## 4 Analysis of Experimental Results
### Simulation Experiment
#### 4.1.2 Comparative Analysis of Performance with Other Algorithms
** & **Algorithm** & **Mean** & **Std** & **Time/s** \\ \hline \multirow{9}{*}{F1} & BOA & \(1.66\times 10^{-14}\) & \(8.70\times 10^{-16}\) & 0.3235 & \multirow{9}{*}{F2} & BOA & \(9.17\times 10^{-12}\) & \(1.11\times 10^{-12}\) & 0.2990 \\  & GWO & \(2.92\times 10^{-70}\) & \(1.03\times 10^{-69}\) & 0.4156 & & GWO & \(1.77\times 10^{-80}\) & \(5.91\times 10^{-80}\) & 0.2193 \\  & PSO & \(7.77\times 10^{-12}\) & \(1.44\times 10^{-11}\) & 0.1773 & & PSO & \(3.89\times 10^{-27}\) & \(1.01\times 10^{-26}\) & 0.1158 \\  & SCA & \(3.48\times 10^{-3}\) & \(1.26\times 10^{-2}\) & 0.3297 & & SCA & \(3.39\times 10^{-21}\) & \(1.02\times 10^{-20}\) & 0.1774 \\  & SSA & \(8.70\times 10^{-9}\) & \(1.59\times 10^{-9}\) & 0.3864 & & \multirow{9}{*}{F2} & SSA & \(6.89\times 10^{-6}\) & \(1.52\times 10^{-6}\) & 0.3061 \\  & WOA & \(5.37\times 10^{-172}\) & 0 & 0.1798 & & WOA & \(5.08\times 10^{-112}\) & \(3.36\times 10^{-111}\) & 0.1298 \\  & GEO & \(5.05\times 10^{-12}\) & \(4.35\times 10^{-12}\) & 0.8909 & & GEO & \(2.58\times 10^{-5}\) & \(9.24\times 10^{-5}\) & 0.7959 \\  & GEO\_DIS & \(1.15\times 10^{-17}\) & \(8.00\times 10^{-17}\) & 0.8448 & & GEO\_DIS & \(4.66\times 10^{-12}\) & \(1.28\times 10^{-11}\) & 0.7581 \\  & IGEO & 0 & 0 & 0.7498 & & IGEO & 0 & 0 & 0.6049 \\  & BOA & \(2.80\times 10^{-16}\) & \(1.98\times 10^{-15}\) & 0.3983 & & BOA & \(5.50\times 10^{-13}\) & \(4.35\times 10^{-13}\) & 0.3228 \\  & GWO & \(1.60\times 10^{-2}\) & \(2.11\times 10^{-2}\) & 0.2654 & & GWO & \(4.58\times 10^{-15}\) & \(7.03\times 10^{-16}\) & 0.2250 \\  & PSO & \(1.28\times 10^{-1}\) & \(8.38\times 10^{-2}\) & 0.1658 & & PSO & \(4.87\times 10^{-15}\) & \(1.17\times 10^{-15}\) & 0.1165 \\  & SCA & \(1.52\times 10^{-2}\) & \(6.12\times 10^{-2}\) & 0.2395 & & SCA & \(4.73\times 10^{-15}\) & \(1.73\times 10^{-15}\) & 0.1896 \\ F3 & SSA & \(2.43\times 10^{-1}\) & \(1.31\times 10^{-1}\) & 0.3889 & & SGA & \(4.55\times 10^{-1}\) & \(8.01\times 10^{-1}\) & 0.3061 \\  & WOA & \(4.31\times 10^{-2}\) & \(8.59\times 10^{-2}\) & 0.1794 & & WOA & \(4.01\times 10^{-15}\) & \(1.98\times 10^{-15}\) & 0.1323 \\  & GEO & GEO & \(4.93\times 10^{-3}\) & \(5.67\times 10^{-3}\) & 0.8387 & & GEO\_DIS & \(4.44\times 10^{-15}\) & 0 & 0.8499 \\  & GEO\_DIS & 0 & 0 & 0.8421 & & GEO\_DIS & \(1.32\times 10^{-11}\) & \(7.77\times 10^{-11}\) & 0.7699 \\  & IGEO & 0 & 0 & 0.8812 & & GEO\_DIS & \(8.88\times 10^{-16}\) & 0 & 0.8077 \\  & BOA & \(8.38\times 10^{0}\) & \(4.70\times 10^{-1}\) & 0.4023 & & BOA & \(2.23\times 10^{1}\) & \(1.90\times 10^{1}\) & 0.3149 \\  & GWO & \(5.98\times 10^{0}\) & \(1.70\times 10^{0}\) & 0.5043 & & GWO & \(2.65\times 10^{-1}\) & \(1.33\times 10^{0}\) & 0.2052 \\  & PSO & \(1.00\times 100\) & \(9.74\times 10^{-10}\) & 0.2299 & & PSO & \(2.75\times 10^{0}\) & \(1.55\times 10^{0}\) & 0.1120 \\  & SCA & \(5.84\times 10^{-1}\) & \(3.88\times 10^{-1}\) & 0.4031 & & SCA & \(5.86\times 10^{-1}\) & \(3.14\times 10^{0}\) & 0.1917 \\ F6 & SSA & \(2.39\times 10^{0}\) & \(2.68\times 10^{-1}\) & 0.4361 & & SGA & \(1.41\times 10^{1}\) & \(6.96\times 10^{0}\) & 0.3525 \\  & WOA & \(9.46\times 10^{-1}\) & \(6.79\times 10^{-2}\) & 0.1927 & & WOA & \(0\) & 0 & 0.1428 \\  & GEO & \(2.60\times 10^{0}\) & \(4.06\times 10^{-1}\) & 0.9985 & & GEO\_DIS & \(4.26\times 10^{-16}\) & \(3.01\times 10^{-15}\) & 0.8278 \\  & GEO & \(2.01\times 10^{-1}\) & \(2.86\times 10^{-1}\) & 0.9769 & & GEO\_DIS & \(4.26\times 10^{-16}\) & \(3.01\times 10^{-15}\) & 0.7984 \\  & IGEO & 0 & 0 & 0 & 0.8386 & & GEO\_DIS & \(0\) & 0 & 0.8366 \\  & BOA & \(4.56\times 10^{-12}\) & \(1.05\times 10^{-12}\) & 0.5778 & & GWO & \(1.40\times 10^{-16}\) & \(3.28\times 10^{-17}\) & 0.4964 \\  & PSO & \(1.49\times 10^{-22}\) & \(9.74\times 10^{-22}\) & 0.2717 & & SCA & \(1.57\times 10^{-10}\) & \(8.96\times 10^{-11}\) & 0.4437 \\ F8 & SSA & \(3.11\times 10^{-23}\) & \(1.43\times 10^{-23}\) & 0.5102 & & WOA & \(-1.80\times 10^{-1}\) & \(3.88\times 10^{-1}\) & 0.2832 \\  & GEO & \(6.93\times 10^{-21}\) & \(1.61\times 10^{-20}\) & 0.9595 & & GEO\_DIS & \(1.61\times 10^{-20}\) & 0.9595 \\  & GEO\_DIS & \(-2.38\times 10^{-1}\) & \(4.28\times 10^{-1}\) & 0.9696 & & GEO\_DIS & \(-1.00\times\[MAE=\frac{\sum\limits_{i=1}^{N_{f}}|m_{i}-o_{i}|}{N_{f}}, \tag{16}\]  
where \(N_{f}\) is the number of benchmark functions, \(m_{i}\) is the average of the optimal results generated by the algorithm, and \(o_{i}\) is the corresponding theoretical optimal value.