## 3 Proposed ATMALS-GSK Algorithm
### Atmals-Gsk
#### 3.2.6 Overall Operation of ATMALS-GSK
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Function**} & \multicolumn{6}{c}{**GSK [16]**} & \multicolumn{6}{c}{**ATMALS-GSK (Proposed)**} \\ \cline{2-11}  & **Best** & **Median** & **Worst** & **Mean** & **STD** & **Best** & **Median** & **Worst** & **Mean** & **STD** \\ \hline
1 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 \\ \hline
3 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 \\ \hline
4 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 \\ \hline
5 & \(1.53\times 10^{1}\) & \(2.01\times 10^{1}\) & \(2.58\times 10^{1}\) & \(2.03\times 10^{1}\) & \(2.79\) & \(2.99\) & \(8.47\) & \(1.00\times 10^{1}\) & 7.57 & 2.71 \\ \hline
6 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 \\ \hline
7 & \(2.46\times 10^{1}\) & \(3.10\times 10^{1}\) & \(3.74\times 10^{1}\) & \(3.07\times 10^{1}\) & \(3.08\) & \(1.27\times 10^{1}\) & \(1.69\times 10^{1}\) & \(1.85\times 10^{1}\) & \(1.63\times 10^{1}\) & 2.21 \\ \hline
8 & \(1.45\times 10^{1}\) & \(1.99\times 10^{1}\) & \(2.58\times 10^{1}\) & \(2.02\times 10^{1}\) & \(2.92\) & \(3.98\) & \(7.97\) & \(1.09\times 10^{1}\) & 7.57 & 2.11 \\ \hline
9 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 \\ \hline
10 & \(7.54\times 10^{2}\) & \(1.10\times 10^{2}\) & \(1.29\times 10^{3}\) & \(1.06\times 10^{3}\) & \(1.33\times 10^{2}\) & \(1.40\times 10^{2}\) & \(5.07\times 10^{2}\) & \(6.57\times 10^{2}\) & \(4.55\times 10^{2}\) & \(1.93\times 10^{2}\) \\ \hline
11 & 0.00 & 0.00 & 1.02\(\times 10^{-8}\) & 0.00 & 0.00 & \(6.40\times 10^{-1}\) & \(1.77\) & \(2.67\) & \(1.67\) & \(7.10\times 10^{-1}\) \\ \hline
12 & \(1.42\times 10^{1}\) & \(7.57\times 10^{1}\) & \(2.69\times 10^{2}\) & \(8.93\times 10^{1}\) & \(7.26\times 10^{1}\) & \(2.12\times 10^{-1}\) & \(1.05\times 10^{1}\) & \(3.45\times 10^{1}\) & \(1.12\times 10^{1}\) & 9.45 \\ \hline
13 & \(9.19\times 10^{-1}\) & 6.56 & 9.73 & 6.56 & 1.41 & \(3.32\times 10^{-1}\) & \(1.80\) & 5.70 & 2.65 & 2.18 \\ \hline
14 & \(5.19\times 10^{-3}\) & 5.42 & \(1.19\times 10^{1}\) & 5.88 & 3.06 & \(3.57\times 10^{-1}\) & \(2.94\) & \(3.56\) & 2.78 & \(9.25\times 10^{-1}\) \\ \hline
15 & \(2.96\times 10^{-3}\) & \(1.75\times 10^{-1}\) & \(5.00\times 10^{-1}\) & \(2.22\times 10^{-1}\) & \(2.13\times 10^{-1}\) & \(1.45\times 10^{-2}\) & \(1.30\times 10^{-1}\) & \(2.63\times 10^{-1}\) & \(1.47\times 10^{-1}\) & \(8.60\times 10^{-2}\) \\ \hline
16 & \(3.29\times 10^{-1}\) & \(9.48\times 10^{-1}\) & \(1.18\times 10^{1}\) & 4.27 & 4.95 & \(4.89\times 10^{-1}\) & \(1.11\) & 1.80 & 1.12 & \(4.70\times 10^{-1}\) \\ \hline
17 & \(9.76\times 10^{-1}\) & 9.94 & \(2.52\times 10^{1}\) & \(1.17\times 10^{1}\) & 7.09 & \(2.26\) & \(1.26\times 10^{1}\) & \(2.27\times 10^{1}\) & \(1.25\times 10^{1}\) & \(9.02\times 10^{1}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Results of GSK and ATMALS-GSK for CEC 2017 benchmark functions in \(D=10\). \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Function**} & \multicolumn{6}{c}{**GSK [16]**} & \multicolumn{6}{c}{**ATMALS-GSK (Proposed)**} \\ \cline{2-10}  & **Best** & **Median** & **Worst** & **Mean** & **STD** & **Best** & **Median** & **Worst** & **Mean** & **STD** \\ \hline \(1\) & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Results of GSK and ATMALS-GSK for CEC 2017 benchmark functions in D = 30.