## 6 Results and Discussions  
The CS implementation by [PERSON] and [PERSON] [15, 16] was utilized in this study. [PERSON] _et al._[26] indicated that a slight variation in CS implementations may cause differences in results. Therefore, the results may not agree with the findings of the previous studies. The model was coded and implemented in the Matlab environment (Matlab R2011b) and simulation results were then obtained. A 10-fold cross validation method was used to avoid over-fitting. For this problem, the best performing architecture was 8-6-1, that is, with one hidden layer and six neurons, which resulted in a total of 54 weights and 7 biases. Hence, this architecture was applied to this study. In a real world application of an optimization technique, it is very difficult to define a stopping criterion. Moreover, in this study, there is an uncertainty in both the inputs and the output of the objective function. The number of iterations, when the obtained results reached an acceptable accuracy of prediction, was chosen as the stopping criterion. The number of objective function evaluations in the implementations of CS and COA in each iteration is the same. Figure 5 depicts the SSE values for the two algorithms in 100 iterations. It is clearly seen that the COA has a faster convergence than the CS. During the first five iterations, the convergence by the COA was very fast. At the 100 th iteration, the SSE values of the neural network trained by the COA and CS were 171.5908 and 768.6833, respectively.  
Table 2 represents the comparison of performance criteria values of the neural networks trained by CS (ANN-CS) and COA (ANN-COA) at different iterations. Theoretically, a prediction model is  
Figure 5: Sum squared error values in 100 iterations.  
In order to evaluate the performance of the proposed approach, the Multiple Linear Regression (MLR) method was applied to the studied problem. Coefficients derived from the MLR method are presented in Table 3. The performance criteria RMSE, MAPE, and \(R\) for the training dataset were calculated as 0.5642, 0.0769, and 0.8904, respectively; while those for the testing dataset were calculated as 0.6174, 0.0753, and 0.8632, respectively. When comparing with the results in Table 2, the ANN-CS and ANN-COA at the 1000 th iteration have smaller RMSE and MAPE values than those obtained from the MLR method as well as bigger \(R\) values for both the training and testing datasets. It can be concluded that the ANN-CS and ANN-COA have a better overall performance than the MLR method in predicting student academic performance.  
Based on the obtained results, it can be concluded that the ANN-COA and ANN-CS can be used to predict student academic performance. However, when prediction accuracy and convergence speed are simultaneously desired, the COA algorithm is found to be more appropriate. The results show that the  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Variable** & **Coefficient** \\ \hline Intercept & –0.4325 \\ \(X_{1}\) & 0.3471 \\ \(X_{2}\) & 0.2758 \\ \(X_{3}\) & 0.1388 \\ \(X_{4}\) & 0.2916 \\ \(X_{5}\) & –0.0090 \\ \(X_{6}\) & 0.0060 \\ \(X_{7}\) & 0.0029 \\ \(X_{8}\) & –0.0798 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Coefficient values for MLR.  
Figure 7: Comparison between actual and predicted values in testing dataset.  
prediction outcome of the ANN-COA model is more accurate and reliable. Hence, the ANN-COA may be acceptable in serving as a predictor of student academic performance.