## 2 Problem Statement  
To better improve the readability of this paper, Table 1 shows the used input parameters and variables. The aim of the SPP is to provide proper services for travel demand that are represented by the stops at stations or between O-D pairs. Due to the complex spatial-temporal distributions of passenger demand, railway companies need to design diverse stop combinations to improve service level. However, a difference in stop patterns would result in a difference in travel speeds among trains, leading to an impact on capacity utilization. Figure 1 illustrates a sample of the impact. In Figure 1a, there are three trains running between \(s_{1}\) and \(s_{4}\) with the same stop pattern. Let the minimal departure headway between adjacent trains at the starting station be denoted by \(I\); then, the final arrival headway at the ending station \(H_{1}=2I\), equal to the departure headway. This means the occupancy time of the three trains is not expanded and the capacity would not be wasted in the timetabling stage. Figure 1b shows three trains with different stop patterns. To ensure operation safety, the departure times of subsequent trains must refer to the stop patterns of preceding trains. Thus, the departure headway is extended to \(2I+2\times t^{\text{stop}}\), where \(t^{\text{stop}}\) represents the additional time of one stop (including the stop time and acceleration/deceleration time). The final arrival headway is \(H_{2}=2I+t^{\text{stop}}\), shorter than the departure headway. In Figure 1c, trains can depart with minimal headway and the departure headway is \(2I\), but the final arrival headway would be \(H_{3}=2I+t^{\text{stop}}\) due to the stop pattern difference, longer than the departure headway. This indicates that a difference in stop patterns would influence the final arrival headway among trains. In Figure 1, \(H_{2}\) and \(H_{3}\) are both longer than \(H_{1}\), which means the occupancy time is expanded and the capacity utilization ratio would decrease, resulting from the diverse stop pattern combination. The core of the CUSPP is that the difference in stop density leads to the difference in travel speeds [49]. If we cannot take the stop distribution balance into account in the strategic line planning stage, the solved stop plan may fall to infeasibility in the scheduling stage. Thus, in spite of providing diverse services to satisfy passengers' travel demand, we should also incorporate capacity utilization into stop planning in the strategic level by balancing the stop distribution among trains. The HSR network is denoted by \(G=(V,E)\), where \(V,E\) are, respectively, the station set and the section set, and the designed train lines are collected in a set \(L=\{l=(V_{l},S_{l},C_{l},D_{l},R_{l})\}\). As for a train \(l\in L\), \(V_{l}=\left(v_{1}^{l},v_{2}^{l},\cdots,v_{h(l)}^{l}\right)\) is the sequence of passing stations on the route of train \(l\) in which \(h(l)\) is the number of passing stations. \(S_{l}=\left(x_{1}^{l},x_{2}^{l},\cdots,x_{h(l)}^{l}\right)\) is the sequence of stop symbols along the route: if \(l\) stops at \(v_{i}^{l},\ i=1,2,\cdots,h(l)\), then \(x_{i}^{l}=1\), otherwise \(x_{i}^{l}=0\); \(C_{l},D_{l},R_{l}\) represent the capacity, starting time, and class of train \(l\). The CUSPP is to incorporate capacity utilization into stop planning and solve the optimal stop plan to match the travel demand of passengers and balance the stop distribution among trains.