# An Optimization Model for a Desert Railway Route Scheme Based on Interval Number and TOPSIS
## 2 Research Methods
### Comprehensive Weight of the Indicators  
There are differences in the importance of evaluation indicators to the decision-making for railway schemes. The calculation methods of the index weight include the objective  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**First-Level Indicators** & **Second-Level Indicators** & **Indicator Type** \\ \hline \multirow{4}{*}{\begin{tabular}{c} Railway design \\ (\(C_{1}\)) \\ \end{tabular} } & Length of the railway line (\(C_{11}\)) & Quantitative \\  & Land requisition amount (\(C_{12}\)) & Quantitative \\  & Project investment (\(C_{13}\)) & Quantitative \\  & Minimum curve radius (\(C_{14}\)) & Quantitative \\  & The ratio of the bridges and tunnels (\(C_{15}\)) & Quantitative \\ \hline \multirow{4}{*}{\begin{tabular}{c} Wind-sand hazard \\ (\(C_{2}\)) \\ \end{tabular} } & Railway length in the moveable dune area (\(C_{21}\)) & Quantitative \\  & The angle between the railway and the wind & Quantitative \\  & direction (\(C_{22}\)) & Quantitative \\  & Temporary land occupation (\(C_{23}\)) & Quantitative \\  & Feasibility of the plant sand control (\(C_{24}\)) & Qualitative \\  & The scale of the sand control work (\(C_{25}\)) & Qualitative \\ \hline \multirow{4}{*}{\
\begin{tabular}{c} Environmental impact \\ (\(C_{3}\)) \\ \end{tabular} } & Impact on nature reserves (\(C_{31}\)) & Qualitative \\  & Impact on the water environment (\(C_{32}\)) & Qualitative \\ \cline{1-1}  & Impact on the wildlife (\(C_{33}\)) & Qualitative \\ \cline{1-1}  & Impact on the vegetation cover (\(C_{34}\)) & Qualitative \\ \cline{1-1}  & Impact on the basic farmland (\(C_{35}\)) & Qualitative \\ \hline \multirow{2}{*}{
\begin{tabular}{c} Operation condition \\ (\(C_{4}\)) \\ \end{tabular} } & Speed limit (\(C_{41}\)) & Qualitative \\  & Track maintenance (\(C_{42}\)) & Qualitative \\ \cline{1-1}  & Operation safety (\(C_{43}\)) & Qualitative \\ \hline \hline \end{tabular}
\end{table}
Table 1: Evaluation index system of the desert railway route.  
weight method and the subjective weight method. The objective weight method determines the weight according to the attribute data of the indicators, and the calculation results are not affected by human factors. However, the weight determined by this method may not conform to the actual importance of the indicator. The subjective weighting method determines the weight according to the subjective judgments of experts to each index. The weight results are commonly not affected by the value of the indicator attribute.  
The intersection of qualitative and quantitative indexes in scheme decision-making for desert railway magnifies the difficulty of index weight calculations. The accuracy of index weight affects the correctness of scheme evaluation. Given the optimization complexity of railway location schemes, any single weighting methodology may lead to inaccurate calculation results. Based on the weight combination method herein, the subjective and objective weights are considered and appropriately combined to determine the comprehensive weights of indicators. As a result, the evaluation results will be more rational and consistent with the actual situation of the railway location scheme optimization.