# Composing Multiple Online Exams: The Bees Algorithm Solution
## 5 Discussion  
In our study, we evaluated the performance of the Bees Algorithm (BA) based on four key criteria: the number of successful solutions, fitness, overlap percentage, and standard deviation. The computational experimentation demonstrated that the BA achieved favorable results in terms of successful solutions, fitness, and standard deviation compared to its rival methods. Specifically, the BA outperformed all competing methods in terms of average fitness in most test cases. However, the PSO methods (both parallel and sequential versions) exhibited a higher success rate, highlighting their advantage over the BA in this particular metric, although the BA outperformed the RA and SA in this metric.  
Figure 8: Average fitness for \(DLR\) = 0.3 for the small question bank.  
Figure 7: Average fitness values when changing the \(DLR\) [0.4–0.7] for the small question bank.  
Amongst the different difficulty levels (\(DLR\)s) considered, the case of \(DLR\) = 0.5 consistently showed the best results in terms of the fitness function, standard deviation, and successful solutions, as indicated in (Tables 3-6). This can be attributed to the nature of our neighborhood move, which selects replacement questions at random. Therefore, it is relatively easier to balance difficulty level values for \(DLR\) = 0.5, since there is an approximately equal number of questions with higher and lower difficulty levels than 0.5. On the other hand, in the case of a \(DLR\) = 0.7, the majority of the questions in the database have a difficulty level lower than 0.7, making it more challenging to generate an exam with that difficulty level.  
Furthermore, the standard deviation results were comparable to those of the PMPSO, according to the computational results. Once again, the case of \(DLR\) = 0.5 exhibited greater a robustness of the algorithm. Additionally, the successful solutions were generally close to the optimal solution, as evident in the results, particularly for \(DLR\) = 0.5. It is worth noting that even better results could have been achieved if we had set a margin of error less than 15%. Furthermore, the BA did not meet the specified overlap threshold reported in [2]. Despite this, our results can be considered reasonable, especially considering the small question bank, which has a limited number of questions per chapter. For instance, taking the first row of Table 4 as an example, the dataset of the small bank for the first ten chapters comprised 614 unique questions, while the total number of generated questions was 10,000. This resulted in a significant overlap percentage.  
Moreover, in line with the results presented in Table 3, there is a direct correlation between the number of exams and the overlap percentage. As expected, as the number of exams increased, the overlap percentage also increased. Additionally, Table 5 revealed that the selected difficulty level (\(DLR\)) could impact the overlap percentage, as previously explained.  
In conclusion, we believe that the BA successfully achieved our research goals by producing near-optimal solutions that satisfied the required difficulty level set by the educator. It displayed robustness with respect to the difficulty level, as evidenced by the small standard deviation.