# Composing Multiple Online Exams: The Bees Algorithm Solution
## 4 Experimental Design and Results
\begin{table}
\begin{tabular}{l l l l l l l l} \hline \hline
**Algorithm** & **Number of** & **Difficulty** & **Number of** & **Success** & **Average** & **Std** & **Average** \\
**Large QB** & **Exams** & **Level** & **Runs** & **Rate** & **Fitness** & **Deviation** & **Overlap** \\ \hline \multirow{3}{*}{Bees Algorithm (BA)} & 100 & 0.5 & 10 & 942 & 3.85 \(\times\) 10\({}^{-5}\) & 3.14 \(\times\) 10\({}^{-5}\) & 0.36 \\  & 200 & 0.5 & 10 & 1905 & 3.72 \(\times\) 10\({}^{-5}\) & 3.08 \(\times\) 10\({}^{-5}\) & 0.56 \\  & 400 & 0.5 & 10 & 3375 & 3.82 \(\times\) 10\({}^{-5}\) & 3.15 \(\times\) 10\({}^{-5}\) & 0.75 \\ \hline \multirow{3}{*}{Parallel Migration PSO (PMPSO) [2]} & 100 & 0.5 & 10 & 1000 & 4.93 \(\times\) 10\({}^{-5}\) & 2.92 \(\times\) 10\({}^{-5}\) & 0.009 \\  & 200 & 0.5 & 10 & 2000 & 4.74 \(\times\) 10\({}^{-5}\) & 2.89 \(\times\) 10\({}^{-5}\) & 0.009 \\  & 400 & 0.5 & 10 & 4000 & 4.76 \(\times\) 10\({}^{-5}\) & 2.88 \(\times\) 10\({}^{-5}\) & 0.009 \\ \hline \multirow{3}{*}{Sequential PSO (SPSO) [2]} & 100 & 0.5 & 10 & 1000 & 4.72 \(\times\) 10\({}^{-5}\) & 2.86 \(\times\) 10\({}^{-5}\) & 0.009 \\  & 200 & 0.5 & 10 & 2000 & 4.77 \(\times\) 10\({}^{-5}\) & 2.88 \(\times\) 10\({}^{-5}\) & 0.009 \\  & 400 & 0.5 & 10 & 4000 & 4.78 \(\times\) 10\({}^{-5}\) & 2.87 \(\times\) 10\({}^{-5}\) & 0.009 \\ \hline \multirow{3}{*}{Random Algorithm (RA) [14]} & 100 & 0.5 & 10 & 151 & 6.41\(\times\) 10\({}^{-4}\) & 6.40\(\times\) 10\({}^{-4}\) & 0.009 \\  & 200 & 0.5 & 10 & 263 & 6.55\(\times\) 10\({}^{-4}\) & 6.39\(\times\) 10\({}^{-4}\) & 0.009 \\  & 400 & 0.5 & 10 & 552 & 6.27\(\times\) 10\({}^{-4}\) & 6.29\(\times\) 10\({}^{-4}\) & 0.009 \\ \hline \multirow{3}{*}{Simulated Annealing (SA) [9]} & 100 & 0.5 & 10 & 178 & 9.07\(\times\) 10\({}^{-4}\) & 9.48\(\times\) 10\({}^{-4}\) & 0.009 \\  & 200 & 0.5 & 10 & 373 & 8.93\(\times\) 10\({}^{-4}\) & 9.29\(\times\) 10\({}^{-4}\) & 0.009 \\ \cline{1-1}  & 400 & 0.5 & 10 & 711 & 8.94\(\times\) 10\({}^{-4}\) & 8.92\(\times\) 10\({}^{-4}\) & 0.009 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Algorithms’ results when changing the number of exams, using the large question bank. For the overlap percentage, it is important to highlight that our method for calculating the overlap percentage differs from the approach used by [2]. The reason behind this discrepancy is that their calculation involves dividing the number of overlapping questions by the number of tests, without considering the total number of questions in the tests. We believe that this method is not accurate for calculating the overlap percentage because when calculating a percentage, it is necessary to consider the relationship between a part and the whole. In other words, both the numerator and the denominator should be of the same type. Since exams are distinct entities from questions, we have developed our own formula for determining the overlap percentage, as shown in Equation (2). Therefore, a direct comparison of the overlap percentage between the algorithms cannot be provided. However, since we have established a baseline for comparison, which is the overlap threshold defined by the user, our ultimate objective is to ensure that the overlap percentage does not exceed this threshold, regardless of the calculation method employed. Observing the obtained results, it is evident that the BA was unable to attain the targeted overlap percentage of 30% for the larger test cases. This outcome is somewhat expected as the likelihood of question repetition increases with a larger number of exams. Table 4 shows the performance of all algorithms when varying the number of exams using the small question bank, while Figure 4 shows a comparison of the algorithms in terms of average fitness values with respect to the number of exams. Figure 4: Average fitness values for different numbers of exams using the small question bank. Figure 3: Average fitness values for different numbers of exams using the large question bank.