## 2 Research Methods
### Selection of Multi-Objective Decision-Making Methods
When determining the relative importance of each objective, objectivity is crucial. The entropy weight method provides an objective way to determine the weights of various decision criteria, reflecting the amount of information and variability of the criteria. The smaller the entropy value of an indicator, the lower its uncertainty and the greater its weight, indicating its higher importance in the evaluation. [PERSON] and [PERSON] proposed the TOPSIS method, which ranks alternatives based on the shortest distance to the ideal solution and the furthest distance from the negative ideal solution [77]. The entropy weight method is an objective way to determine weights, used in the TOPSIS method to determine attribute weights [78]. Combining the entropy weight method with TOPSIS, known as the entropy weight TOPSIS method, not only enhances the objectivity of weight determination but also enhances the scientific and rational nature of the decision-making process. The entropy weight TOPSIS method, by quantifying each scheme's relative distance to the ideal and negative ideal solutions, provides a clear, quantified decision-support tool, helping to choose the best scheme from many feasible Pareto optimal solutions that meet the needs and context of the decision-makers [76]. Therefore, this paper opts for a comprehensive decision-making based on the entropy weight TOPSIS method, selecting the optimal solution from the Pareto solution set. According to research by [PERSON] and others, normalization is the most commonly used method in entropy weight TOPSIS calculations [79]. The detailed steps of the entropy weight TOPSIS method are as follows:  
The entropy weight method is an objective weighting method used in multi-criteria decision analysis to determine the weights of various indicators. By measuring the variability of each indicator, it effectively prevents the subjective determination of weights and the information overlap among multiple indicators. An indicator's entropy value is inversely proportional to its certainty level; the smaller the entropy value, the lower the uncertainty and, consequently, the higher its weight. This indicates that the indicator has a higher significance in the evaluation [80]. Given that the original data may vary in dimension and magnitude, they are first subject to dimensionless processing through range standardization, with the formula as follows for positive indicators:  
\[r_{ij}=\frac{x_{ij}-\min(x_{i})}{\max(x_{i})-\min(x_{i})} \tag{1}\]  
For negative indicators, the standardization formula is as follows:  
\[r_{ij}=\frac{\max(x_{i})-x_{ij}}{\max(x_{i})-\min(x_{i})} \tag{2}\]  
In the formula, \(x_{ij}\) represents the original value of the \(j\)-th evaluation object on the \(i\)-th indicator, and \(r_{ij}\) represents the corresponding standardized value. After standardizing the data, the weight of each indicator is calculated using the following formula:  
\[p_{ij}=\frac{r_{ij}}{\sum_{j=1}^{n}r_{ij}} \tag{3}\]  
In the formula, \(n\) represents the number of evaluation objects. Entropy is used to measure the variability of an indicator, with the formula as follows:  
\[e_{i}=-\frac{1}{ln(n)}\sum_{j=1}^{n}p_{ij}ln\left(p_{ij}\right) \tag{4}\]The coefficient of variation reflects the amount of effective information an indicator carries. The larger the coefficient of variation, the greater the weight of the indicator. The formula is as follows:  
\[d_{i}=1-e_{i} \tag{5}\]  
Finally, by normalizing the coefficients of variation for all indicators, the weights of each indicator can be obtained. These weights reflect the relative importance of each indicator in the overall evaluation. The formula for this process is as follows:  
\[w_{i}=\frac{d_{i}}{\sum_{i=1}^{m}d_{i}} \tag{6}\]  
In the formula, m represents the total number of indicators. The next step involves determining the positive and negative ideal solutions. The positive ideal solution consists of the maximum values from each column, while the negative ideal solution is composed of the minimum values from each column.