## 5 Testing the Proposed Algorithm
### Boxplots of execution times for each input instance  
The experimental results presented in Tables 4 and 5 and Figure 3 demonstrate that the average timetables produced by the proposed algorithm (local version of PSO) were very close to the best timetables found. This fact highlights the algorithm's stability and efficiency. Moreover, results presented in Tables 4 and 5 and Figure 4 indicate that its execution time depended mainly on the presence of co-teaching cases. More precisely, input instances involving co-teaching required a much longer execution time compared to the ones that did not involve co-teaching. In fact, it can be statistically proven that the average execution time was linearly correlated to the quantity of teaching hours for input instances without co-teaching. Next, we present the best scores achieved by the integer programming method introduced by [PERSON] et al. (2012) in Table 6.  
Figure 4: Box plots of execution times for each input instance (after 30 Monte Carlo runs). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & & \multicolumn{2}{c}{**CSO** [11]} & \multicolumn{2}{c}{**Local Version of PSO**} \\
**Instance** & & \multicolumn{2}{c}{**Score**} & \begin{tabular}{c} **Exec. Time** \\ **(min)** \\ \end{tabular} & \
\begin{tabular}{c} **Score** \\ **(min)** \\ \end{tabular} &
\begin{tabular}{c} **Exec. Time** \\ **(min)** \\ \end{tabular} \\ \hline \multirow{4}{*}{1} & best & 11 & 25 min 16 s & **7** & 37 min 17 s \\  & worst & 23 & 30 min 11 s & 20 & 40 min 42 s \\  & Ave. & 16.4 & 28 min 24 s & 12.97 & 38 min 2 s \\  & STD & 2.5 & 1 min 11 s & 2.35 & 2 min \\  & CV & 15\% & 4.16\% & 18.1\% & 5.25\% \\ \hline \multirow{4}{*}{2} & best & 18 & 32 min 30 s & **13** & 44 min 3 s \\  & worst & 30 & 37 min 37 s & 21 & 48 min 11 s \\  & Ave. & 22.83 & 35 min 12 s & 17.3 & 45 min 10 s \\  & STD & 2.7 & 1 min 6 s & 1.65 & 1 min 5 s \\  & CV & 12\% & 3.1\% & 9.5\% & 2.2\% \\ \hline \multirow{4}{*}{3} & best & 5 & 2 min 51 s & **4** & 1 min 20 s \\  & worst & 10 & 4 min 27 s & 10 & 1 min 50 s \\  & Ave. & 7.5 & 3 min 42 s & 8.3 & 1 min 40 s \\  & STD & 0.96 & 24 s & 1.7 & 15 s \\  & CV & 12.8\% & 10.8\% & 20.5\% & 15\% \\ \hline \multirow{4}{*}{4} & best & 5 & 7 min 35 s & **3** & 6 min 45 s \\  & worst & 14 & 9 min 42 s & 10 & 10 min 15 s \\  & Ave. & 9.67 & 8 min 42 s & 7.25 & 9 min 10 s \\  & STD & 1.87 & 35 s & 1.6 & 47 s \\  & CV & 19.3\% & 6.7\% & 22\% & 7.5\% \\ \hline \multirow{4}{*}{5} & best & 0 & 1 min 57 s & 0 & 1 min 10 s \\  & worst & 1 & 2 min 50 s & 3 & 1 min 40 s \\  & Ave. & 0.13 & 2 min 13 s & 0.88 & 1 min 20 s \\  & STD & 0.34 & 13 s & 0.99 & 12 s \\  & CV & \(-\) & 9.5\% & \(-\) & 15\% \\ \hline \multirow{4}{*}{7} & best & 24 & 42 min 13 s & **6** & 67 min 19 s \\  & worst & 47 & 49 min 20 s & 26 & 68 min 30 s \\  & Ave. & 34.7 & 45 min 42 s & 18.6 & 67 min 45 s \\  & STD & 5.98 & 2 min 18 s & 4 & 15 s \\  & CV & 17\% & 5\% & 21.5\% & 0.37\% \\ \hline \multirow{4}{*}{8} & best & 11 & 1 min 9 s & 11 & 40 s \\  & worst & 12 & 1 min 25 s & 12 & 50 s \\  & Ave. & 11.03 & 1 min 18 s & 11.2 & 46 s \\  & STD & 0.18 & 4 s & 0.39 & 3 s \\  & CV & 1.6\% & 5.4\% & 3.5\% & 6.5\% \\ \hline \multirow{4}{*}{9} & best & 2 & 2 min 51 s & 2 & 1 min 53 s \\  & worst & 2 & 3 min 24 s & 4 & 2 min 10 s \\  & Ave. & 2 & 3 min 6 s & 2.5 & 2 min 1 s \\  & STD & 0 & 7 s & 0.74 & 10 s \\  & CV & 0\% & 3.9\% & \(-\) & 8.3\% \\ \hline \multirow{4}{*}{10} & best & 10 & 2 min 20 s & 10 & 1 min 29 s \\  & worst & 12 & 2 min 51 s & 13 & 1 min 40 s \\  & Ave. & 10.6 & 2 min 30 s & 11.4 & 1 min 34 s \\  & STD & 0.55 & 10 s & 0.97 & 7 s \\  & CV & 5.2\% & 6.8\% & 8.5\% & 7.4\% \\ \hline \multirow{4}{*}{11} & best & 18 & 4 min 52 s & 19 & 2 min 57 s \\  & worst & 20 & 7 min 11 s & 23 & 3 min 15 s \\  & Ave. & 18.67 & 5 min 38 s & 20.5 & 3 min 5 s \\  & STD & 0.6 & 39 s & 1.63 & 13 s \\  & CV & 3.2\% & 11.6\% & 7.9\% & 7.2\% \\ \hline \hline \end{tabular}
\end{table} 
Table 5: CSO algorithm [11] versus local-based PSO (The best score between the two algorithms is indicated by bold).