## 4 Results
### Assessment-Test Generation (TG)
#### 4.3.2 TG Using Genetic Structures
The results are shown in Table 9 and are compared with the previous results of previous versions of genetic algorithms. The running time of the genetic algorithm is significantly influenced by the parameters of the experiment, such as the population size and the number of generations. The larger the population or the number of generations, the longer the running time, because the algorithm requires more iterations to evaluate and optimize the solutions. The complexity of the genetic algorithm is generally \(\mathcal{O}(NG*P*K)\), where NG is the number of generations, P is the population size and K is the number of items desired in a test. This means that the algorithm becomes slower as the population size or the number of generations increases, and the running time will increase significantly for large datasets. Compared to a previous algorithm, the current implementation demonstrated a shorter running time, which suggests a performance optimization, but the same principles of complexity apply. The parameters must be chosen carefully to balance the running time and the quality of the solutions. In order to express the correlations between the three parameters (N, K and NG) and their combined and individual influence on the runtime, we have designed, implemented and run a multiple linear regression model. The setup of this model was performed using the Ordinary Least Squares (OLS) technique to estimate the coefficients of a linear function describing the relationship between the independent variables N (number of items), K (number of items per test), and NG (number of generations), and the dependent variable Runtime (execution time). The algorithm was implemented on a training dataset, and the model was trained to minimize the sum of squared errors between the predicted and actual values of Runtime. Error measures such as MSE (Mean Squared Error), RMSE (Root Mean Squared Error), and \(R^{2}\) were used to evaluate the performance. Thus, the regression function has the next form:  
\[Runtime=\beta_{0}+\beta_{1}N+\beta_{2}K+\beta_{3}NG \tag{16}\] \begin{table}
\begin{tabular}{l l l l l l} \hline \hline \multirow{2}{*}{**Run**} & **Obtained** & \multirow{2}{*}{\
\begin{tabular}{l} **Initial** \\ **Difficulty** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{l} **Final Fitness** \\ **Value** \\ \end{tabular} } & \multirow{2}{*}{**Runtime (s)**} & \multirow{2}{*}{**Population**} \\  & & & & & \\ \hline Run 1 & 0.383 & 0.584 & 0.584 & 12.63 & 463.505 \\ Run 2 & 0.402 & 0.585 & 0.589 & 11.85 & 457.852 \\ Run 3 & 0.331 & 0.585 & 0.583 & 13.81 & 442.229 \\ Run 4 & 0.374 & 0.587 & 0.587 & 13.41 & 442.998 \\ Run 5 & 0.357 & 0.584 & 0.586 & 13.35 & 438.508 \\ Run 6 & 0.367 & 0.586 & 0.590 & 15.13 & 438.234 \\ Run 7 & 0.363 & 0.587 & 0.586 & 12.12 & 449.449 \\ Run 8 & 0.372 & 0.589 & 0.599 & 21.35 & 428.399 \\ Run 9 & 0.333 & 0.588 & 0.586 & 15.37 & 427.699 \\ Run 10 & 0.370 & 0.589 & 0.589 & 15.32 & 439.631 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Obtained data after the genetic-based implementation. where  
* \(\beta_{0}\) is the intercept (the constant term),
* \(\beta_{1}\), \(\beta_{2}\), and \(\beta_{3}\) are the coefficients that determine the influence of each variable (N, K, NG) on Runtime. The linear regression model scored well in the performance evaluation, with an MSE of 0.331 and an RMSE of 0.576, indicating a relatively low mean error. The MAE is 0.429, suggesting that the mean absolute error is quite small, and the MAPE is 0.045, meaning a very low mean percentage error. With an \(R^{2}\) of 0.975, the model explains 97.5% of the variability in the data, indicating excellent performance. The coefficients obtained for each feature, such as N (coefficient 0.000921372), K (coefficient 1.87163 \(\times\) 10\({}^{-5}\)), and NG (coefficient 0.0118544), indicate the influence of each variable on runtime, and the intercept (\(-\)0.19403) represents the estimated value of Runtime when all predictors are zero.