## 4 Benchmark Function Testing and Analysis
### Comparison of ADGMPSO to Other Mainstream Evolutionary Algorithms
** & **Measure** & **PSO** & **BOA** & **WOA** & **SSA** & **GWO** & **ADGMPSO** \\ \hline \multirow{3}{*}{\(f_{1}\)} & Best & \(2.42\times 10^{-1}\) & \(4.12\times 10^{-13}\) & **0** & \(2.67\times 10^{-10}\) & \(3.60\times 10^{-140}\) & **0** \\  & Average & \(4.34\times 10^{-1}\) & \(7.02\times 10^{-13}\) & **0** & \(1.78\times 10^{-6}\) & \(1.95\times 10^{-137}\) & **0** \\  & STD & \(1.41\times 10^{-1}\) & \(1.73\times 10^{-13}\) & **0** & \(3.41\times 10^{-6}\) & \(4.31\times 10^{-137}\) & **0** \\ \hline \multirow{3}{*}{\(f_{2}\)} & Best & \(2.94\times 10^{-1}\) & \(4.49\times 10^{-39}\) & \(8.31\times 10^{-232}\) & \(8.69\times 10^{-6}\) & \(8.76\times 10^{-80}\) & **0** \\  & Average & \(4.71\times 10^{-1}\) & \(2.24\times 10^{-13}\) & \(4.50\times 10^{-220}\) & \(7.12\times 10^{-4}\) & \(1.41\times 10^{-78}\) & **0** \\  & STD & \(1.47\times 10^{-1}\) & \(9.96\times 10^{-13}\) & **0** & \(6.59\times 10^{-4}\) & \(1.57\times 10^{-78}\) & **0** \\ \hline \multirow{3}{*}{\(f_{3}\)} & Best & \(2.25\times 10^{1}\) & \(4.97\times 10^{-13}\) & \(1.08\times 10^{2}\) & \(1.03\times 10^{-6}\) & \(2.01\times 10^{-46}\) & **0** \\  & Average & \(4.93\times 10^{1}\) & \(7.61\times 10^{-13}\) & \(2.11\times 10^{3}\) & \(9.00\times 10^{-4}\) & \(3.30\times 10^{-38}\) & **0** \\  & STD & \(1.70\times 10^{1}\) & \(1.53\times 10^{-13}\) & \(1.72\times 10^{3}\) & \(2.07\times 10^{-3}\) & \(1.51\times 10^{-37}\) & **0** \\ \hline \multirow{3}{*}{\(f_{4}\)} & Best & \(2.02\times 10^{-1}\) & \(3.59\) & \(3.63\times 10^{-4}\) & \(3.93\times 10^{-9}\) & \(1.01\times 10^{-9}\) & \(9.24\times 10^{-32}\) \\  & Average & \(5.92\times 10^{-1}\) & \(4.67\) & \(6.96\times 10^{-4}\) & \(4.34\times 10^{-6}\) & \(3.22\times 10^{-1}\) & \(4.01\times 10^{-27}\) \\  & STD & \(1.89\times 10^{-1}\) & \(6.28\times 10^{-1}\) & \(2.96\times 10^{-4}\) & \(6.39\times 10^{-6}\) & \(2.77\times 10^{-1}\) & \(1.31\times 10^{-26}\) \\ \hline \multirow{3}{*}{\(f_{5}\)} & Best & \(7.57\times 10^{-1}\) & \(1.19\times 10^{-9}\) & \(1.63\times 10^{-7}\) & \(2.04\times 10^{-5}\) & \(1.49\times 10^{-37}\) & \(9.97\times 10^{-290}\) \\  & Average & \(1.67\) & \(1.40\times 10^{-9}\) & \(1.48\times 10^{1}\) & \(1.75\times 10^{-4}\) & \(1.90\times 10^{-35}\) & **1.35\times 10^{-247}\)** \\  & STD & \(6.85\times 10^{-1}\) & \(1.56\times 10^{-10}\) & \(1.89\times 10^{1}\) & \(1.12\times 10^{-4}\) & \(3.07\times 10^{-35}\) & **0** \\ \hline \multirow{3}{*}{\(f_{6}\)} & Best & \(7.10\times 10^{-3}\) & \(1.44\times 10^{-4}\) & \(2.09\times 10^{-5}\) & \(7.98\times 10^{-5}\) & \(5.42\times 10^{-5}\) & \(3.19\times 10^{-6}\) \\  & Average & \(1.54\times 10^{-1}\) & \(4.44\times 10^{-4}\) & \(8.19\times 10^{-4}\) & \(3.49\times 10^{-4}\) & \(3.04\times 10^{-4}\) & \(1.76\times 10^{-4}\) \\  & STD & \(5.96\times 10^{-3}\) & \(2.50\times 10^{-4}\) & \(1.04\times 10^{-3}\) & \(2.75\times 10^{-4}\) & \(1.81\times 10^{-4}\) & \(2.35\times 10^{-4}\) \\ \hline \multirow{3}{*}{\(f_{7}\)} & Best & \(1.61\times 10^{1}\) & **0** & **0** & \(1.53\times 10^{-12}\) & **0** & **0** \\  & Average & \(2.57\times 10^{1}\) & **0** & **0** & \(6.09\times 10^{-7}\) & **0** & **0** \\  & STD & \(8.33\) & **0** & **0** & \(1.26\times 10^{-6}\) & **0** & **0** \\ \hline \multirow{3}{*}{\(f_{8}\)} & Best & \(1.36\times 10^{-1}\) & \(4.37\times 10^{-15}\) & \(\textbf{8.88\times 10^{-16}}\) & \(1.75\times 10^{-6}\) & \(4.44\times 10^{-15}\) & \(\textbf{8.88\times 10^{-16}}\) \\  & Average & \(1.67\) & \(5.07\times 10^{-10}\) & \(3.93\times 10^{-15}\) & \(3.43\times 10^{-4}\) & \(7.99\times 10^{-15}\) & \(\textbf{8.88\times 10^{-16}}\) \\  & STD & \(7.36\times 10^{-1}\) & \(1.58\times 10^{-10}\) & \(2.72\times 10^{-15}\) & \(3.21\times 10^{-4}\) & \(1.76\times 10^{-15}\) & **0** \\ \hline \multirow{3}{*}{\(f_{9}\)} & Best & \(4.13\times 10^{-1}\) & **0** & **0** & \(1.41\times 10^{-13}\) & **0** & **0** \\  & Average & \(5.58\times 10^{To make it easier to compare how fast the algorithms converged and how accurate they were, the convergence curves were generated for the ten benchmark test functions.