## 6 Conclusions  
A robust predictive model for the Retained Stability Index (RSI) of asphalt mixes has been developed in this study. A hybrid ML approach, including the ANN and GEP tools, was utilized in the model development. The model considered the most common influential parameters on the moisture susceptibility of asphalt pavements, including F%, Ab%, AC%, and Va%. Overall, 150 HMA samples were prepared using local aggregate and asphalt materials in Jordan. The water susceptibility of the mixes was evaluated through the measured RSI value. The Bayesian regularization algorithm, known for its ability to provide a robust generalization ANN model, was used to predict new reliable combinations of datasets. The following are the main findings of this research work:  
* The relative importance analysis of the network implied that AC% has the highest impact on the RSI value with a contribution rate of 35.6%, followed by Va%, F%, and Ab% with contributions of 33.5%, 22.4%, and 8.5%, respectively.
* The datasets generated by the ANN were combined with the experimental dataset and fed into the GEP tool to develop the final prediction model in terms of a simple mathematical function.
* The proposed GEP model proved its high accuracy and sensitivity in predicting the RSI of asphalt mixes, considering the impact of the input variables. The overall performance measures of the model result in a very high (R\({}^{2}\)) value of 96.6% and very low error values of 0.530 and 0.659 for MAE and RMSE. The experimental-to-predicted RSI values of the model have an average of 1.00 and a low coefficient of variation of 0.841.
* In addition to the performance measures, a parametric analysis was conducted to evaluate the model sensitivity concerning every input variable. The result trends were confirmed with the ANN connection weight analysis and previous results found in the literature. It was found that increasing F%, Ab%, and Va% in asphalt mixes can reduce the RSI value, whereas increasing AC% can enhance the moisture susceptibility of the mixes by increasing the RSI value.
* Overall, the proposed model is accurate and provides a straightforward mathematical equation for predicting the RSI value of asphalt mixes. It can be recommended to assess the moisture sensitivity of asphalt mixes without performing destructive testing, which would save natural resources and experimental effort. It can also help to improve the moisture damage performance of the mixes prior to the design phase.  
It must be mentioned that the model is limited by the bitumen grade, traffic condition, and aggregate properties used. For future research, it would be recommended to develop another predictive model that further considers mix design parameters for asphalt mixes prepared at various levels of compaction and for mixes constructed with recycled asphalt materials and different bitumen grades, aggregate types, and graduations.  
**Author Contributions:** Conceptualization: Y.S.J.; Methodology: Y.S.J. and M.J.A.-K.; Data curation: Y.S.J. and M.R.; Formal analysis and investigation: Y.S.J., M.J.A.-K. and M.R.; Visualization: Y.S.J.; Software: Y.S.J. and M.J.A.-K.; Writing--original draft: Y.S.J., M.J.A.-K. and M.R.; Writing--review and editing: Y.S.J. All authors have read and agreed to the published version of the manuscript.  
**Funding:** The authors declare that no funds, grants, or other support were received during the preparation of this manuscript.  
**Data Availability Statement:** Data will be available upon reasonable request.  
**Conflicts of Interest:** The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.