# A Hybrid Adaptive Particle Swarm Optimization Algorithm for Enhanced Performance
## 6 Conclusions and Future Work  
With the rapid advancement of intelligent population optimization algorithms, researchers have proposed numerous novel and effective population-based optimization methods, resulting in significant achievements in related optimization research. The evolution of algorithmic improvement strategies is keeping pace with contemporary developments, highlighting the vast potential of population intelligence algorithms. This paper focuses on the particle swarm optimization algorithm, enhancing it through four distinct improvement strategies and ultimately proposing an adaptive selection PSO algorithm. To validate the effectiveness and applicability, we conducted a series of test experiments that compared the improved algorithm against the standard particle swarm algorithm, and other metaheuristic algorithms on multiple benchmark test functions. The experimental results indicate that our algorithm shows the better performance in accuracy, stability and convergence. To verify the application effect of the algorithm in practice, we applied the improved algorithm to real-world engineering applications, comparing its results with optimal solutions derived from other metaheuristic algorithms. The experimental results indicate that our algorithm surpasses other comparative algorithms in both optimality and developmental efficiency. The enhancements significantly boost its optimization capabilities, resulting in a reduced computational burden, accelerated convergence speed, and robust performance, enabling more better solutions in various engineering application problems. Although the performance of the algorithm has been enhanced, there is still room for further improvement. For example, mechanisms such as genetic algorithms and simulated annealing can be integrated to enhance the global search capability or combined with deep learning [36], recurrent neural networks [37; 38], and graph neural networks [39] \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Target** & **APSO** & **GWO** & **WOA** & **SSA** & **BOA** \\ \hline X1 & 3.50199 & 3.50100 & 3.51049 & 3.50001 & 3.46810 \\ X2 & 0.70018 & 0.70000 & 0.70000 & 0.70000 & 0.72225 \\ X3 & 17.00134 & 17.00000 & 17.99377 & 17.00840 & 17.90395 \\ X4 & 7.76516 & 8.30000 & 8.00951 & 7.92448 & 7.55602 \\ X5 & 8.09576 & 8.19997 & 8.30000 & 7.98620 & 7.81613 \\ X6 & 3.89346 & 3.83175 & 3.81628 & 3.89522 & 3.89545 \\ X7 & 5.49781 & 5.50000 & 5.50000 & 5.50000 & 5.37177 \\ \hline
**Optimal value** & **1343.7430** & 1344.6980 & 1348.9670 & 1353.1812 & 7433E+13 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: The optimal values of various swarm optimization algorithms for reducer design. to optimize the hyperparameters; the dimensionality disaster can be mitigated and the computational efficiency can be improved by subspace decomposition, parallel computing and sparse coding; and the inertia weights and acceleration coefficients can be dynamically adjusted using reinforcement-based learning or fuzzy logic to balance the local and global exploration capabilities. Conceptualization, Z.J. and L.-B.H. ; Methodology, D.Z. and X.-Y.L. ; Validation, Z.J. and X.-Y.L. ; Formal analysis, L.-B.H. ; Investigation, D.Z. ; Writing--original draft, Z.J. and X.-Y.L. ; Writing--review & editing, L.-B.H. ; Visualization, D.Z. All authors have read and agreed to the published version of the manuscript. This work was supported by the Scientific Research Start-up Funds of Guangdong Ocean University under Grant 060302112201; the Scientific Research Innovation Team Project of Guangxi Minzu Normal University under Grant KYTD202406; and the Integrated Characteristic Construction Project of \"Institution (Research Institute)-Discipline (Degree Program)-Team (Think Tank)-Innovation Platform-Incubation Project\" at Guangxi Minzu Normal University under Grant 1024/10300130. Not applicable. The original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding author.