# A Multi-Objective Bio-Inspired Optimization for Voice Disorders Detection: A Comparative Study
## 4 Results and Discussion

Table 5: Optimization results of NSGA-II, MOEA/D, and SPEA-II with KNN classifier across three datasets (SLI, SVD, and VOICED). The best results were highlighted with boldface style. Table 7 presents the results of the comparison between the three optimizers with the MLP classifier across three datasets. SPEA-II generally performed well, achieving the lowest IGD for SII and SVD, suggesting strong proximity to the true Pareto-front, while NSGA-II had the lowest IGD for VOICED. For HV, SPEA-II consistently achieved the highest averages, especially on SVD and VOICED, indicating good coverage of the objective space. SPEA-II also excelled in Spacing, achieving the most uniform solution distribution, especially notable in the VOICED dataset. Spread results showed that both SPEA-II and NSGA-II maintained good solution diversity, with SPEA-II achieving the best values on SVD. Overall, SPEA-II shows strong and consistent optimization performance across metrics and datasets, suggesting it is the most robust algorithm for MLP-based multi-objective optimization. Table 8 displays the optimization performance of NSGA-II, MOEA/D, and SPEA-II with the SVM classifier across (SLI, SVD, and VOICED). NSGA-II achieves the best IGD on SLI and VOICED, indicating the highest proximity to the true Pareto-front, while SPEA-II performs best on SVD. For HV, NSGA-II outperforms the other algorithms on SLI, and SPEA-II achieves a high HV on SVD, implying superior objective space coverage on those datasets. In terms of Spacing, SPEA-II performs well with the lowest variance across SLI and SVD, indicating a more uniform distribution. MOEA/D shows mixed performance, and all algorithms report zero values for all metrics on VOICED, likely due to convergence issues. Overall, NSGA-II and SPEA-II demonstrate strong performance across the metrics, particularly on SLI and SVD, with NSGA-II generally excelling in HV and IGD. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Algorithm**} & \multirow{2}{*}{**Optimizer**} & \multirow{2}{*}{**Datasets**} & \multicolumn{2}{c}{**IGD**} & \multicolumn{2}{c}{**HV**} & \multicolumn{2}{c}{**Spacing**} & \multicolumn{2}{c}{**Spread**} \\ \cline{3-10}  & & & **AVG** & **STD** & **AVG** & **STD** & **AVG** & **STD** & **AVG** & **STD** \\ \hline \multirow{8}{*}{RF} & \multirow{3}{*}{MOEA/D} & SLI & 96.778 & 8.740 & 2.127 & 0.601 & 1.531 & 1.617 & **1.851** & 0.334 \\  & & SVD & 99.845 & 12.100 & 2.735 & 0.499 & **0.032** & 0.121 & 1.065 & 0.242 \\  & & VOICED & 102.911 & 11.032 & 5.645 & 0.977 & **0.031** & 0.091 & 1.134 & 0.329 \\ \cline{2-10}  & \multirow{3}{*}{SPEA-II} & SLI & **24.067** & 16.246 & **6.658** & 1.814 & 0.806 & 0.943 & 1.812 & 0.303 \\  & & SVD & 35.683 & 11.060 & 5.145 & 0.663 & 0.443 & 0.527 & **1.716** & 0.377 \\  & & VOICED & 35.017 & 9.462 & 10.327 & 1.392 & 0.265 & 0.173 & 1.773 & 0.319 \\ \cline{2-10}  & \multirow{3}{*}{NSGA-II} & SLI & 32.548 & 10.323 & 5.810 & 0.550 & **0.361** & 0.240 & 1.771 & 0.388 \\  & & SVD & **31.781** & 6.828 & **5.585** & 0.615 & 0.217 & 0.190 & 1.706 & 0.426 \\ \cline{2-10}  & & VOICED & **31.795** & 11.075 & **10.585** & 1.300 & 0.541 & 0.509 & **1.847** & 0.276 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Optimization results of NSGA-II, MOEA/D, and SPEA-II with RF classifier across three datasets (SLI, SVD, and VOICED). The best results were highlighted with boldface style.