# A Multi-Objective Bio-Inspired Optimization for Voice Disorders Detection: A Comparative Study
## 4 Results and Discussion  
This section presents the experiments conducted and the results obtained for NSGA-II, MOEA-D, and SPEA-II on three datasets (SLI, SVD, and VOICED). The three optimizers were assessed using four base machine learning classifiers (RF, KNN, MLP, and SVM). Table 5 presents the performance of three multi-objective optimization algorithms --NSGA-II, MOEA/D, and SPEA-II-- when paired with the KNN classifier across three datasets: SLI, SVD, and VOICED. It provides the average (AVG) and standard deviation (STD) for four key metrics: Inverted Generational Distance (IGD), Hypervolume (HV), Spacing, and Spread. Analyzing the IGD metric, NSGA-II achieved the lowest IGD value on the SLI dataset (15.506), indicating that it closely approximates the Pareto-front in this case. On the other hand, SPEA-II performed best on the SVD and VOICED datasets, with IGD values of 31.787 and 30.161, respectively. This suggests that SPEA-II is effective at finding solutions near the Pareto-front in these datasets. In terms of HV, which measures the volume covered by the solutions in objective space, both NSGA-II and SPEA-II obtained the highest values across all datasets. Specifically, NSGA-II performed best on the SLI dataset (20.139), while SPEA-II excelled on the SVD (15.245) and VOICED (21.192) datasets. Regarding the Spacing and Spread metrics, which evaluate solution distribution and diversity, SPEA-II generally outperformed in Spacing, with values of 0.900 and 0.765 for the SLI and SVD datasets. This indicates a more evenly distributed set of solutions. Conversely, NSGA-II achieved lower values for Spread on the SLI dataset, signifying a balanced diversity across objectives. Overall, NSGA-II performs robustly on the SLI dataset, while SPEA-II demonstrates strong performance on the SVD and VOICED datasets, highlighting the dataset-specific strengths of the different optimizers. Table 6 displays the performance results of the RF classifier. Looking at IGD, SPEA-II achieves the lowest values on SLI and VOICED, suggesting more precise Pareto-front approximations, while NSGA-II performs similarly on SVD, with an IGD of 31.781. In the HV metric, SPEA-II consistently scores highest across all datasets, indicating a strong coverage in objective space. NSGA-II follows closely, particularly with VOICED where it achieves a high HV of 10.585. Spacing and Spread metrics indicate solution distribution and diversity. MOEA/D's spacing is minimal on SVD and VOICED, with values near zero (0.032 and 0.031), implying evenly distributed solutions. In contrast, Spread is generally consistent across optimizers. Overall, SPEA-II demonstrates reliable performance across datasets with balanced spacing and spread. \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}{*}{KNN} & \multirow{3}{*}{MOEA/D} & SLI & 95.244 & 9.578 & 5.117 & 1.078 & 1.750 & 1.848 & **1.724** & 0.437 \\  & & SVD & 95.645 & 6.450 & 3.577 & 1.032 & 1.108 & 1.339 & 1.593 & 0.484 \\  & & VOICED & 95.912 & 11.388 & 5.158 & 1.493 & 1.376 & 1.841 & **1.709** & 0.428 \\ \cline{2-10}  & & SLI & 22.735 & 11.863 & 19.865 & 3.070 & **0.900** & 0.691 & 1.623 & 0.304 \\  & & SVD & **31.787** & 11.190 & **15.245** & 2.013 & 0.765 & 0.583 & **1.844** & 0.128 \\  & & VOICED & **30.161** & 11.881 & **21.192** & 2.285 & 1.243 & 1.308 & 1.575 & 0.385 \\ \cline{2-10}  & & SLI & **15.506** & 9.425 & **20.139** & 2.595 & 1.163 & 0.681 & 1.589 & 0.209 \\  & & SVD & 36.502 & 12.645 & 13.836 & 1.711 & **0.528** & 0.599 & 1.728 & 0.356 \\  & & VOICED & 34.781 & 15.437 & 19.868 & 2.881 & **1.073** & 1.288 & 1.654 & 0.356 \\ \hline \hline \end{tabular}
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