# A Hybrid Adaptive Particle Swarm Optimization Algorithm for Enhanced Performance
## 4 Experiments
### Comparative Analysis of the Enhanced Algorithm and the Alternative PSO Optimization Techniques  
To evaluate the overall performance of the enhanced algorithm, we conducted a series of tests using 10 functions as a benchmark. The detailed results of these evaluations are shown in Table 4. As shown in Table 4, the improved algorithm APSO has calculated the mean, standard deviation, and optimal values by randomly comparing ten different test functions. The results indicate that the improved APSO algorithm demonstrates superior performance across most of the test functions, achieving the global minimum on \(F_{14}\). Based on the optimal values, the APSO algorithm ranks first among the nine functions and second on \(F_{5}\). Its mean, standard deviation, and optimal value outperform those of other algorithms in most cases, with the particularly impressive optimal value reflecting the stability of the improved algorithm. In this set of test functions, the algorithm's optimal value significantly impacts the results, aligning closely with the theoretical optimal value of the test function. This illustrates the improvement of the improved algorithm in terms of the effectiveness and feasibility of the optimization search. It is worth mentioning that several PSO control algorithms obtain the same average and optimal values on the \(F_{10}\) function, which reflects the fact that the control algorithms tend to fall into local optimality.  
Figure 4 illustrates the convergence effects of the improved APSO algorithm compared to the NIPSO, IMPSO, CLPSO, and IFEHPSO algorithms across various test functions. As evidenced by the convergence curve graphs, the improved APSO algorithm converges  
Figure 3: Convergence curves of the algorithms APSO and PSO for 200 iterations on nine functions.  
significantly faster than the other particle swarm improvement algorithms in most cases after 200 iterations, quickly reaching the optimal level. Among these, the convergence rates of the improved APSO algorithm on functions \(F_{1}\), \(F_{2}\), \(F_{3}\), and \(F_{4}\) are nearly identical, with a faster convergence speed compared to other algorithms. This suggests that the improved algorithm effectively enhances convergence speed.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Function** & **Algorithm** & \(\mathbf{V_{avg}}\) & \(\mathbf{V_{std}}\) & \(\mathbf{V_{opt}}\) \\ \hline \multirow{6}{*}{\(F_{1}\)} & APSO & 2.51E-149 & 6.89E-149 & 8.89E-156 \\  & NIPSO & 1.57E-11 & 8.45E-1 & 1.89E-51 \\ \cline{1-1}  & IMPPSO & 5.76E-02 & 2.39E-01 & 2.93E-38 \\ \cline{1-1}  & CLPSO & 1.30E+01 & 6.59E+00 & 2.39E-05 \\ \cline{1-1}  & IFEHPSO & 2.47E-05 & 3.83E-05 & 4.81E-08 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Performance comparison of the improved algorithm APSO with other representative algorithms on 10 functions, where \(V_{avg}\), \(V_{std}\) and \(V_{opt}\) denote the average, standard deviation and optimal values of the solution, respectively.  
Figure 4: Convergence curves of the proposed algorithm APSO and the four other representative algorithms of for 200 iterations on nine functions.