## 4 Experimental Results
### Experiment on the Effect of the Improved PSO Algorithm  
#### 4.3.1 Comparison with Basic Particle Swarm Algorithm  
To further illustrate the advantages of the improved PSO algorithm, experiments were conducted using the basic PSO algorithm and the improved PSO algorithm in the case of a larger number of inputs (large-scale system), and the number of iterations and the time taken to generate the test cases were recorded. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multicolumn{2}{c}{**Project**} & \multicolumn{2}{c}{**INF**} & \multicolumn{2}{c}{**No. of Variables**} \\ \hline RCCS & \(\left(\overline{C_{1}C_{2}}\right)\left(\overline{C_{1}C_{3}}\right)\left( \overline{C_{2}C_{3}}\right)\left(C_{2}\cup\left(\overline{\left((C_{1} \overline{C_{4}})C_{4}\right)\cup(C_{3}C_{4})}\right)\right)\) & 4 \\ \hline \multirow{4}{*}{TCAS II} & \(a(\left(c\cup d\cup e\right)\cup af\cup c(f\cup g\cup h\cup i))\cup(a\cup b)(c \cup d\cup e)i\) & 9 \\  & \(\left(ac\cup bd\right)e\left(\hat{t}\cup\overline{g}\cup i\right)\left( \overline{h}\cup\bar{k}\right)\) & 10 \\  & \(a\overline{b}\overline{c}\overline{d}ef(g\cup\overline{g}(h\cup i))\left( \overline{h}\cup\bar{l}\cup m\right)\) & 13 \\  & \(a\overline{b}\overline{c}(f(g\cup\overline{g}(h\cup i))(\overline{m}\cup d)) \cup\overline{n}(\bar{h}\cup\bar{l}\overline{m})\) & 14 \\ \hline \multicolumn{2}{c}{Large cause–effect graph} & \(\overline{(\overline{a}\cup d)(e\cup h\cup k\cup o)}\left(\overline{b}\cup a \right)\left(\overline{c}\cup a\right)\left(\overline{d}\cup c\right)\left( \overline{d}\cup b\right)\left(\overline{r}\cup a\right)\left(\overline{\bar{ q}\cup h}\right)\left(\overline{p}\cup o\right)\) & 11 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: INF specifications as part of the system. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Project**} & \multicolumn{2}{c}{**Greedy Algorithms**} & \multicolumn{2}{c}{**Heuristic Algorithms**} & \multicolumn{2}{c}{**Algebraic Methods**} & \multirow{2}{*}{**Proposed**} \\  & **IPOG** & **PICT** & **ABCS** & **GSTG** & **TMWOA** & **TConfig** & **Jenny** \\ \hline RCCS & 6 & 5 & 5 & 5 & 6 & 6 & 6 & 5 \\ \hline \multirow{4}{*}{TCAS II} & 8 & 9 & 8 & 8 & 8 & 9 & 8 & 6 \\  & 10 & 9 & 8 & 8 & 8 & 9 & 10 & 6 \\  & 10 & 9 & 8 & 8 & 9 & 9 & 10 & 6 \\  & 10 & 10 & 9 & 9 & 9 & 9 & 10 & 7 \\ \hline Large cause–effect graph & 10 & 9 & 9 & 8 & 9 & 9 & 9 & 7 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Experimental results of different systems. The parameters of the basic particle swarm algorithm used in this study were set as follows: The number of particles was set to 100. Because the coverage of the initially generated test cases into pairs of tests was already high, \(c_{1}\) and \(c_{2}\) were set to 1.2, the \(\omega_{max}\) was set to 0.6, the \(\omega_{min}\) was set to 0.4, and the maximum number of iterations (\(N_{g}\)) was set to 8000. The weight (\(\omega\)) was updated via Equation (14):  
\[\omega=\omega_{max}-\frac{(\omega_{max}-\omega_{min})*iter}{ger} \tag{14}\]  
where \(iter\) is the number of current iterations. The parameters of the improved particle swarm algorithm used in this paper were set as follows: the number of particles was set to 100, \(c_{1}\) and \(c_{2}\) were set to 1.2, the initial value of the \(\omega\) was 0.8, and the maximum number of iterations (\(N_{g}\)) was 8000. The weight (\(\omega\)) was updated via Equation (11), and \(IR_{1}\) was taken as 0.001 and \(IR_{2}\) was taken as 0.002. The test was performed 20 times. The results obtained in each execution are shown in Table 8, and a statistical analysis of the results in Table 8 is shown in Table 9, where NA indicates that the search results exceeded the maximum number of iterations. From Tables 8 and 9, it can be seen that the proposed improved PSO algorithm significantly reduces the number of iterations needed to generate test cases when compared with the basic PSO algorithm, thereby reducing the amount of time required to generate test cases.