## 6 Comprehensive Analysis Based on the FAEWM  
### Determination of Weights Based on the Factor Analysis Method  
In the sensitivity analysis, nine indexes were chosen to evaluate the different schemes, and this particular index was excluded because the value of the number of stops was too small. In order to streamline the evaluation indexes and facilitate the evaluation of the schemes, the FAM was used to simplify the remaining eight indexes. Using the FAM is a process of downscaling high-dimensional data. The original variables are linearly combined into principal ingredients by studying the internal dependencies between the original variables. To minimize the loss of information on the original variables, multiple indexes are transformed into several comprehensive indexes independent of each other. This allows the comprehensive indexes to reflect the vast majority of the information of the original variables. The flowchart of the FAM is shown in Figure 8.  
The detailed steps of the factor analysis method are outlined below. Xi denotes the eight indexes obtained from the simulation results, \(i\) is the serial number of the indexes, and \(p\) is the number of traffic condition grouping (refer to (8)). \[X=[X_{1},X_{2},\cdots,X_{i}]^{T} \tag{8}\]  
Figure 7: Improvement ratio of Scheme 4 compared to Scheme 1. (**a**) Delay, (**b**) travel time, (**c**) CO emission, and (**d**) number of conflicts. where \(X_{i}\) can be represented as:  
\[ \begin{bmatrix}X_{1}\\ X_{2}\\ \vdots\\ X_{i}\end{bmatrix} = \begin{bmatrix}\alpha_{11}&\alpha_{12}&\cdots&\alpha_{1p}\\ \alpha_{21}&\alpha_{22}&\cdots&\alpha_{2p}\\ \vdots&\vdots&\cdots&\vdots\\ \alpha_{i1}&\alpha_{i2}&\cdots&\alpha_{ip}\end{bmatrix}\begin{bmatrix}F_{1}\\ F_{2}\\ \vdots\\ F_{p}\end{bmatrix} + \begin{bmatrix}\varepsilon_{1}\\ \varepsilon_{2}\\ \vdots\\ \varepsilon_{i}\end{bmatrix}  \tag{9}\]  
where the coefficient matrix \(\alpha_{ip}\) is the factor loadings, \(A=(\alpha_{ip})\) is the factor loading matrix, \(F\) is the common factor, and \(\varepsilon\) is the special factor. Step 1: Standardization of the Raw Data  
* Consistent processing  
The eight selected indexes encompass various characteristics, with larger values indicating preferable scheme performance for positive indexes while smaller values indicate better performance for inverse indexes. To maintain consistency among the indexes, all are transformed into positive indexes, normalized using (10). \[{x^{\prime}}_{ip}=\max\{x_{i}\}-x_{ip} \tag{10}\]
* Dimensionless processing  
As different indexes have different dimensions, the difference in magnitude of the values can be very large, which may result in indexes with smaller magnitudes being ignored. Therefore, it is necessary to eliminate the dimensions of all indexes. The linear normalization method is used for processing, and the specific calculation formula is shown in (11). \[{x^{\prime\prime}}_{ip}=\frac{{x^{\prime}}_{ip}-\min\{{x_{ip}}^{\prime}\}}{\max \{{x_{ip}}^{\prime}\}-\min\{{x_{ip}}^{\prime}\}}\ \ (i=1\text{ to }10;\ p=1\text{ to }45) \tag{11}\]  
Figure 8: Flowchart of the FAM. where \(\tilde{x}_{ip}\) denotes the standardized index, \(\min\{{x_{ip}}^{\prime}\}\) denotes the minimum value of the index, and \(\max\{{x_{ip}}^{\prime}\}\) denotes the maximum value of the index. Step 2: Correlation test  
Before conducting factor analysis, it is necessary to conduct the KMO and Bartlett's sphericity tests to determine whether the original variables are strongly correlated or not. If the correlation is weak, factor analysis may not be suitable or informative for the given variables. * KMO test  
The KMO value is within [0, 1], where a higher value indicates a stronger correlation among the variables. A KMO value above 0.7 is generally considered suitable for factor analysis, implying that the variables are sufficiently interrelated to proceed with the analysis. * [PERSON]'s test of sphericity  
[PERSON]'s test of sphericity is used to assess the interdependence among variables.