# A Multi-Objective Bio-Inspired Optimization for Voice Disorders Detection: A Comparative Study
## 4 Results and Discussion
The MLP and RF classifiers are the most computationally intensive, particularly on the SLI dataset, with average times of 7619.2 s and 7936.3 s, respectively, which may reflect the higher complexity and resource demand of these models in training with NSGA-II. For smaller datasets like VOICED, all classifiers have lower optimization times, with KNN and SVM exhibiting particularly fast runtimes (8.319 s for KNN and 14.633 s for SVM). SVM shows consistently low optimization times across datasets, which may make it more practical for large-scale or real-time applications requiring NSGA-II optimization. The table highlights the computational demands of NSGA-II optimization, which vary substantially across classifiers and datasets, impacting its feasibility depending on the available resources and time constraints. Furthermore, a statistical analysis is conducted to guarantee the significant difference in performance between the three evolutionary optimizers across the four machine learning algorithms and datasets. First, the Kolmogorov-Smirnov (KS) normality test is used to ensure the validity of the data distribution before computing the Analysis of Variance (ANOVA) test. If at least one dataset was abnormal, the Kruskal-Wallis test is calculated instead. The algorithms' performance was evaluated using IGD and Hypervolume metrics over 15 independent runs. The test results exhibited a low \(p\)-value less than the significance level of 0.05, indicating a significant difference in the performance of the algorithms. Generally speaking, NSGA-II is the best optimizer overall. While KNN performs best for SLI, MLP outperforms others in SVD, and SVM achieves the best IGD for VOICED, with MLP leading in HV, making NSGA-II and MLP a strong but not always the optimal solution. NSGA-II and MLP were used to compute the non-conformity scores for the three datasets. The split conformal prediction with softmax-based nonconformity scores is employed. Using the MAPIE Library [35], the CPs for all runs and all Pareto-fronts were computed, with the average (Avg.) and standard deviation (Std.) were reported for the non-conformity scores, as shown in Table 10. The results show a strong performance of the SLI dataset with a high accuracy of 0.987 and low nonconformity scores (\(0.015\pm 0.079\)), indicating well-calibrated predictions and reliable uncertainty estimates. Conversely, the SVD and VOICED datasets exhibit lower accuracy (0.743 and 0.706, respectively) and higher nonconformity scores (0.253-0.318), suggesting increased model uncertainty or data challenges. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Algorithm**} & \multirow{2}{*}{**Datasets**} & \multicolumn{2}{c}{**Optimization Time (s)**} \\ \cline{3-4}  & & **AVG** & **STD** \\ \hline \multirow{3}{*}{KNN} & SLI & 61.408 & 1.051 \\  & SVD & 20.021 & 0.266 \\  & VOICED & 8.319 & 0.947 \\ \hline \multirow{3}{*}{MLP} & SLI & 7619.222 & 913.322 \\  & SVD & 3237.941 & 450.743 \\  & VOICED & 849.334 & 192.432 \\ \hline \multirow{3}{*}{RF} & SLI & 7936.300 & 197.448 \\  & SVD & 4493.705 & 580.553 \\ \cline{1-1}  & VOICED & 1045.188 & 65.990 \\ \hline \multirow{3}{*}{SVM} & SLI & 834.729 & 25.778 \\ \cline{1-1}  & SVD & 242.100 & 6.263 \\ \cline{1-1}  & VOICED & 14.633 & 0.130 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Optimization time of the NSGA-II over all classifiers and datasets. Table 11 presents a comparative overview of our proposed methods along with recent State-of-the-Art approaches from the literature. Although we acknowledge that the comparison is not strictly fair due to differences in datasets, feature extraction strategies, and optimization objectives, the table is intended to provide a contextual reference to understand current trends. In particular, while many previous studies report high performance--particularly on the full SVD or mixed datasets (e.g., SVD + MEEI)--our experiments were conducted on different bases.