## 3 Background
### Binary Harris Hawks Optimizer (BHHO)
The IDA-LightGBM and IDA-ETR combinations were selected for further evaluation based on their clinical relevance and computational efficiency. The results of this phase are summarized in Table 6. Both combinations demonstrated strong predictive accuracy and feature reduction, but IDA-LightGBM emerged as the most clinically significant and computationally efficient model. In its best run, IDA-LightGBM selected only 18 features while achieving a MAE of 13.96 mg/dL and a RMSE of 15.76 mg/dL. It also maintained a high CEG Zone A percentage of 94.74%, ensuring that all predictions were clinically acceptable. The hyperparameters of the LightGBM model were fine-tuned to further improve performance, with _n_estimators_ set to 670 and _reg_alpha_ set to 3.1. This refinement lowered the MAE to 13.17 mg/dL and the RMSE to 15.36 mg/dL. The mean computational time was recorded at 311.72 s, underscoring the model's robustness and efficiency. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Model**} & \multirow{2}{*}{**Matric**} & **Selected Features** & **Fitness (Zone A\%)** & **RMSE (mg/dL)** & **MAE (mg/dL)** & **Time** **Costs (Sec)** \\ \hline \multirow{4}{*}{IDA-RF} & Mean & **33.13** & **81.84** & 18.37 & 16.06 & 611.93 \\ \cline{2-6}  & STD & 4.59 & 0.3 & 0.65 & 0.65 & 37.58 \\ \cline{2-6}  & Best & **31** & 84.21 & 18.13 & **15.04** & 623.64 \\ \hline \multirow{4}{*}{BHHO-RF} & Mean & 45.3 & 72.9 & 19.08 & 16.8 & 969.58 \\ \cline{2-6}  & STD & 4.98 & 8.86 & 1.21 & 1.05 & 52.42 \\ \cline{2-6}  & Best & 35 & 84.21 & 17.45 & 15.70 & 995.61 \\ \hline \multirow{4}{*}{bGWO-RF} & Mean & 45.83 & 81.32 & 18.33 & 16.16 & 719.44 \\ \cline{2-6}  & STD & 4.37 & 1.57 & 0.50 & 0.43 & 16.99 \\ \cline{2-6}  & Best & 46 & 84.21 & **17.15** & 15.43 & 726.55 \\ \hline \multirow{4}{*}{GA-RF} & Mean & 33.43 & 81.58 & **18.28** & **15.95** & 131.84 \\ \cline{2-6}  & STD & 3.34 & 2.04 & 0.64 & 0.46 & 23.59 \\ \cline{1-1} \cline{2-6}  & Best & 38 & 84.21 & 17.64 & 15.35 & 121.39 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: _Cont._IDA-ETR also performed well, selecting 13 features in its best run with a MAE of 12.43 mg/dL and a RMSE of 14.39 mg/dL. The model achieved a best-case CEG Zone A percentage of 92.11% and required a mean computational time of 321.32 s.

Although IDA-ETR demonstrated superior feature reduction and accuracy, IDA-LightGBM emerged as the best model due to its greater clinical significance, based on the higher percentage of Zone A and balanced performance metrics. Despite the iterative optimization of the IDA and the gradient boosting mechanism of LightGBM, the overall computational complexity was effectively managed, as the model achieved efficient runtime and significant reduction in the feature set. This balance of computational efficiency, predictive accuracy, and clinical relevance underscores the practicality of IDA-LightGBM for non-invasive blood glucose monitoring. #### 5.4.3 Convergence Evaluation and Clarke Error Grid Analysis (CEG)

The convergence curves of the top models, presented in Figure 10, illustrate the rapid optimization capability of IDA-LightGBM, which reached convergence within the first half of the iterations. This efficiency underscores its ability to balance exploration and exploitation effectively. The CEG analysis was used to verify the clinical safety of the two best models from phase two, IDA-LightGBM and IDA-ETR. As shown in Figure 11, the IDA-LightGBM model exhibited superior clinical safety with 94.74% of predictions in Zone A and no predictions in Zones C, D, or E. IDA-ETR followed with 92.11% of predictions in Zone A and similarly no predictions in dangerous zones. These results confirm the outcomes from Phase Two, confirming IDA-LightGBM as the best-performing model. #### 5.4.4 Accuracy of Predicted BGL Values for Best Model

The best IDA-LightGBM model exhibited superior performance by selecting 18 features from an initial set of 69 HRV features derived from PPG signals, as denoted by the feature vector \(D\) in Equation (22).