## 6 Conclusions  
In this study, the Wilcoxon rank sum test was employed to ascertain rating scores for hydrogeologic parameters, and a data-driven methodology for determining parameter weights was developed. This novel method was then compared with SPSA, CA, and LRA. The Pearson and Spearman correlation coefficients between the vulnerability index and nitrate concentration were also utilized to validate the assessment results. The results demonstrated that the correlation between the vulnerability index and nitrate concentration improved significantly after the revision of the rating scores. The findings further underscore the conclusion that SPSA, CA, and LRA are not universally applicable to all hydrogeologic environments, particularly within the confines of the present study area. The primary conclusions derived from this study are as follows: (1) The primary limitation of Aller's general DRASTIC model and the pesticide DRASTIC model pertains to the high degree of subjectivity inherent in determining the rating scores and weights of the parameters. (2) The data-driven weighting method proposed in this paper (solved by MC and GA) accounts for both individual factors and the relationships between factors, thereby enabling the optimal weights to be obtained. (3) The discrepancy between the level of change in nitrate concentrations over extended periods and the outcomes of the vulnerability assessment can be employed to ascertain the reliability and practicality of the assessment results from a temporal perspective. (4) The key to a comprehensive groundwater vulnerability assessment is the rationalization of the rating ranges of parameters and their corresponding rating scores, which should be the focus of future work.  
This paper established a new, effective data-driven method based on the Monte Carlo and Genetic Algorithm methods to determine weights. In this way, the revision of the rating scores and weights will no longer be a separate step but a continuous and simple process. This paper also proposed a new method to verify the accuracy of the assessment from a time perspective based on changes in nitrate concentration. These methods are applicable to a variety of hydrogeological environments. It was found that the establishment of rating scores is a key process that can effectively improve results. All of this will raise awareness of groundwater-specific vulnerability assessments and strengthen the protection and management of groundwater quality.  
The following supporting information can be downloaded at: [[https://www.mdpi.com/article/10.3390/app15052866/s1](https://www.mdpi.com/article/10.3390/app15052866/s1)]([https://www.mdpi.com/article/10.3390/app15052866/s1](https://www.mdpi.com/article/10.3390/app15052866/s1)).  
Investigation, Y.Z. ([PERSON]), Y.W. and W.F.; Data curation, L.P. and Y.Z. ([PERSON]); Writing--original draft, X.H.; Visualization, H.Y. All authors have read and agreed to the published version of the manuscript.  
This work was supported by the Pilot Project of Basic Research Operating Expenses System of Hebei Academy of Sciences, China (2025 PF05).  
Institutional Review Board Statement: Not applicable.  
Informed Consent Statement: Not applicable.  
Data Availability Statement: Data is contained within the article and Supplementary Material.  
The authors declare no conflict of interest.