## 7 Experimentation and Analysis
### Algorithm Performance Validation
#### 7.1.1 Algorithm Convergence Accuracy Comparison
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Function**} & \multirow{2}{*}{**Algorithm**} & \multirow{2}{*}{\begin{tabular}{c} **Optimal Fitness** \\ **Value (Best)** \\ \end{tabular} } & \begin{tabular}{c} **Optimal Average** \\ **Fitness Value** \\ **(Mean)** \\ \end{tabular} & \begin{tabular}{c} **Wost Fitness Value** \\ **(Wors0)** \\ \end{tabular} & \
\begin{tabular}{c} **Standard Deviation** \\ **(std)** \\ \end{tabular} &
\begin{tabular}{c} **Execution Time** \\ **(time/s)** \\ \end{tabular} \\ \hline \multirow{4}{*}{F1} & SOA & 0.10189 & 5.2172 & 22.5419 & 6.4643 & 0.39195 \\  & GLSOAG & 0 & 0 & 0 & 0 & 0.498 \\  & PSO & 848.517 & 1869.6404 & 3908.9756 & 815.7032 & 0.12593 \\  & BSA & 73,522.0487 & 101,333.1552 & 143,129.9851 & 17,564.2267 & 0.071708 \\ \hline \multirow{4}{*}{F2} & SOA & 0.006745 & 0.068868 & 0.19523 & 0.049741 & 0.39925 \\  & GLSOAG & 0 & 0 & 0 & 0.50927 \\  & PSO & 15.9454 & 33.1065 & 75.0612 & 14.7272 & 0.13522 \\  & BSA & 103.5301 & 104,582.873.94747 & 2,948,498.9857.917.849 & 537,482,491.234.5394 & 0.086811 \\ \hline \multirow{4}{*}{F3} & SOA & 2982017 & 4283.2554 & 9427.3995 & 2415.4114 & 1.1094 \\  & GLSOAG & 0 & 0 & 0 & 0 & 1.2398 \\  & PSO & 4152.5825 & 1330.3578 & 33,716.7383 & 767,1933 & 0.82269 \\  & BSA & 117,226.8808 & 1,361,575.7543 & 4,584,154.2511 & 1,146,319.7512 & 0.14069 \\ \hline \multirow{4}{*}{F4} & SOA & 32463 & 12.3258 & 35.9679 & 6.4512 & 0.40825 \\  & GLSOAG & 0 & 0 & 0 & 0 & 0.49713 \\  & PSO & 85.62 & 19.2599 & 27.1729 & 4.0878 & 0.12995 \\  & BSA & 85.529 & 94.5168 & 97.7731 & 2,4046 & 0.067545 \\ \hline \multirow{4}{*}{F5} & SOA & 37.2416 & 1153.4488 & 13218.3689 & 2559.3805 & 0.48161 \\  & GLSOAG & 26.4181 & 28.0335 & 28.8747 & 0.72861 & 0.58244 \\  & PSO & 36.179563 & 1920.30926 & 611,417.0837 & 127,599.8267 & 0.20264 \\  & BSA & 182.7788,829.9194 & 414,347,488.6429 & 782,024,183.872 & 131,350,299.603 & 0.081211 \\ \hline \multirow{4}{*}{F6} & SOA & 1.3364 & 2.6604 & 5.1701 & 1.1264 & 0.40324 \\  & GLSOAG & 2.8421 & 3.3503 & 4.3602 & 0.38173 & 0.51008 \\  & PSO & 741.7764 & 1555.5296 & 3973.8031 & 655.1895 & 0.12772 \\  & BSA & 65,881.8923 & 99.757.7783 & 126,563.8163 & 15,900.1703 & 0.069297 \\ \hline \multirow{4}{*}{F7} & SOA & 0.027411 & 0.11834 & 0.24167 & 0.056301 & 0.94493 \\  & GLSOAG & 1.9783 \(\times\) 10 \({}^{5}\) & 0.0041197 & 0.0024492 & 0.0046695 & 1.10664 \\  & PSO & 0.24647 & 2.3547 & 16.6521 & 3.6025 & 0.65944 \\  & BSA & 16.3829 & 37.6198 & 66.7535 & 13.463 & 0.12505 \\ \hline \multirow{4}{*}{F8} & SOA & -411.3306 & -3702.2739 & -3305.0695 & 300.8211 & 0.53173 \\  & GLSOAG & \(-7542.1057\) & -5914.4544 & -4738.9804 & 597.9198 & 0.66205 \\  & PSO & \(-8281.9138\) & \(-6690.496\) & \(-5039.6653\) & 956.78885 & 0.2263 \\  & BSA & \(-2291.5917\) & \(-234.8074\) & 1424.281 & 912.5663 & 0.07873 \\ \hline \multirow{4}{*}{F9} & SOA & 0.04167 & 20.6716 & 66.6697 & 17.495 & 0.4826 \\  & PSO & 175.2434 & 228.7973 & 289.4694 & 29.095 & 0.227 \\  & BSA & 200.7324 & 332.7867 & 434.4687 & 55.8202 & 0.08009 \\ \hline \multirow{4}{*}{F10} & SOA & 0.061061 & 0.58776 & 2.3559 & 0.59806 & 0.50405 \\  & GLSOAG & \(4.4049\times 10^{-16}\) & \(4.4409\times 10^{-16}\) & \(4.4409\times 10^{-16}\) & 0 & 0.5281 \\  & PSO & 6.2356 & 9.1883 & 11.6268 & 1.1818 & 0.24945 \\  & BSA & 19.6193 & 20.109 & 20.6144 & 0.19772 & 0.08905 \\ \hline \multirow{4}{*}{F11} & SOA & 0.22178 & 0.88621 & 1.2442 & 0.21608 & 0.56276 \\  & GLSOAG & 0 & 0 & 0 & 0 & 0.59022 \\  & PSO & \(-9284\) & 15.8564 & 23.9352 & 3.9212 & 0.31196 \\  & BSA & 648.5074 & 925.735 & 115.7598 & 109.3825 & 0.08455 \\ \hline \multirow{4}{*}{F12} & SOA & 0.050399 & 2.5794 & 7.553 & 2.8399 & 1.8174 \\  & GLSOAG & 0.23442 & 0.32958 & 0.50286 & 0.065709 & 1.9678 \\ \cline{1-1}  & PSO & 6.4277 & 70.4202 & 663.4862 & 135.9194 & 1.5425 \\ \cline{1-1}  & BSA & 593,474,501.3352 & 1,129,032,378.01 & 2,086,760,320.8523 & 353,184,502.9145 & 0.21039 \\ \hline \hline \end{tabular}   
and the average fitness value corresponding to the optimal solution (mean).