# Optimization of Parametric Equalizer Filters in In-Vehicle Audio Systems with a Genetic Algorithm
## 4 Results
Conversely, the worst fitness value of 6.9 was observed in run 2, indicating some variability in the optimization process. Overall, these results demonstrate the algorithm's capability to consistently find good solutions within the defined solution space. In addition, statistical analyses were performed to assess the consistency and reliability of the genetic algorithm's performance by calculating the mean, standard deviation, and variance of these fitness values. The results are presented in Table 5.  
The statistical analysis provided in Table 5 highlights the genetic algorithm's robustness. The low standard deviation and variance values across the best, worst, and average fitness metrics indicate that the algorithm consistently produces reliable and effective results. Particularly, the low best fitness values demonstrate that the genetic algorithm effectively optimizes the filter parameters, ensuring the speaker output closely aligns with the ideal contour. The high variance in the worst fitness values suggests that the algorithm occasionally produces less optimal results; however, the overall consistency remains high. The obtained parameters were applied to the modeling software created to calculate the speaker output, and the simulation results were obtained. Additionally, the filter  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Run No** & **Best Fitness Value** & **Worst Fitness Value** & **Average Fitness Value** \\ \hline
1 & 3.7278 & 6.4818 & 5.2462 \\ \hline
2 & 3.9119 & 6.9003 & 5.2295 \\ \hline
3 & 3.7849 & 6.8531 & 5.3337 \\ \hline
4 & 3.1401 & 5.3548 & 4.264 \\ \hline  
parameters were loaded into the vehicle multimedia sound system, and the speaker output was measured. In all measurements, the filter parameters providing the best fitness values were applied. To evaluate the performance of the model and algorithm, the correlation and RMSE between the simulation results and the ideal contour, between the experimental results and the ideal contour, as well as between the simulation and experimental results, were calculated within the effective operating frequency range of the speaker. The obtained findings are shown in Table 6.  
The Pearson correlation and RMSE values in Table 6 indicate the performance of the model and algorithm. The best overall performance was observed in run 9, consistent with the findings in Table 5. The best results in terms of fitness, as well as correlation and RMSE values, were obtained in run 9. The filter parameters optimized in this run provided the highest similarity to the ideal contour and the best agreement between the simulation and experimental results. However, some differences between the simulation and experimental results were observed. These discrepancies can be attributed to factors not included in the model, such as the unknown frequency responses of the cables, vehicle multimedia system, and audio analyzer. These elements were not modeled, which affected the similarity between the simulation and the experimental results. To illustrate the specific filter parameters that achieved these optimal results, the parameters obtained from run 9 are detailed in Table 7.  
The simulation and experimental results are presented together in Figure 10 and compared with the ideal contour. Here, the blue line represents the simulation results, the red line represents the experimental results, and the black line represents the ideal contour. \begin{table}
\begin{tabular}{c c c c c c c} \hline \multirow{2}{*}{**Run No**} & \multicolumn{2}{c}{**Simulation vs. Ideal**} & \multicolumn{2}{c}{**Experimental vs.