## Appendix B  
Appendix B shows the experimental results of the algorithm for the remaining 11 test functions on the CEC2005 function test set, with population size 30, maximum 200 iterationsper iteration, and 30 consecutive experiments. The test function images and algorithm convergence curves are shown in Figure A3, and the optimization search results are shown in Table A1.  
Figure A3: Graph of test functions F13–F23 and convergence curves. Subgraphs F13 to F23 represent the experimental results of the SOA, GLSOAG, PSO, and BSA algorithms on test functions F13 to F23, with a population size set to 30 and a maximum of 200 iterations per run, conducted over 30 consecutive trials.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Function** & **Algorithm** & \begin{tabular}{c} **Optimal Fitness** \\ **Value (Best)** \\ \end{tabular} & \begin{tabular}{c} **Optimal Average** \\ **Fitness Value (Mean)** \\ \end{tabular} & \
\begin{tabular}{c} **Worst Fitness Value** \\ **(Worst)** \\ \end{tabular} &
\begin{tabular}{c} **Standard Deviation** \\ **(std)** \\ \end{tabular} \\ \hline \multirow{4}{*}{F13} & SOA & 4.9798 & 51.6276 & 590.287 & 108.3764 \\  & GLSOAG & 1.9928 & 2.2889 & 2.5467 & 0.13587 \\  & PSO & 18.1896 & 53.7617.386 & 474,553.7391 & 99,723.3998 \\  & BSA & 949,836,950.6584 & 1,896,355,671.2548 & 2,857,432,666.067 & 516,219,373.3826 \\ \hline \multirow{4}{*}{F14} & SOA & 0.99817 & 2.3495 & 7.8757 & 1.6055 \\  & GLSOAG & 0.998 & 4.1338 & 12.6705 & 3.9855 \\  & PSO & 0.998 & 0.998 & 0.998 & 1.9729 \(\times 10^{-7}\) \\  & BSA & 0.99803 & 289.6592 & 499.9984 & 236.757 \\ \hline \multirow{4}{*}{F15} & SOA & 0.000312 & 0.00050141 & 0.0007643 & 0.00012827 \\  & GLSOAG & 0.0003244 & 0.00057332 & 0.0014677 & 0.00020271 \\  & PSO & 0.00082966 & 0.0074862 & 0.02979 & 0.0096691 \\  & BSA & 0.0029545 & 0.18329 & 3.1969 & 0.58528 \\ \hline \multirow{4}{*}{F16} & SOA & \(-1.0316\) & \(-1.0316\) & \(-1.0316\) & \(1.9184\times 10^{-6}\) \\  & GLSOAG & \(-1.0316\) & \(-1.0316\) & \(-1.0315\) & \(2.2611\times 10^{-5}\) \\  & PSO & \(-1.0316\) & \(-1.0315\) & \(-1.0308\) & \(0.00017922\) \\  & BSA & \(-1.0316\) & \(-1.0316\) & \(-1.0316\) & \(1.8047\times 10^{-8}\) \\ \hline \multirow{4}{*}{F17} & SOA & 0.39789 & 0.39797 & 0.39827 & 0.00010292 \\  & GLSOAG & 0.39789 & 0.39915 & 0.40409 & 0.0013292 \\  & PSO & 0.39789 & 0.39792 & 0.398 & \(3.2008\times 10^{-5}\) \\  & BSA & 0.39789 & 0.57961 & 2.3596 & 0.52479 \\ \hline \multirow{4}{*}{F18} & SOA & 3 & 3.0001 & 3.0012 & 0.00024521 \\  & GLSOAG & 3 & 3.0003 & 3.0013 & 0.0003614 \\  & PSO & 3 & 3.0027 & 3.022 & 0.0048401 \\  & BSA & 3 & 6.6575 & 84.2493 & 15.5486 \\ \hline \multirow{4}{*}{F19} & SOA & \(-3.8628\) & \(-3.8613\) & \(-3.8588\) & 0.0011141 \\  & GLSOAG & \(-3.8626\) & \(-3.8594\) & \(-3.842\) & 0.0043059 \\  & PSO & \(-3.8628\) & \(-3.8606\) & \(-3.8549\) & 0.0033719 \\  & BSA & \(-3.8628\) & \(-3.8205\) & \(-3.5396\) & 0.075609 \\ \hline \multirow{4}{*}{F20} & SOA & \(-3.3204\) & \(-3.2647\) & \(-3.1221\) & 0.062981 \\  & GLSOAG & \(-3.3185\) & \(-3.2366\) & \(-3.1488\) & 0.065412 \\  & PSO & \(-3.3217\) & \(-3.0713\) & \(-1.7053\) & 0.29896 \\  & BSA & \(-3.322\) & \(-3.1994\) & \(-2.1964\) & 0.28526 \\ \hline \multirow{4}{*}{F21} & SOA & \(-9.8569\) & \(-5.4287\) & \(-2.6035\) & 1.505 \\  & GLSOAG & \(-8.8325\) & \(-5.2406\) & \(-4.9738\) & 0.84682 \\  & PSO & \(-10.1532\) & \(-7.9739\) & \(-2.6159\) & 2.8463 \\  & BSA & \(-10.1532\) & \(-4.573\) & \(-0.55998\) & 3.3014 \\ \hline \multirow{4}{*}{F22} & SOA & \(-10.3465\) & \(-5.7904\) & \(-5.0634\) & 1.7437 \\  & GLSOAG & \(-10.1537\) & \(-5.4932\) & \(-4.9498\) & 1.3779 \\ \cline{1-1}  & PSO & \(-10.4029\) & \(-9.0311\) & \(-1.8364\) & 2.6623 \\ \cline{1-1}  & BSA & \(-10.4029\) & \(-4.6252\) & \(-0.65267\) & 3.2957 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Experimental results of F13–F23 test functions.