# A Cyclical Non-Linear Inertia-Weighted Teaching-Learning-Based Optimization Algorithm
## 4 Benchmark Tests
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**No.** & **Function** & **Formulation** & **C** & **D** & **Range** & **MinFunVal** \\ \hline _f1_ & Sphere & \(f(x)=\sum\limits_{i=1}^{D}x_{i}^{2}\) & U & 30 & \([-100,100]\) & 0 \\ _f2_ & SumSquares & \(f(x)=\sum\limits_{i=1}^{D}x_{i}^{2}\) & U & 30 & \([-100,100]\) & 0 \\ _f3_ & Tablet & \(f(x)=10^{x}x_{i}^{2}+\sum\limits_{i=1}^{D}x_{i}^{2}\) & U & 30 & \([-100,100]\) & 0 \\ _f4_ & Schwefel 1.2 & \(f(x)=\sum\limits_{i=1}^{D}(\sum\limits_{i=1}^{D}x_{i})\) & U & 30 & \([-100,100]\) & 0 \\ _f5_ & Schwefel 2.22 & \(f(x)=\sum\limits_{i=1}^{D}\left[x_{i}^{2}+\sum\limits_{i=1}^{D}\left[x_{i}^{ 2}+\sum\limits_{i=1}^{D}\left[x_{i}^{2}+\sum\limits_{i=1}^{D}\left[x_{i}^{2} \right]\right]\right]\right)-\) & U & 30 & \([-10,10]\) & 0 \\ _f6_ & Schwefel 2.21 & \(f(x)=\max\limits_{i=1}^{D}\left[x_{i}\right],1\leq i\leq D\) & U & 30 & \([-100,100]\) & 0 \\ _f7_ & [PERSON] & \(f(x)=\sum\limits_{i=1}^{D}x_{i}^{2}+(\sum\limits_{i=1}^{D}\left(0.55x_{i} \right)+\sum\limits_{i=1}^{D}\left(0.55x_{i}\right)^{4}\) & U & 30 & \([-5,10]\) & 0 \\ _f8_ & [PERSON] & \(f(x)=\sum\limits_{i=1}^{D}\left[100\left(x_{i+1}-x_{i}^{2}\right)^{2}+(1-x_{i} )^{2}\right]\) & U & 30 & \([-4,4]\) & 0 \\ _f9_ & [PERSON] & \(f(x)=\frac{\sin^{2}(\sum\limits_{i=1}^{D}\left[x_{i}^{2}+\sum\limits_{i=1}^{D} \right)-0.5}{(1+0.001(x_{i}^{2}+x_{i}^{2}))^{2}}-0.5\) & M & 2 & \([-10,10]\) & \(-1\) \\ _f10_ & Dropwave & \(f(x)=-\frac{1+\cos(\left[\sqrt{x_{i}^{2}+x_{i}^{2}}\right])}{\cos(3x_{i}^{2}+ \sum\limits_{i=1}^{D}\left[x_{i}^{2}+\sum\limits_{i=1}^{D}\right]}\) & M & 2 & \([-2,2]\) & \(-1\) \\ _f11_ & [PERSON] & \(f(x)=x_{i}^{2}+2x_{i}^{2}-0.3\cos(3x_{1}x_{i})\cdot\cos(4\pi x_{2})+0.7\) & M & 2 & \([-100,100]\) & 0 \\ _f12_ & Bohachevsky2 & \(f(x)=x_{i}^{2}+2x_{i}^{2}-0.3\cos(3x_{1}x_{i})\cdot\cos(4\pi x_{2})+0.3\) & M & 2 & \([-100,100]\) & 0 \\ _f13_ & Sax Hump & \(f(x)=x_{i}^{2}-2.1x_{i}^{4}-\sum\limits_{i=1}^{D}x_{i}^{4}+x_{i}x_{i}^{2}-4x_{i} ^{2}\) & M & 2 & \([-5,5]\) & \(-1.03163\) \\ _f14_ & Camel Back & \(f(x)=[1+(x_{1}+x_{2}+1)^{2}(19-14x_{1}+3x_{1}^{2}-\) & & & & \\ _f14_ & Goldstein-Price & \(14x_{2}+6x_{1}x_{2}+3x_{2}^{2})\times\left]\times\left[30+(2x_{1}-3x_{2})^{ 2}\times\right.\) & M & 2 & \([-2,2]\) & 3 \\  & & \((18-32x_{1}+12x_{1}^{2}+48x_{2}-36x_{1}x_{2}+27x_{2}^{2})\) & & & & \\ _f15_ & Ackley & & M & 30 & \([-32,32]\) & 0 \\  & & \(\exp\left(\sum\limits_{i=1}^{D}\cos(2\pi x_{i})\right)+20+e\) & & & & \\ _f16_ & Schwefel 2.26 & \(f(x)=-\sum\limits_{i=1}^{D}\left(x_{i}\sin(\sqrt{x_{i}})\right)\) & M & 30 & \([-500,500]\) & \(-837.9658\) \\ _f17_ & Multimod & \(f(x)=\sum\limits_{i=1}^{D}\left[x_{i}\right]\) & M & 30 & \([-10,10]\) & 0 \\ _f18_ & Rastrigin & \(f(x)=\sum\limits_{i=1}^{D}\left(x_{i}^{2}-10\cos(2\pi x_{i})+10\right)\) & M & 30 & \([-5.12,5.12]\) & 0 \\ _f19_ & Griewank & \(f(x)=\frac{1}{200}\sum\limits_{i=1}^{D}x_{i}^{2}-\sum\limits_{i=1}^{D}\cos( \frac{x_{i}}{\sqrt{4}})+1\) & M & 30 & \([-600,600]\) & 0 \\ _f20_ & NCRastrigin & \(f(x)=\sum\limits_{i=1}^{D}\left(x_{i}^{2}-10\cos(2\pi y_{i})+10\right)\), & & & \\  & & \(\text{where }x_{i}=\left\{\begin{array}{ll}x_{i}&|x_{i}|<0.5\\ 0.5 round(2x_{i})&|x_{i}|\geq 0.5\\ \end{array}\right.\) & M & 30 & \([-5.12,5.12]\) & 0 \\ _f21_ & Weierstrass & \(D\sum\limits_{i=0}^{D}\left[x_{i}^{2}\cos(2\pi b^{4}(x_{i}+0.5))\right]\) & M & 30 & \([-0.5,0.5]\) & 0 \\  & & \(\text{where }a=0.5,b=3,km=20\) & & & & \\ \hline \hline \end{tabular} U: Unimodal, M: Multimodal.  
\end{table} 
Table 1: The benchmark functions adopted in the paper. CNIWTLBO and most of TLBO variants. In this experiment, the maximum fitness function evaluation is 80,000 for all benchmark functions, and the other specific parameters of algorithms are given in Table 2.  
Each benchmark function in Table 1 is independently experimented 30 times with PSO, ABC, DE, TLBO and CNIWTLBO algorithms and comparative results. Each algorithm is terminated after running for 80,000 FEs or when it reached the global minimum value in advance.