## 3 Experimental Results and Discussion
\begin{table}
\begin{tabular}{l l l l} \hline \hline
**Functions** & **Range** & **Dim** & \(\mathbf{F_{min}}\) \\ \hline \(f_{1}(x)=\sum\sum_{i=1}^{x}x_{i}^{2}\) & \([-100,100]\) & 30 & 0 \\ \(f_{2}(x)=\sum\sum_{j_{min}}^{x}[x_{i}]+\prod_{i=1}^{x}[x_{i}]\) & \([-10,10]\) & 30 & 0 \\ \(f_{3}(x)=\sum_{i=1}^{x}\left(\sum_{j_{min}}^{x}\right)^{2}\) & \([-100,100]\) & 30 & 0 \\ \(f_{4}(x)=\min\left(\left|x\right|\right|\),\(1\leq i\leq n\right)\) & \([-100,100]\) & 30 & 0 \\ \(f_{5}(x)=\sum_{i=1}^{x}100\left(x_{i+1}-x_{i}^{2}\right)^{2}+(x_{i}-1)^{2}\) & \([-30,30]\) & 30 & 0 \\ \(f_{6}(x)=\sum_{i=1}^{x}\left(\left[x_{i}+0.5\right]\right)^{2}\) & \([-100,100]\) & 30 & 0 \\ \(f_{7}(x)=\sum_{i=1}^{x}\alpha t^{4}+\text{random}[0,1)\) & \([-1.28,1.28]\) & 30 & 0 \\ \(f_{8}(x)=\sum_{i=1}^{x}-x_{i}\sin\left(\sqrt{\left|x\right|}\right)\) & \([-500,500]\) & 30 & \(-418.9892\times\text{dim}\) \\ \(f_{9}(x)=\sum_{i=1}^{x}\left[x_{i}^{2}-10\cos(2\pi x_{i})+10\right]\) & \([-5.12,5.12]\) & 30 & 0 \\ \(f_{10}(x)=-20\exp\left(-02\sqrt{\frac{1}{2}\sum_{i=1}^{x}\alpha t^{2}}\right)\) & \([-32,32]\) & 30 & 0 \\ \(-\exp\left((1/n)\sum_{i=1}^{x}\cos(2\pi x_{i})\right)+20\) & & & \\ \(+e\) & \([-32,32]\) & 30 & 0 \\ \(f_{11}(x)=1/4000\sum_{i=1}^{x}\sum_{i}^{2}\sum_{i}^{2}-\prod_{i=1}^{x}\cos \left(x_{i}/\sqrt{i}\right)+20\) & & & \\ \(f_{21}(x)=\pi/n\left\{\sum_{i=1}^{x}\left(x_{i}-1\right)^{2}\left[1+10\sin^{ 2}(\pi x_{i})\right]+\left(y_{i}-1\right)^{2}\right\}\) & \([-50,50]\) & 30 & 0 \\ \(+\sum_{i=1}^{x}\alpha\left(x_{i},10,100,4\right)+\pi/n!\cos(\pi y_{i})\) & & & \\ \(y_{i}=1+x_{i}+(1/4)(u_{i},\alpha,k,m)\) & & & \\ \(\left\{k(x_{i}-a)^{n}\right\}\) & \(x_{i}>a\) & & \\ \(\left\{0\right\}\) & \(-a<x_{i}<a\) & & \\ \(\left\{k-(x_{i}-a)^{n}\right\}\) & \(x_{i}<-a\) & & \\ \(f_{3}(x)=0.1\{\sum_{i=1}^{x}\left(x_{i}-1\right)^{2}\left[1+\sin^{2}(3\pi x _{i}+1)\right]\) & \([-50,50]\) & 30 & 0 \\ \(\left.+(x_{i}-1\right)^{2}\left[1+\sin^{2}(2\pi x_{i})\right]\}\) & & & \\ \(+0.1\sin^{2}(3\pi x_{i})\) & & & \\ \(+\sum_{i=1}^{x}\alpha\left(x_{i},5.100,4\right)\) & & & \\ \(f_{4}(x)=\left(\left(1/300\right)+\sum_{i=1}^{x}\left(1/j+\sum_{i=1}^{x}\left(x _{i}-a_{i}\right)^{6}\right)^{-1}\) & \([-65,65]\) & 2 & 1 \\ \(f_{5}(x)=\sum_{i=1}^{x}\left[a_{i}-x_{i}\left(9/x_{i}+bx_{i}\right)\right]^{ 2}/b_{i}^{2}+bx_{i}x_{i}^{2}\) & \([-5,5]\) & 4 & 0.0003 \\ \(f_{6}(x)=4\pi_{i}^{2}-2x_{i}^{2}+1/3!/a_{i}^{2}+x_{i}x_{i}^{2}-4x_{i}^{2}\) & \([-5,5]\) & 2 & \(-1.0316\) \\ \(f_{7}(x)=\left(x_{i}-2\right).51/4\pi^{2}x_{i}^{2}+5/7\pi x_{i}-6^{2})+10(1-(1 /8\pi))\cos x_{i}+10\) & \([-5,5]\) & 2 & 0.398 \\ \(f_{8}(x)=\left[1+(x_{i}-x_{i})^{2}\left(19-14x_{i}+3x_{i}^{2}-14x_{i}+6x_{i}x_{ i}+3x_{i}^{2}\right)\right]\) & \([-2,2]\) & 2 & 3 \\ \(\times[30\) & & & \\ \(+(2x_{1}-3x_{2})^{2}\) & & & \\ \(\times(18-32x_{1}+12x_{i}^{2}+48x_{2}\) & & & \\ \(-36x_{1}x_{2}+27x_{i}^{2})\) & & & \\ \(f_{19}(x)=-\sum_{i=1}^{x}\alpha\left[x-\sum_{j=1}^{x}\alpha\left(y_{i}-p_{i} \right)^{2}\right]\) & \([1,3]\) & 3 & \(-3.86\) \\ \(f_{20}(x)=-\sum_{i=1}^{x}\alpha\exp\left[-\sum_{j=1}^{x}\alpha\left(y_{i}-p_{i} \right)^{2}\right]\) & \([0,1]\) & 6 & \(-3.32\) \\ \(f_{21}(x)=-\sum_{i=1}^{x}\left[(X-4)(X-a)^{T}+c_{i}\right]^{-1}\) & \([0,10]\) & 4 & \(-10.1532\) \\ \(f_{22}(x)=-\sum_{i=1}^{x}\left[(X-4)(X-a)^{T}+c_{i}\right]^{-1}\) & \([0,10]\) & 4 & \(-10.4028\) \\ \(f_{23}(x)=-\sum_{i=1}^{x}\alpha\left[(X-4)(X-a)^{T}+c_{i}\right]^{-1}\) & \([0,10]\) & 4 & \(-10.5363\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Benchmark functions. The data make it clear that GSLEO-AEFA receives the near optimal solution in seven of the seven single-modal functions (F1-F7). It is absolutely critical to note that the achievement of GSLEO-AEFA is a significant improvement over the original AEFA and other algorithms in F1-F7. This improvement is expected due to the introduction of LEO, which improves GSLEO-AEFAs ability to do local search. As a result, there is significant improvement in exploitation too.