# A Hybrid Adaptive Particle Swarm Optimization Algorithm for Enhanced Performance
## 4 Experiments
### A Comparison of Our Algorithm APSO with Other Metaheuristic Algorithms  
Based on a comparison of the APSO algorithm with other metaheuristic algorithms in Table 5, APSO ranks among the top two in terms of mean, standard deviation, and optimal value. Notably, the optimal value of the improved APSO algorithm is 0 in the test functions \(F_{9}\), \(F_{13}\), and \(F_{14}\), achieving the best results for these functions. This outcome demonstrates \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Function** & **Algorithm** & \(V_{\text{arg}}\) & \(V_{std}\) & \(V_{opt}\) \\ \hline \multirow{6}{*}{\(F_{2}\)} & APSO & 1.09E-74 & 1.91E-74 & 2.27E-77 \\  & NIPSO & 1.61E-16 & 8.60E-16 & 2.45E-28 \\  & IMPPSO & 7.82E+00 & 3.94E+01 & 1.26E-19 \\  & CLPSO & 8.94E+08 & 3.71E+09 & 8.39E+01 \\  & IFEHPSO & 2.37E-02 & 1.80E-02 & 9.57E-04 \\ \hline \multirow{6}{*}{\(F_{3}\)} & APSO & 5.45E-134 & 2.93E-133 & 5.37E-153 \\  & NIPSO & 3.32E-11 & 1.79E-10 & 1.29E-47 \\  & IMPPSO & 3.71E+00 & 2.80E+01 & 8.26E-35 \\  & CLPSO & 6.79E+02 & 2.77E+02 & 9.67E+01 \\  & IFEHPSO & 5.69E-04 & 1.25E-03 & 1.63E-06 \\ \hline \multirow{6}{*}{\(F_{4}\)} & APSO & 6.36E-75 & 2.12E-74 & 6.09E-78 \\  & NIPSO & 1.10E-21 & 5.06E-21 & 1.68E-33 \\  & IMPPSO & 2.63E-02 & 1.21E-01 & 5.53E-20 \\  & CLPSO & 3.31E+00 & 3.34E+00 & 0.80E+08 \\  & IFEHPSO & 2.73E-03 & 2.83E-03 & 8.62E-05 \\ \hline \multirow{6}{*}{\(F_{5}\)} & APSO & 3.86E+01 & 4.80E+01 & 2.88E+01 \\  & NIPSO & 2.89E+01 & 3.64E-02 & 2.74E+01 \\  & IMPPSO & 1.16E+03 & 4.14E+03 & 2.87E+01 \\  & CLPSO & 9.31E+03 & 9.60E+03 & 5.20E+01 \\  & IFEHPSO & 2.89E+01 & 3.00E-02 & 2.89E+01 \\ \hline \multirow{6}{*}{\(F_{9}\)} & APSO & \(-2.57\)E+52 & 1.38E+53 & \(-7.68\)E+53 \\  & NIPSO & \(-1.77\)E+02 & 1.64E+01 & \(-2.47\)E+02 \\  & IMPPSO & \(-1.77\)E+02 & 3.11E+01 & \(-2.47\)E+02 \\  & CLPSO & \(-1.76\)E+02 & 4.57E+00 & \(-2.41\)E+02 \\  & IFEHPSO & \(-1.77\)E+02 & 2.91E+01 & \(-2.47\)E+02 \\ \hline \multirow{6}{*}{\(F_{10}\)} & APSO & 6.20E-34 & 3.34E-33 & 3.07E-77 \\  & NIPSO & 1.54E-11 & 3.85E-11 & 4.30E-18 \\ \cline{1-1}  & IMPPSO & 4.64E-25 & 1.59E-24 & 2.41E-44 \\ \cline{1-1}  & CLPSO & 1.52E-01 & 4.97E-01 & 3.91E-28 \\ \cline{1-1}  & IFEHPSO & 9.43E-05 & 1.64E-04 & 1.29E-06 \\ \hline \multirow{6}{*}{\(F_{11}\)} & APSO & 2.36E-31 & 4.38E-47 & 2.36E-31 \\ \cline{1-1}  & NIPSO & 5.22E-02 & 1.64E-01 & 1.10E-06 \\ \cline{1-1}  & IMPPSO & 1.94E-04 & 3.59E-04 & 4.68E-07 \\ \cline{1-1}  & CLPSO & 3.07E+12 & 1.16E+13 & 1.21E+07 \\ \cline{1-1}  & IFEHPSO & 1.88E-07 & 3.92E-07 & 3.92E-11 \\ \hline \multirow{6}{*}{\(F_{12}\)} & APSO & 0.00E+00 & 0.00E+00 & 0.00E+00 \\ \cline{1-1}  & NIPSO & 1.35E-14 & 3.31E-14 & 4.77E-25 \\ \cline{1-1}  & IMPPSO & 5.97E-01 & 1.82E+00 & 1.54E-05 \\ \cline{1-1}  & CLPSO & 1.06E-04 & 1.81E-04 & 1.34E-07 \\ \cline{1-1}  & IFEHPSO & 7.65E-08 & 2.28E-07 & 5.62E-11 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: _Cont._the algorithm's accuracy and convergence efficiency in locating the global optimal solution. Although the SSA algorithm surpasses APSO in optimal value for functions \(F_{1}\), \(F_{3}\), and \(F_{4}\), APSO outperforms in overall performance, ranking first in the average results for 7 out of 10 functions, thereby indicating strong performance.