# Analyzing the Performance of the Multiple-Searching Genetic Algorithm to Generate Test Cases
## 6 Parametric Analysis
### Mutation Operation  
The mutation probabilities used in GAs are usually low [36,37]. Many researchers define the mutation probability as \(M_{p}=1/n\), where n is the length of the chromosome [38, 39, 40]. However, high mutation probabilities increase the searchability in global optima. If the mutation probability is too high, the resulting chromosomes could be similar to those generated by a random search [41]. The mutation operation mechanism of the MSGA specifies that the conservative and explorer chromosomes have different mutation probabilities. [PERSON] et al. (2004) [1] assigned a higher mutation probability for explorer chromosomes to get the optimal solution. In this study, conservative chromosomes were given a mutation probability of \(1/n\) while explorer chromosomes had been tested a mutation probability of \(1/n\) and a high mutation probability, ranging from 0.1 to 0.5 with increments of 0.1 (Table 7). The conservative and explorer chromosomes were applied the mutation operator with one-point. The MSGA was executed 100 times per mutation probability. The optimal mutation probability for MSGA to generate test cases was found to be \(1/n\) and 0.1 (Table 7). The higher mutation probability provides a better global optimum. The different mutation probabilities of conservative and explorer chromosomes can avoid local optima. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Pair of Values** & **\(t\)-Test** & **Mann-Whitney (\(p\)-Value)** \\ \hline uniform (0.8) vs. one-point (0.6) & 0.011437 & \(<\)0.00001 \\ uniform (0.8) vs. one-point (0.7) & 0.016065 & \(<\)0.00001 \\ uniform (0.8) vs. one-point (0.8) & 0.006913 & \(<\)0.00001 \\ uniform (0.8) vs. one-point (0.9) & 0.003068 & \(<\)0.00001 \\ uniform (0.8) vs. one-point (1.0) & 0.000960 & \(<\)0.00001 \\ uniform (0.8) vs. two-point (0.6) & 0.029574 & \(<\)0.00001 \\ uniform (0.8) vs. two-point (0.7) & 0.117917 \({}^{*}\) & \(<\)0.00001 \\ uniform (0.8) vs. two-point (0.8) & 0.033398 & \(<\)0.00001 \\ uniform (0.8) vs. two-point (0.9) & 0.020169 & \(<\)0.00001 \\ uniform (0.8) vs. two-point (1.0) & 0.039893 & \(<\)0.00001 \\ uniform (0.8) vs. uniform (0.6) & 0.115698 \({}^{*}\) & \(<\)0.00001 \\ uniform (0.8) vs. uniform (0.7) & 0.078426 \({}^{*}\) & \(<\)0.00001 \\ uniform (0.8) vs. uniform (0.9) & 0.191008 \({}^{*}\) & \(<\)0.00001 \\ uniform (0.8) vs. uniform (1.0) & 0.161153 \({}^{*}\) & \(<\)0.00001 \\ \hline \hline \end{tabular} \({}^{*}\) is value greater than 0.05.  
\end{table} 
Table 6: Statistical comparison between the uniform with a 0.8 and the others. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Crossover** & **Crossover** & \multicolumn{3}{c}{**Best Value**} & \multicolumn{3}{c}{**Average Value**} & \multicolumn{3}{c}{**Wost Value**} \\ \cline{3-7}
**Operation** & **Probability** & **Time (s)** & **No. of Generations** & **Time (s)** & **No. of Generations** \\ \hline  & 0.6 & 49.1 & 3 & 108.09 & 10.56 & 717.00 & 100 \\  & 0.7 & 42.7 & 2 & 107.96 & 9.83 & 703.20 & 100 \\ One-point & 0.8 & 48.3 & 3 & 116.47 & 11.42 & 709.10 & 100 \\  & 0.9 & 51.1 & 3 & 123.00 & 12.52 & 718.60 & 100 \\  & 1.0 & 42.7 & 2 & 134.84 & 14.36 & 803.30 & 100 \\ \hline  & 0.6 & 47.7 & 3 & 89.08 & 10.15 & 553.20 & 100 \\  & 0.7 & 44.5 & 3 & 81.18 & 8.06 & 633.20 & 100 \\ Two-point & 0.8 & 44.0 & 2 & 90.36 & 10.03 & 690.50 & 100 \\  & 0.9 & 43.3 & 2 & 94.20 & 10.89 & 571.40 & 100 \\  & 1.0 & 43.4 & 2 & 88.70 & 9.85 & 597.90 & 100 \\ \hline  & 0.6 & 49.6 & 3 & 82.65 & 6.96 & 542.30 & 100 \\  & 0.7 & 49.5 & 3 & 84.14 & 7.71 & 617.20 & 100 \\ Uniform & 0.8 & 49.3 & 3 & 76.56 & 5.81 & 1153.30 & 9 \\  & 0.9 & 55.3 & 4 & 83.25 & 6.65 & 667.60 & 100 \\  & 1.0 & 42.2 & 6 & 81.68 & 6.76 & 531.40 & 100 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Effect of crossover operator for test case generation using the MSGA. In this study, we more heavily focused on comparing the 0.1 mutation probability with the others (Table 8).