## 3 Background
### Binary Harris Hawks Optimizer (BHHO)
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Model**} & \multirow{2}{*}{**Matrix**} & **Selected Features** & **Fitness (Zone A\%)** & **RMSE (mg/dL)** & **MAE (mg/dL)** & **Time Costs (Sec)** \\ \hline LightGBM & - & 69 & 68.42 & 18.10 & 16.16 & 1 \\ \hline \multirow{3}{*}{IDA-LightGBM} & Mean & 35.2 & **86.14** & 17.68 & **14.81** & 468.10 \\ \cline{2-7}  & STD & **4.28** & 1.91 & 1.22 & 0.87 & 27.94 \\ \cline{2-7}  & Best & 33 & **89.47** & 17.03 & 14.64 & 494 \\ \hline \multirow{3}{*}{BHHO-LightGBM} & Mean & 46.40 & 75.53 & 18.31 & 16.38 & 690.65 \\ \cline{2-7}  & STD & 5.22 & 10.90 & 3.66 & 1.44 & 105.44 \\ \cline{2-7}  & Best & 50 & 86.84 & **16.37** & **13.42** & 745.35 \\ \hline \multirow{3}{*}{bGWO-LightGBM} & Mean & 46.23 & 84.47 & **17.63** & 15.21 & 521.51 \\ \cline{2-7}  & STD & 5.41 & **1.42** & **0.65** & **0.66** & 65.73 \\ \cline{2-7}  & Best & 48 & 86.84 & 16.92 & 14.36 & 543.51 \\ \hline \multirow{3}{*}{GA-LightGBM} & Mean & **34.6** & 84.65 & 17.65 & 15.00 & **97.70** \\ \cline{2-7}  & STD & 4.88 & 2.26 & 1.01 & 0.85 & 22.71 \\ \cline{2-7}  & Best & **32** & 89.47 & 17.36 & 14.71 & **64.2** \\ \hline \multirow{3}{*}{ETR} & - & 69 & 76.32 & 16.52 & 14.61 & 1 \\ \cline{2-7}  & Mean & **34.17** & **84.74** & **17.11** & **15.04** & 392.59 \\ \cline{2-7}  & STD & 4.84 & 1.25 & 0.61 & 0.68 & 83.53 \\ \cline{2-7}  & Best & **27** & 86.84 & **15.7** & **12.61** & 428.09 \\ \hline \multirow{3}{*}{BHHO- ETR} & Mean & 45.5 & 76.66 & 17.95 & 15.96 & 550.28 \\ \cline{2-7}  & STD & 4.31 & 7.28 & 0.92 & 0.83 & 132.40 \\ \cline{2-7}  & Best & 38 & 86.84 & 17.18 & 15.08 & 387.08 \\ \hline \multirow{3}{*}{bGWO-ETR} & Mean & 46.1 & 84.12 & 17.17 & 15.27 & 482.62 \\ \cline{2-7}  & STD & **3.37** & **1.07** & **0.58** & **0.50** & **13.26** \\ \cline{2-7}  & Best & 47 & 86.84 & 15.71 & 14.19 & 480.67 \\ \hline \multirow{3}{*}{GA-ETR} & Mean & 34.7 & 84.39 & 17.16 & 15.15 & 99.82 \\ \cline{2-7}  & STD & 4.20 & 1.91 & 0.72 & 0.62 & 22.17 \\ \cline{2-7}  & Best & 37 & 86.84 & 16.18 & 14.22 & 88.49 \\ \hline \multirow{3}{*}{RF} & - & 69 & 68.42 & 18.12 & 16.02 & 1 \\ \cline{2-7}  & STD & 4.84 & 16.02 & 16.02 & 1 & \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Performance of the models during phase 1 in terms of selected features, fitness, RMSE, MAE, and time costs, evaluated on the testing split of the dataset. The data showcasing the best performance for each metric are highlighted in bold. The IDA-LightGBM combination emerged as the top-performing model, achieving the lowest mean MAE of 14.81 mg/dL with a standard deviation of 0.87 mg/dL. In its best run, it recorded an RMSE of 17.03 mg/dL, an MAE of 14.64 mg/dL, and the highest CEG Zone A percentage of 89.47%, affirming its strong clinical relevance. The model effectively reduced the feature set by 52.2%, selecting 33 features in its best run. Furthermore, it required a mean computational time of 468.10 s, showcasing a well-rounded performance in terms of accuracy, efficiency, and feature reduction. The IDA-ETR combination closely followed, achieving a mean MAE of 15.04 mg/dL with a standard deviation of 0.68 mg/dL. In its best run, it recorded a MAE of 12.61 mg/dL and a CEG Zone A percentage of 86.84%. Across all runs, the model selected an average of 34.17 features. Its mean computational time was 392.59 s, offering competitive results while maintaining a balance between feature reduction and accuracy. In contrast, models incorporating the Genetic Algorithm (GA) exhibited lower performance, with higher mean MAE and RMSE values. While GA-LightGBM demonstrated the shortest computational time of 97.70 s, its performance metrics were not competitive. These results underscore the superiority of IDA in achieving a good balance between feature reduction, predictive accuracy, and computational efficiency. #### 5.4.2 Phase 2: Refining Top-Performing Models

Phase Two focused on refining the top-performing combinations from Phase One.