## 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} \hline \hline
**Fan.** & **IADE [50]** & **GJO-JOS [51]** & **QSCCA [52]** & **cSM [53]** & **FOWPO [54]** & **ATMALS-GSK** \\ \hline
1 & \(8.49\times 10^{2}\pm 6.38\times 10^{3}\) & \(2.10\times 10^{3}\pm 1.10\times 10^{3}\) & \(3.39\times 10^{3}\pm 3.66\times 10^{3}\) & \(2.30\times 10^{3}\pm 3.01\times 10^{3}\) & \(8.87\times 10^{4}\pm 4.38\times 10^{-4}\) & \(0.00\pm 0.00\) \\ \hline
3 & \(3.00\times 10^{2}\pm 7.95\times 10^{-1}\) & \(6.40\times 10^{2}\pm 2.50\times 10^{2}\) & \(3.09\times 10^{2}\pm 2.95\times 10^{2}\) & \(9.89\times 10^{2}\pm 10.17\times 10^{-9}\) & \(4.53\times 10^{-4}\pm 3.42\times 10^{-6}\) & \(0.00\pm 0.00\) \\ \hline
4 & \(1.94\times 10^{4}\pm 0.00\) & \(5.00\times 10^{2}\pm 1.70\times 10^{4}\) & \(4.07\times 10^{2}\pm 9.72\) & \(8.07\times 10^{4}\pm 1.02\times 10^{4}\) & \(5.43\times 15.2\times 10^{4}\) & \(1.99\pm 2.10\) \\ \hline
5 & \(7.93\times 10^{2}\pm 1.47\times 10^{1}\) & \(6.00\times 10^{2}\pm 5.60\times 10^{4}\) & \(5.17\times 10^{2}\pm 4.78\) & \(8.61\times 10^{4}\pm 2.20\times 10^{4}\) & \(5.49\times 10^{4}\pm 1.39\times 10^{4}\) & \(1.53\times 10^{4}\pm 1.90\times 10^{4}\) \\ \hline
6 & \(6.65\times 10^{2}\pm 4.63\) & \(6.10\times 10^{2}\pm 5.90\) & \(6.00\times 10^{2}\pm 3.52\times 10^{-2}\) & \(4.13\times 10^{-4}\pm 8.21\times 10^{-4}\) & \(4.61\times 10^{-2}\pm 3.07\times 10^{-2}\) & \(6.82\times 10^{-5}\pm 3.39\times 10^{-5}\) \\ \hline
7 & \(9.04\times 10^{2}\pm 7.38\times 10^{1}\) & \(8.30\times 10^{2}\pm 6.20\times 10^{4}\) & \(7.27\times 10^{2}\pm 6.06\) & \(1.33\times 10^{2}\pm 2.61\times 10^{4}\) & \(7.91\times 10^{4}\pm 1.13\times 10^{4}\) & \(4.33\times 10^{4}\pm 1.15\times 10^{4}\) \\ \hline
8 & \(9.24\times 10^{2}\pm 3.24\times 10^{3}\) & \(8.90\times 10^{2}\pm 4.60\times 10^{4}\) & \(8.14\times 10^{2}\pm 4.32\) & \(1.01\times 10^{2}\pm 2.82\times 10^{4}\) & \(5.60\times 10^{4}\pm 1.19\times 10^{4}\) & \(1.35\times 10^{4}\pm 1.29\times 10^{4}\) \\ \hline
9 & \(5.44\times 10^{3}\pm 4.41\times 10^{2}\) & \(1.20\times 10^{3}\pm 4.40\times 10^{2}\) & \(9.00\times 10^{2}\pm 4.28\times 10^{-3}\) & \(9.32\times 10^{2}\pm 8.65\times 10^{2}\) & \(1.90\times 10^{4}\pm 2.15\times 10^{4}\) & \(1.79\times 10^{4}\pm 2.37\times 10^{-2}\) \\ \hline
10 & \(4.75\times 10^{3}\pm 1.12\times 10^{3}\) & \(5.00\times 10^{3}\pm 1.70\times 10^{3}\) & \(1.57\times 10^{3}\pm 2.19\times 10^{2}\) & \(2.85\times 10^{3}\pm 4.80\times 10^{2}\) & \(2.02\times 10^{3}\pm 3.11\times 10^{2}\) & \(2.80\times 10^{4}\pm 5.90\times 10^{2}\) \\ \hline
11 & \(1.22\times 10^{3}\pm 4.95\times 10^{3}\) & \(1.20\times 10^{3}\pm 4.20\times 10^{4}\) & \(1.11\times 10^{3}\pm 1.86\) & \(1.61\times 10^{2}\pm 5.33\times 10^{4}\) & \(1.26\times 10^{4}\pm 4.65\) & \(1.46\times 10^{4}\pm 1.73\times 10^{4}\) \\ \hline
12 & \(5.57\times 10^{4}\pm 4.87\times 10^{4}\) & \(1.20\times 10^{7}\pm 1.10\times 10^{7}\) & \(1.80\times 10^{4}\pm 1.44\times 10^{4}\) & \(8.87\times 10^{5}\pm 8.87\times 10^{5}\) & \(2.92\times 10^{2}\pm 1.78\times 10^{2}\) & \(3.84\times 10^{4}\pm 2.62\times 10^{3}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 14: Comparison of the average and standard deviation results (Mean \(\pm\) STD) of ATMALS-GSK with existing metaheuristics over 51 runs for \(D=30\) on CEC 2017. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Fan.