# An Advanced Crow Search Algorithm for Solving Global Optimization Problem
## 4 Numerical Examples
### Benchmark Function Problems
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Fun**} & \multirow{2}{*}{**Index**} & \multicolumn{6}{c}{**Algorithm**} \\ \cline{3-10}  & & **ACS** & **Conventional** & **HS** & **DE** & **GO** & **SS** & **GA** \\ \hline \multirow{3}{*}{\(f1\)} & BF & \(1.648\times 10^{-13}\) & \(3.416\times 10^{-5}\) & \(2.280\times 10^{-3}\) & \(5.594\times 10^{0}\) & \(1.361\times 10^{-3}\) & \(4.905\times 10^{-9}\) & \(4.447\times 10^{-6}\) \\  & MF & \(9.166\times 10^{-12}\) & \(1.054\times 10^{-4}\) & \(1.067\times 10^{-1}\) & \(9.928\times 10^{1}\) & \(1.799\times 10^{-1}\) & \(7.454\times 10^{-9}\) & \(1.038\times 10^{-4}\) \\  & Std & \(1.281\times 10^{-11}\) & \(6.157\times 10^{-5}\) & \(1.134\times 10^{-1}\) & \(9.165\times 10^{1}\) & \(3.703\times 10^{-1}\) & \(1.465\times 10^{-9}\) & \(1.437\times 10^{-4}\) \\  & BF & \(6.511\times 10^{-7}\) & \(5.118\times 10^{-1}\) & \(1.274\times 10^{-2}\) & \(3.360\times 10^{-5}\) & \(3.545\times 10^{-1}\) & \(2.477\times 10^{-3}\) & \(2.827\times 10^{-5}\) \\ \multirow{3}{*}{\(f2\)} & MF & \(6.843\times 10^{-5}\) & \(1.493\times 10^{0}\) & \(1.764\times 10^{-2}\) & \(2.358\times 10^{-1}\) & \(5.134\times 10^{0}\) & \(1.053\times 10^{0}\) & \(1.537\times 10^{-4}\) \\  & Std & \(7.103\times 10^{-5}\) & \(6.184\times 10^{-1}\) & \(2.859\times 10^{-3}\) & \(2.938\times 10^{-3}\) & \(7.628\times 10^{0}\) & \(1.256\times 10^{0}\) & \(1.744\times 10^{-4}\) \\  & BF & \(7.314\times 10^{-9}\) & \(4.392\times 10^{0}\) & \(1.081\times 10^{3}\) & \(3.612\times 10^{2}\) & \(5.409\times 10^{2}\) & \(7.628\times 10^{-1}\) & \(6.919\times 10^{2}\) \\ \multirow{3}{*}{\(f3\)} & MF & \(2.980\times 10^{-6}\) & \(9.869\times 10^{0}\) & \(3.426\times 10^{3}\) & \(1.376\times 10^{3}\) & \(1.340\times 10^{3}\) & \(4.734\times 10^{0}\) & \(2.276\times 10^{3}\) \\  & Std & \(4.618\times 10^{-6}\) & \(4.004\times 10^{1}\) & \(1.137\times 10^{3}\) & \(8.058\times 10^{2}\) & \(9.813\times 10^{2}\) & \(4.891\times 10^{0}\) & \(9.368\times 10^{2}\) \\ \multirow{3}{*}{\(f4\)} & BF & \(3.277\times 10^{-7}\) & \(7.622\times 10^{-1}\) & \(2.729\times 10^{0}\) & \(1.391\times 10^{1}\) & \(3.172\times 10^{0}\) & \(1.229\times 10^{0}\) & \(1.608\times 10^{1}\) \\  & MF & \(7.729\times 10^{-5}\) & \(2.682\times 10^{0}\) & \(3.733\times 10^{0}\) & \(2.569\times 10^{0}\) & \(7.949\times 10^{0}\) & \(4.523\times 10^{0}\) & \(2.468\times 10^{1}\) \\ \multirow{3}{*}{\(f5\)} & Std & \(1.092\times 10^{-4}\) & \(1.112\times 10^{0}\) & \(6.870\times 10^{-1}\) & \(6.344\times 10^{3}\) & \(1.352\times 10^{0}\) & \(2.623\times 10^{0}\) & \(5.934\times 10^{0}\) \\  & BF & \(6.970\times 10^{-8}\) & \(2.489\times 10^{1}\) & \(2.604\times 10^{1}\) & \(2.021\times 10^{3}\) & \(2.778\times 10^{1}\) & \(2.231\times 10^{1}\) & \(3.549\times 10^{0}\) \\ \multirow{3}{*}{\(f5\)} & MF & \(8.623\times 10^{0}\) & \(6.917\times 10^{1}\) & \(1.254\times 10^{2}\) & \(5.880\times 10^{4}\) & \(2.734\times 10^{2}\) & \(1.700\times 10^{2}\) & \(3.619\times 10^{2}\) \\  & Std & \(1.240\times 10^{1}\) & \(6.094\times 10^{1}\) & \(6.013\times 10^{1}\) & \(8.939\times 10^{4}\) & \(4.733\times 10^{2}\) & \(3.320\times 10^{2}\) & \(6.670\times 10^{2}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Comparison results with other algorithms using the benchmark function.