(\pm\) 5.02E-15 & 3.00 E \(\pm\) 1.53E-15 & 3.00 E \(\pm\) 6.18E-16 & 3.00 E \(\pm\) 5.82E-16 \\ \hline _f15_ & 1.48E+00 \(\pm\) 3.85E-01 & 3.14E-13 \(\pm\) 3.06E-14 & 2.56E-14 \(\pm\) 6.07E-15 & 4.45E-15 \(\pm\) 2.85E-16 & 8.88E-16 \(\pm\) 0.00 \\ \hline _f16_ & \(-\)8.79E+03 \(\pm\) 4.27E+02 & \(-\)1.24E+04 \(\pm\) 1.81E+02 & \(-\)1.15E+04 \(\pm\) 1.58E+03 & \(-\)9.18E+03 \(\pm\) 7.65E+02 & **-7.33E+03 \(\pm\) 1.66E+02** \\ \hline _f17_ & 7.55E-67 \(\pm\) 1.63E-66 & 6.83E-19 \(\pm\) 1.62E-19 & 5.03E-31 \(\pm\) 0.00 & 0.00E+00 \(\pm\) 0.00E+00 & **0.00E+00 \(\pm\) 0.00E+00** \\ \hline _f18_ & 1.12E+02 \(\pm\) 2.24E+01 & 1.32E-13 \(\pm\) 2.48E-13 & 9.02E+01 \(\pm\) 8.57E+00 & 7.21E+00 \(\pm\) 5.78E+00 & 0.00E+00 \(\pm\) 0.00E+00 \\ \hline _f19_ & 6.69E-03 \(\pm\) 5.46E-04 & 7.15E-03 \(\pm\) 6.86E-04 & 0.00E+00 \(\pm\) 0.00E+00 & 0.00E+00 \(\pm\) 0.00E+00 & **0.00E+00 \(\pm\) 0.00E+00** \\ \hline _f20_ & 1.78E+02 \(\pm\) 3.22E+01 & 2.01E-14 \(\pm\) 1.67E-14 & 6.82E+01 \(\pm\) 8.75E+00 & 1.48E+01 \(\pm\) 2.76E+00 & 0.00E+00 \(\pm\) 0.00E+00 \\ \hline _f21_ & 6.13E+01 \(\pm\) 2.12E+01 & 1.36E-02 \(\pm\) 8.06E-03 & 1.38E+01 \(\pm\) 5.84E-01 & 0.00E+00 \(\pm\) 0.00E+00 & **0.00E+00** \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Performance comparisons of PSO, ABC, DE, TLBO, CNIWTLBO in term of fitness value.