# A Multi-Objective Evaluation Method for Smart Highway Operation and Management
## 5 Application Results and Discussion
### Objective Weights Calculation and Discussion  
This study investigated five smart highways that were renovated, expanded, and upgraded to become smart highways from their original state. These highways were located in various provinces and cities in China, including Jiangxi, Shanghai, and Beijing. The varied topographical, infrastructural, climatic, and natural resource conditions in different provinces require a multifaceted approach to smart highway implementation. The utilization of advanced technologies included perception technology and Internet of Things (IoT) technology. Furthermore, the directions for applying smart highway upgrades varied, reflecting the distinct characteristics of each highway's design. For example, Highway A was mainly improved in three areas: traffic flow, emergency response, and maintenance operations. Conversely, Highway B was mainly upgraded in two areas, road detection facilities and service areas, aiming to provide a broader range of services. According to the data collected from these smart highways, scores for each smart highway were calculated using the existing conceptual model, resulting in Table 7.  
Data normalization was carried out according to Equations (13) and (14) to derive the normalized evaluation matrix. In the calculation of the weight matrix \(\mathbf{P}\), \(x_{ij}\) serves as the numerator. Hence, a threshold range was defined for \(x_{ij}\) to standardize the denominator, with values ranging from 0.0020 to 0.9960. Consequently, this process yielded the normalized standard matrix \(\mathbf{P}\).  
\[\mathbf{P}=\left(\begin{array}{cccc}0.0020&0.9960&0.6935\\ 0.2926&0.5189&0.9960\\ 0.8839&0.5984&0.7367\\ 0.3129&0.9960&0.5422\\ 0.9960&0.0020&0.0020\end{array}\right)\]  
Utilizing Equations (15)-(18) to apply the entropy weight method to the normalized data enables the calculation of the entropy value \(e_{j}\), information redundancy \(\mathbf{g}_{j}\), and the weight \(\mathbf{w}_{j}\) for each indicator. The results are shown in Table 8.  
Applying Equations (19)-(22) of the critic method to the normalized data allows us to determine the standard deviation \(\mathbf{s}_{j}\), correlation coefficient \(\mathbf{r}_{j}\), information content \(\mathbf{c}_{j}\), and the weight \(\mathbf{w}_{j}\) for each indicator. The results are shown in Table 9.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Highways** & **Highway A** & **Highway B** & **Highway C** & **Highway D** & **Highway E** \\ \hline A1 score & 91.1 & 92.24 & 94.56 & 92.32 & 95 \\ A2 score & 100 & 95.2 & 96 & 100 & 90 \\ A3 score & 95 & 96.4 & 95.2 & 94.3 & 91.8 \\ \hline \hline \end{tabular}
\end{table}
Table 7: Smart highway scoring table.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Weight Values** & \(\mathbf{e}_{j}\) & \(\mathbf{g}_{j}\) & \(\mathbf{w}_{j}\) \\ \hline A1 & 0.7782 & 0.2218 & 0.4157 \\ A2 & 0.8387 & 0.1613 & 0.3023 \\ A3 & 0.8495 & 0.1505 & 0.2820 \\ \hline \hline \end{tabular}
\end{table}
Table 8: Entropy weight method calculation results.  
The weight deviation of the target layers from the two objective weight methods is relatively small, showing a maximum deviation of just 4.67%. This suggests that the two objective weight methods can effectively and accurately portray the current developmental trajectory of smart highways.  
In terms of objective weights derived from the comparison of data from various highways, it was observed that the facility structure still garners the highest level of attention, followed by electromechanical facilities, with operations and services ranking last. This disparity from the weights ranking obtained through subjective methods indicates a significant emphasis on the conditions of various facility types in the surveyed smart highway projects in China.