## 6 Conclusions  
In this paper, we propose a capacity-utilization-oriented approach for stop planning in the strategic line planning stage by trading off the matching between supply and demand and the stop distribution balance among trains. A bi-level programming model is established based on Stackelberg game theory to describe the interaction and conflicts between railway companies and passengers, where the two levels, respectively, focus on stop plan optimization and evaluation feedback by passenger flow assignment. In the model, stop distribution imbalance is measured by the difference in stop time ratios along the same segment, and the additional time ratio is adopted to describe the travel inefficiency \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Direct Travel** & **[0,50]** & **(50,100]** & **(100,150]** & **(150,200]** & **>200** \\ \hline OSP & 0.7724 & 0.6008 & 0.5112 & 0.4532 & 0.4437 \\ ISP & 0.7779 & 0.5968 & 0.5218 & 0.4726 & 0.4508 \\ \hline \hline \end{tabular}
\begin{tabular}{c} OSP: optimized stop plan; ISP: initial stop plan. \\ \end{tabular}
\end{table} 
Table 7: Comparison of average additional time ratios in different ranges of direct travel time. Figure 9: Illustration of the distributions of the additional time ratios of passengers. (The squares show the zones with descent trend of the OSP, compared to the ISP). in passengers' journeys. An adaptive hybrid GA-SAA algorithm is designed where the Metropolis strategy in SAA is incorporated into GA to further improve the neighborhood searching efficiency. According to the problem characteristics and optimization degree of the CUSPP, several adaptive operations are proposed, including the encoding form, genetic operators, neighborhood searching strategies, etc. The performance of the proposed approach is evaluated by real data based on the local network of the Beijing-Shanghai High-speed Railway Line. It is indicated that the proposed approach can not only mitigate stop distribution imbalance, but also improve the service level. It can further balance the stop distribution of the two directions of the same segment, benefiting train circulation. Train stop ratios would become more balanced with the mitigating of stop distribution imbalance, which means the two indexes can be simultaneously improved. As for the service index, the additional time ratio would decrease with an increase in direct travel time. There is a descent trend of additional time ratios in the OSP, indicating that the proposed approach is beneficial to improving the travel efficiency and service level for passengers, especially for medium-distance and long-distance passengers. This demonstrates that the proposed approach can benefit the simultaneous improvement of capacity utilization and service level. The proposed approach would guide operators to make decisions in practical operation and it can also be implemented in other transportation systems, such as the URT and regional railway system. In spite of the mentioned good performance, our future research can be improved and extended in several aspects. First, we would further improve the proposed approach, including the model formulation, solving scale (for example, the population size) and efficiency, solution accuracy, etc. Second, we need to consider more theoretical and practical factors in the SPP to improve the accuracy and feasibility of the approach. Third, the CUSPP focuses on the spatial balance of stop distribution, so we can extend the SPP into the problem of the spatial-temporal balance of stop distribution to further improve the operation efficiency and service level for different space-time zones. Conceptualization, S.Z. and J.W. ; methodology, S.Z. ; software, S.Z. and J.W. ; validation, S.Z., L.Z. and Z.L. ; formal analysis, S.Z. ; investigation, X.L. ; resources, X.S. ; data curation, J.W. and L.Z. ; writing--original draft preparation, S.Z. ; writing--review and editing, J.W. ; visualization, L.Z. and X.L. ; supervision, X.S. ; project administration, S.Z. and X.S. ; funding acquisition, S.Z. and X.S.