# Bilateral Matching Decision Model and Calculation of High-Speed Railway Train Crew Members
## 5 Conclusions  
The main conclusions obtained in this paper are as follows:  
1. Considering the gaps in the research field of high-speed railway crew planning regarding crew matching, this study seeks the optimal matching scheme among crew members based on job matching degree. It provides technical means to solve this problem, verifies the validity of the constructed models and algorithms, optimizes the composition of train crews, and offers decision-making support for high-speed railway crew management and optimization.  
2. A multi-objective optimization model of one-to-many bilateral matching is constructed for the high-speed railway crew matching problem, based on the decision theory of bilateral matching and the theory of complete preference order. This expands the application field of bilateral matching theory.  
3. When solving the one-to-many bilateral matching model with an optimization solver, the solver fails to obtain a solution within an acceptable time frame as the problem size increases. Therefore, a genetic algorithm (GA) is designed to solve the problem for large-scale scenarios. Analysis of the results shows that Gurobi excels in both solving speed and objective function value, making it suitable for scenarios with high requirements for both time and quality. Although GA is well-suited for solving large and complex problems, its performance in terms of runtime and objective function value is inferior to Gurobi. In scenarios that require higher solution precision, it is advisable to optimize the algorithm to achieve higher-quality solutions.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline
**Number of** & & & & & & & & & & & & & & & \\
**Chief** & & & & & & & & & & & & & & & & \\
**Stewards** & & & & & & & & & & & & & & & & \\ \hline
90 & \(\widetilde{u}=\{(B_{1},\{A_{66},A_{125},A_{258}\}),(B_{2},\{A_{258},A_{35},A_{ 134}\})\cdots(B_{99},\{A_{95},A_{154},A_{176}\}),(B_{00},\{A_{14},A_{74},A_{ 254}\})\}\) & 387.8 & 22,111.5 \\
120 & \(\widetilde{u}=\{(B_{1},\{A_{66},A_{125},A_{258}\}),(B_{2},\{A_{258},A_{75},A_{ 134}\})\cdots(B_{99},\{A_{95},A_{154},A_{176}\}),(B_{00},\{A_{14},A_{74},A_{ 254}\})\}\) & 664.7 & 39,868.5 \\
150 & \(\widetilde{u}=\{(B_{1},\{A_{66},A_{125},A_{258}\}),(B_{2},\{A_{258},A_{75},A_{ 134}\})\cdots(B_{99},\{A_{95},A_{154},A_{176}\}),(B_{00},\{A_{14},A_{74},A_{ 254}\})\}\) & 1322.2 & 62,912.0 \\ \hline \hline \end{tabular}
\end{table}
Table 9: Simulation time and results under different problem scales.  
4. This paper only considers the problem-solving method based on the complete preference order information of the matching subject. To further improve the universality of the model, future work will consider the bilateral matching decision-making methods of the crew under different conditions, such as uncertain information and multi-attribute information, and will fully consider the matching relationship between the manager and the managed.  
Conceptualization, W.L. and Y.L. ([PERSON]); methodology, W.L.; software, Y.J.; validation, W.L. and Y.L. ([PERSON]); formal analysis, R.X. All authors have read and agreed to the published version of the manuscript.  
Lanzhou Jiaotong University Gansu Provincial Key Laboratory Open Project Approval (2024064).  
Not applicable.  
The datasets generated during and analyzed during the current study are available from the corresponding author upon reasonable request.  
The authors declare no conflicts of interest.