# Composing Multiple Online Exams: The Bees Algorithm Solution
## 4 Experimental Design and Results
Based on the outcomes presented in Table 4 and Figure 4, it is evident once again that the BA generated exams with smaller fitness values compared to all other competing methods. This indicates that the exams produced by the BA were closer to the desired _DLR_. However, it should be noted that the two variants of PSO achieved an optimal success rate, which the BA did not attain, albeit with a small margin. Nevertheless, the BA exhibited a significantly higher success rate compared to the RA and SA. For standard deviation, both the BA and PSO methods demonstrated comparable values, suggesting stability across different runs for the obtained results. In contrast, the RA and SA exhibited much higher deviations, indicating instability in the outcomes across multiple runs. On the other hand, the BA once again fell short of achieving the desired overlap percentage, as calculated using our method. Figure 5 illustrates the runtime behavior (in seconds) of the Bees Algorithm when varying the number of exams for question banks of different sizes. It can be observed from the figure that as the size of the question bank increases, the runtime also significantly increases, which is expected. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Algorithm** & **Number of** **Exams** & **Difficulty** **Level** & **Number of** **Runs** & **Successful** **Solutions** & **Average** **Fitness** & **Std** **Deviation** & **Average** **Overlap** \\ \hline \multirow{4}{*}{BA} & 100 & 0.5 & 10 & 949 & \(3.26\times 10^{-5}\) & \(3.08\times 10^{-5}\) & 0.93 \\  & 200 & 0.5 & 10 & 1346 & \(3.32\times 10^{-5}\) & \(2.95\times 10^{-5}\) & 0.96 \\  & 400 & 0.5 & 10 & 3841 & \(3.34\times 10^{-5}\) & \(2.95\times 10^{-5}\) & 0.98 \\ \hline \multirow{4}{*}{PMPSO [2]} & 100 & 0.5 & 10 & 1000 & \(4.91\times 10^{-5}\) & \(2.85\times 10^{-5}\) & 0.16 \\  & 200 & 0.5 & 10 & 2000 & \(4.79\times 10^{-5}\) & \(2.92\times 10^{-5}\) & 0.16 \\  & 400 & 0.5 & 10 & 4000 & \(4.80\times 10^{-5}\) & \(2.89\times 10^{-5}\) & 0.16 \\ \hline \multirow{4}{*}{SPSO [2]} & 100 & 0.5 & 10 & 1000 & \(4.72\times 10^{-5}\) & \(2.84\times 10^{-5}\) & 0.16 \\  & 200 & 0.5 & 10 & 2000 & \(4.78\times 10^{-5}\) & \(2.88\times 10^{-5}\) & 0.16 \\  & 400 & 0.5 & 10 & 4000 & \(4.85\times 10^{-5}\) & \(2.89\times 10^{-5}\) & 0.16 \\ \hline \multirow{4}{*}{RA [14]} & 100 & 0.5 & 10 & 63 & \(1.28\times 10^{-3}\) & \(1.25\times 10^{-3}\) & 0.16 \\  & 200 & 0.5 & 10 & 125 & \(1.32\times 10^{-3}\) & \(1.28\times 10^{-3}\) & 0.16 \\  & 400 & 0.5 & 10 & 291 & \(1.33\times 10^{-3}\) & \(1.32\times 10^{-3}\) & 0.16 \\ \hline \multirow{4}{*}{SA [9]} & 100 & 0.5 & 10 & 94 & \(1.56\times 10^{-3}\) & \(1.53\times 10^{-3}\) & 0.16 \\  & 200 & 0.5 & 10 & 205 & \(1.47\times 10^{-3}\) & \(1.46\times 10^{-3}\) & 0.16 \\ \cline{1-1}  & 400 & 0.5 & 10 & 388 & \(1.55\times 10^{-3}\) & \(1.55\times 10^{-3}\) & 0.16 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Algorithms’ results when changing the number of exams using the small question bank. Figure 5: Bees Algorithm’s runtime when changing the number of exams. The subsequent experiment involves modifying the required difficulty level (\(DLR\)) using the large question bank. The results of all algorithms for this experiment are presented in Table 5, while Figure 6 provides a side-by-side comparison of the algorithms in terms of their average fitness values. From these findings, it can be observed that the BA outperforms the PSO methods in terms of average fitness in three out of five instances (\(DLR\) = 0.4, 0.5, and 0.6), while having a slightly worse fitness for a \(DLR\) = 0.7, and much worse fitness for a \(DLR\) = 0.3. Nevertheless, the BA outperforms the RA and SA consistently in all instances. Also, the BA and both PSO algorithms demonstrate comparable standard deviations in most instances, outperforming the RA and SA.