# Research and Application of an Improved Sparrow Search Algorithm
## 5 Discussion and Conclusions  
In this paper, we propose an improved sparrow search algorithm by considering problems such as the poor optimization-seeking ability of current heuristic algorithms in multi-objective association rule mining. The method employs an adaptive Weibull distribution to enhance the ability of the algorithm to jump out of the local optimum in different iteration periods. An enhancement search strategy and a multidirectional learning strategy are introduced, to expand the search range of population individuals. The main conclusions of this paper can be summarized in two aspects: (1) Firstly, comparing with SSA in 10 standard function tests, its optimization searching accuracy is improved by tens of orders of magnitude in most of the functions; at the same time, the standard deviation performs much better and, on the other hand, the convergence speed is also improved, which proves the effectiveness of the improved strategy in this paper. (2) Applying the improved algorithm to multi-objective association rule mining was the final research purpose of this paper. On five different sizes of datasets, the AWSSA took the lead in multiple objective function values, especially on two large-scale datasets, Abalone and Wine. The lift was improved by about 1.5 times compared with SSA, and the confidence was also improved by about 5 percent. On the other hand, while maintaining the high quality of association rules obtained, the AWSSA did not mine the largest number of rules, but combined with the performance on function values, the AWSSA was significantly more comprehensive.  
This study confirms that the AWSSA has excellent performance in multi-objective association rule mining. However, considering the limitations of the application scenarios in this paper, they need to be applied to more fields in future work, such as cluster analysis and other directions to verify the performance of the AWSSA. Meanwhile, considering the complexity of the algorithm, a parallel version of this paper's algorithm could be proposed in the next step, and parallelization could accelerate the search process and reduce the overall computation time, especially when coping with larger datasets in practical applications.  
Conceptualization, L.H. and D.W.; methodology, L.H.; software, L.H.; validation, L.H. and D.W.; formal analysis, L.H. and D.W.; investigation, L.H. and D.W.; resources,  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & **Algorithm** & **Iris** & **Australian** & **Flag** & **Abalone** & **Wine** \\ \hline \multirow{4}{*}{Mean} & SSA & 8.8 & 20.05 & 17.7 & 23.35 & 21.65 \\  & WOA & 9.5 & 15.5 & 14.0 & 14.6 & 31.45 \\  & PSO & 10.6 & 19.45 & 14.2 & 19.05 & 18.9 \\  & SMA & 19.1 & 25.5 & 17.9 & 20.8 & 19.6 \\  & AWSSA & 9.2 & 25.3 & 24.15 & 29.65 & 21.25 \\ \hline \multirow{4}{*}{Std} & SSA & 1.32 & 3.70 & 2.65 & 4.65 & 4.65 \\  & WOA & 3.80 & 4.12 & 6.85 & 2.83 & 14.30 \\ \cline{1-1}  & PSO & 3.13 & 5.67 & 5.30 & 2.45 & 2.40 \\ \cline{1-1}  & SMA & 20.29 & 13.59 & 14.81 & 10.85 & 13.20 \\ \cline{1-1}  & AWSSA & 1.24 & 3.10 & 4.25 & 4.65 & 4.88 \\ \hline \hline \end{tabular}
\end{table}
Table 7: Average number of rules composing the Pareto front.  
D.W.; data curation, L.H. and D.W.; writing--original draft preparation, L.H.; writing--review and editing, L.H. and D.W.; visualization, L.H. and D.W.; supervision, L.H. and D.W.; project administration, L.H. and D.W.; funding acquisition, D.W. All authors have read and agreed to the published version of the manuscript.  
This research was supported in part by the National Science Foundation of China under Grant 62362030.  
Not applicable.  
Publicly available datasets were analyzed in this study. This data can be found here: [[https://archive.ics.uci.edu/](https://archive.ics.uci.edu/)]([https://archive.ics.uci.edu/](https://archive.ics.uci.edu/)).  
The authors declare no conflicts of interest.