## 4 Discussion
### Limitations and Future Work  
The hybrid GP-XGBoost approach is effective but faces challenges in computation and practical use. GP's symbolic regression can create complex equations that are hard to use in real-time. XGBoost also needs significant computing power for its iterative training on enhanced datasets. This may not be feasible for small engineering firms or in developing areas. To address this, future studies can focus on simplifying GP-generated equations or applying dimensionality reduction techniques. Cloud-based or easy-to-use software can make the models more accessible.  
Overfitting is another issue in machine learning. It can produce good results on training data but poor results on new data. This study used normalization and cross-validation, but more work is needed. Testing with data from different regions can help. Techniques like dropout regularization and ensemble methods can reduce overfitting. Tools like SHAP values can show how features affect predictions. This will build trust and support the wider use of the models.  
One limitation of this study is the inherent dependency between some input parameters, particularly the LL and the PI. Since the PI is calculated directly from the LL and the PL, this introduces collinearity, which may affect the stability and interpretability of feature importance in the models. Although the hybrid GP-XGBoost model is capable of handling such dependencies, future research could benefit from employing dimensionality reduction techniques or regularization methods to mitigate these effects and enhance model robustness.  
Building upon the findings and acknowledging the limitations of this study, several directions for future research are proposed to enhance the robustness, generalizability, and interpretability of the predictive models for the compression index (\(C_{c}\)):  
* Future studies should explore dimensionality reduction techniques, such as Principal Component Analysis (PCA), to transform correlated features into uncorrelated components. Alternatively, regularization methods like LASSO regression can be applied to reduce the influence of redundant variables.
* The current dataset, while comprehensive, lacks geographical and geological diversity. Future work should incorporate larger, multi-regional datasets that cover a wider range of soil types, climatic conditions, and geotechnical properties.
* To ensure the generalizability of the proposed model, future research should involve external validation using independent datasets from different projects or geographical locations.
* Although the GP-XGBoost hybrid model offers high accuracy, its complex symbolic equations can hinder interpretability. Future studies could focus on developing simplified symbolic models by incorporating genetic simplification algorithms or rule-based pruning techniques to generate more concise, physically interpretable expressions that align with geotechnical principles.
* While the hybrid GP-XGBoost model demonstrated strong performance, future research could explore advanced ensemble techniques such as stacking, blending, or meta-learning frameworks to further enhance predictive accuracy. Additionally, integrating deep learning models like Recurrent Neural Networks (RNNs) or Attention Mechanisms could improve the capture of complex temporal and spatial patterns in geotechnical data.