# Optimization of Multi-Day Flexible EMU Routing Plan for High-Speed Rail Networks
## 1 Introduction
### Summary of Literature Review  
In summary, extensive research--both domestic and international--has explored EMU routing plans from multiple perspectives, establishing a relatively mature theoretical foundation in areas such as circulation frameworks, optimization models, and algorithmic strategies. These studies have offered valuable references for EMU routing planning in China's high-speed railway network. However, limited attention has been paid to multi-day EMU routing plans that incorporate flexible maintenance arrangements and dynamic coupling/decoupling operations. The relevant literature is summarized in Table 1.  
However, most existing studies focus on single-day EMU routing and often assume fixed depot assignments without considering the flexibility of inspection site selection and  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**References** & **Model Type \({}^{*}\)** & **Background \({}^{*}\)** & **Objective \({}^{*}\)** & **Solution Methods** & **Variable Maintenance Depot** & **Coupling/ Decoupling Operation** & **Number of Days Days** \\ \hline
[6] & BIP & R & TUA & CPLEX & ✓ & two days \\ \hline
[11] & MIP & R & RSCP & Branch-and-bound & & one day \\ \hline
[13] & MIP & R & RSCP & Local search heuristic & & one day \\ \hline
[15] & MILP & R & RSS & Two-stage iterative solution & ✓ & two days \\ \hline
[16] & MILP & R & EMURP & Two-stage branch-and-bound & ✓ & & two days \\ \hline
[21] & BIP & R & RSCP & Branch-and-price & ✓ & one day \\ \hline
[23] & MINLP & URT & TFP + RSCP & Cplex & ✓ & one day \\ \hline
[24] & BIP & URT & TFP + RSCP & Multiobjective Chaos Particle Swarm & ✓ & one day \\ \hline
[25] & MILP & URT & RSCP & Cplex & ✓ & one day \\ \hline
[26] & MILP & URT & TFP + RSCP & Branch-and-price & ✓ & one day \\ \hline
**Our paper** & MILP & R & EMURP & Gurobi and heuristic & ✓ & ✓ & six days \\ \hline \hline \end{tabular}  
* R: rail; URT: urban rail transit; BIP: binary integer programming; MILP: mixed-integer linear programming; MIP: mixed-integer programming; TFP: train formation plan; RSS: rolling stock scheduling; RSCP: rolling stock circulation plan; TUA: train unit assignment; EMURP: EMU routing plan.  
\end{table}
Table 1: Comparison of selected literature on EMU routing plans.  
dynamic coupling/decoupling operations. This limits the adaptability of these models to real-world high-speed railway networks, where multi-day demand fluctuations and operational constraints are significant. Furthermore, although the urban rail transit domain has explored flexible train formations and multi-day scheduling, these approaches are not directly applicable to high-speed railway systems due to fundamental differences in service patterns, turnaround constraints, and maintenance requirements.  
To bridge this gap, this study proposes a novel flexible multi-day EMU routing optimization model that explicitly incorporates flexible inspection site selection and dynamic coupling/decoupling operations. The proposed approach aims to enhance practical applicability, improve operational efficiency, and better support large-scale high-speed railway networks with variable multi-day demand.