# Research and Application of an Improved Sparrow Search Algorithm
## 4 Solving Multi-Objective Association Rule Mining with the AWSSA
### Simulation Result Analysis  
Analyzing the experimental results based on Table 6, it can be observed that the AWSSA did not show significant superiority over the other algorithms on smaller datasets, such as the Iris dataset. In these cases, it achieved only a moderate level in terms of three different objective function values. The problem complexity of the smaller datasets was relatively low, resulting in insignificant performance differences between the five algorithms. The AWSSA performed much better in all three objective function values when the number of transactions and the number of dimensions of the dataset increased. It performed especially better in terms of lift, where it was much better than the other algorithms. In addition, the AWSSA also maintained a high level of support and confidence. This suggests that the AWSSA has a very proficient capacity for identifying optimization.  
In Table 7, further analysis shows that the AWSSA found a good number of rules on multiple datasets. In contrast, although the SMA algorithm could also find multiple  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Algorithm**} & \multicolumn{3}{c}{**Iris**} & \multicolumn{3}{c}{**Australian**} & \multicolumn{3}{c}{**Flag**} & \multicolumn{3}{c}{**Abalone**} & \multicolumn{3}{c}{**Wine**} \\  & **Sup** & **Conf** & **Lift** & **Sup** & **Conf** & **Lift** & **Sup** & **Conf** & **Lift** & **Sup** & **Conf** & **Lift** \\ \hline SSA & 0.09 & 0.83 & 27.73 & 0.21 & 0.80 & 100.49 & 0.15 & 0.78 & 57.78 & 0.07 & 0.74 & 230.20 & 0.06 & 0.59 & 598.46 \\ WOA & 0.07 & 0.76 & 61.15 & 0.16 & 0.72 & 117.90 & 0.11 & 0.76 & 48.73 & 0.05 & 0.68 & 324.54 & 0.02 & 0.72 & 471.40 \\ PSO & 0.06 & 0.76 & 51.81 & 0.16 & 0.72 & 82.49 & 0.12 & 0.67 & 39.12 & 0.05 & 0.70 & 574.94 & 0.05 & 0.49 & 381.49 \\ SMA & 0.04 & 0.83 & 43.81 & 0.07 & 0.79 & 59.30 & 0.05 & 0.83 & 47.78 & 0.02 & 0.77 & 465.12 & 0.03 & 0.71 & 209.20 \\ AWSSA & 0.09 & 0.87 & 35.59 & 0.21 & 0.86 & 161.79 & 0.16 & 0.83 & 71.62 & 0.07 & 0.76 & 586.21 & 0.06 & 0.65 & 1183.62 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Average objective function value of Pareto front.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Datasets** & **Rows** & **Binary Attributes** \\ \hline Iris & 150 & 43 \\ Australian & 690 & 98 \\ Flag & 194 & 340 \\ Abalone & 4177 & 83 \\ Wine & 4898 & 117 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Datasets selected for experiments.  
rules, the average objective function values of these rules were relatively low, i.e., the rules were of poor quality. This phenomenon stemmed from the fact that the SMAs fell into local optima in the early stages, where the populations were rapidly clustered together and lacked the ability to break away from the local optima, resulting in a large number of poor-quality solutions in the Pareto-optimal set. The AWSSAs had a strong potential to break away from the local optima, thanks to the Weibull distribution strategy adopted and had excellent exploration capabilities under the augmented search and multidirectional learning strategies. As a result, the AWSSA was able to find a large number of rules while keeping their quality high. This further validates that the AWSSA strikes a good balance between exploration and exploitation.