## 5 Conclusions  
This study proposed a hybrid GP-XGBoost model for predicting the compression index (\(C_{c}\)) of clayey soils, integrating the symbolic regression capabilities of Genetic Programming (GP) with the robust predictive power of Extreme Gradient Boosting (XGBoost). The model demonstrated superior performance compared to traditional empirical methods and standalone machine learning models, achieving an R\({}^{2}\) of 0.927 with significantly reduced prediction errors. The feature importance analysis highlighted key geotechnical parameters--such as the liquid limit (LL), the plasticity index (PI), the initial void ratio (\(e_{0}\)), and the natural moisture content (\(w_{n}\))--as critical factors influencing soil compressibility, aligning with established soil mechanics principles.  
Despite the promising results, this study acknowledges several limitations, including parameter dependencies (e.g., the LL and the PI), limited dataset diversity, and potential overfitting risks. To address these challenges, future research should incorporate dimensionality reduction techniques, external validation with independent datasets, and simplified symbolic models for enhanced interpretability. Additionally, expanding the dataset to include diverse soil types and environmental conditions will improve the model's generalizability in real-world applications.  
The findings of this research offer valuable insights for geotechnical engineers involved in foundation design, settlement analysis, and infrastructure planning, providing a data-driven approach to complement traditional soil mechanics theories. By advancing predictive modeling techniques and addressing the identified limitations, future studies can further improve the accuracy, reliability, and practical applicability of machine learning models in geotechnical engineering.  
Conceptualization, A.B. and K.K.; methodology, A.B.; software, K.K.; validation, A.B., H.A.-N. and Y.L.; formal analysis, A.B., H.A.-N. and Y.L.; investigation, K.K.; resources, K.K.; data curation, K.K.; writing--original draft preparation, A.B.; writing--review and editing,  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Model Comparison** & \(R^{2}\) & **MSE (\(p\)-Value)** & **MAE (\(p\)-Value)** \\ \hline GP vs. MLR & 0.027 & 0.002 & 0.001 \\ GP-XGBoost vs. MLR & 0.149181 & 0.09012 & \textless{}0.001 \\ XGBoost vs. GP & 0.091134 & 0.189196 & \textless{}0.001 \\ GP-XGBoost vs. GP & 0.029736 & 0.106369 & 0.001 \\ GP-XGBoost vs. XGBoost & 0.432 & 0.289 & 0.315 \\ \hline \hline \end{tabular}
\end{table}
Table 17: [PERSON]’s HSD test results (\(p\)-values).  
H.A.-N. and Y.L.; visualization, K.K.; supervision, H.A.-N.; project administration, A.B. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
The original contributions presented in this study are included in the article. Further inquiries can be directed to the corresponding authors.  
The authors declare no conflicts of interest.  
The following abbreviations are used in this manuscript:  
\(C_{c}\)  
Compression Index  
Multiple Linear Regression  
Genetic Programming  
xGBoost  
eXtreme Gradient Boosting  
MAE  
Mean Absolute Error  
MSE  
Mean Squared Error  
\(R^{2}\)  
Coefficient of Determination  
ML  
Machine Learning  
LL  
Liquid Limit  
Plasticity Index  
\(e_{0}\)  
Void Ratio  
\(w\)  
Water Content