## 5 Discussion
### Impact of Revision Weights
Each thread started at 2-3 s intervals and the thread start time was used as a random seed to generate one million random weight vectors for the calculation. Each thread completes the calculation in approximately 10 s and is recalculated using the new time as a random seed. The six threads performed 24 h calculations (continuously) and tested approximately 50 billion random weight vectors. The results show that a large number of the results are consistent with a single calculation result, which proves that the MC method converges to the global optimal solution. The results obtained from the MC and GA methods are almost identical (Table 5), which confirms the existence and uniqueness of the optimal solution. Therefore, from a mathematical point of view, the optimum weights exist in the solution space and are the optimum solutions for Equation (7), which can be searched as accurately as possible by the two methods. Based on this result and perspective, it can be concluded that the data-driven approach is applicable to various hydrogeological settings. Unlike the CA method, both the MC and GA methods show that using all eight parameters yields better results than the use of fewer parameters. This result differs from those of many previous studies [2; 13; 14] but is consistent with the conclusion of [PERSON] [59]. The reason for this is that all parameters are related rather than independent; even if a parameter itself does not significantly differ, it may amplify the difference within or between other parameters with minor differences. Both the results of the weights derived from the objective data overcome the subjectivity and indicate that the most important factors are the depth to the water table and land use type, followed by the hydraulic conductivity, topography, infiltration coefficients, aquifer thickness, and landform. The least important factor is the net recharge, which agrees with the result of [PERSON] et al. [60]. This is different from all results derived from other methods used in this study. Whether it is SPSA, CA, or LRA, only a single factor is considered, regardless of the relationship between the factors. However, both the MC and GA consider not only factors but also the relationship between the factors. Therefore, the MC and GA methods yield the best Pearson's factor. Table 6 shows a comparison of the performances of the methods used in this study. [PERSON]'s common and pesticide DRASTIC models are the simplest methods for the determination of the vulnerability indexes because only parameter data need to be prepared and the calculation is simple. The modification of the rating scores and weights requires more preparation and calculations. Certainly, modifying only the rating scores is easier and faster than modifying both the rating scores and weights. With respect to the determination of reasonable weights, SPSA is relatively easier than CA and LRA. The former requires only simple statistics, while the latter methods require the preparation of more data, complex computations, and more time. Unlike CA and LRA, the data-driven methods (MC and GA) are simple. They are common methods to solve this problem. The time required to calculate weights using MC and GA is less than ten seconds and hundreds of microseconds, respectively. The difference between the MC and GA lies in the computational efficiency and implementation difficulty. To achieve the same accuracy, more calculations and time are needed for the MC method. Correspondingly, the implementation of GA is more difficult than that of MC. Nonetheless, both methods are very fast and efficient. Based on this study, the data-driven approaches are the best approaches. Table 6 shows that the best results are obtained with the MC and GA methods compared with the use of modified rating scores and original weights. This indicates that SPSA, CA, and LRA are not suitable for various hydrogeological settings. A reasonable explanation is that these methods only consider every single factor individually, regardless of the relationship among the factors.