## 1 Introduction
Due to the advantages of hybrid algorithms [40; 41; 42], in recent years, to improve the searching capability of GA for particular problems, many researchers incorporate other optimization algorithms into GA, such as SAA [43], particle swarm optimization [44], sequential quadratic programming [45], support vector machine [46], and so on. According to the mentioned railway planning process, which can be viewed as a complex system project, each stage would impact the whole planning system [47; 48]. Due to the complex and imbalanced distribution of passenger demand, railway companies need to design different combinations of stop patterns to provide diverse services for passengers, leading to differences in stop density and travel speeds. Since the designed stop plan would be passed on to the scheduling stage where the final time information would be determined, the imbalanced patterns and travel speeds result in a change in occupancy time in the operation period, impacting the capacity utilization of HSR lines [49]. If it cannot be tackled, the stop plan may be infeasible in the scheduling stage. In recent years, some researchers studied the SPP concerned with stop distribution balance to reduce the impact of stop pattern difference on capacity utilization [50; 51; 52; 53]. [PERSON] [50] analyzed the impact of the stop patterns of trains with different speed classes on line capacity by statistical methods, and deduced quantified relations between the two sides. [PERSON] et al. [51] studied SPP considering the balance of stop number and accessibility among stations by a non-linear programming model, which was solved by a hybrid solving approach. [PERSON] et al. [52] deduced the adjacent headways of train groups and established the SPP model to minimize the occupancy time of train lines that was solved under SAA. [PERSON] et al. [53] studied the planning of a benchmark train working diagram based on an event-activity network where the temporal distribution balance and capacity utilization were taken into account. However, these studies mainly focus on the scheduling stage, not the line planning stage, where the matching between supply and demand was not involved. The main contribution of this paper is to incorporate capacity utilization into the SPP in the strategic line planning stage to trade off the matching between supply and demand and the stop distribution balance among trains. The capacity-utilization-orientedSPP (CUSPP) is formulated by a bi-level programming model based on Stackelberg game theory to describe the interaction between railway companies and passenger demand in stop planning. An adaptive hybrid solving algorithm combined with Genetic Algorithm (GA) and SAA is proposed according to the problem characteristics and optimization degree of the CUSPP to improve the searching efficiency. The case study on practical data demonstrates the validity of the proposed approach. This paper is organized as follows. Section 2 formulates the CUSPP, Section 3 constructs the bi-level programming model for the CUSPP based on Stackelberg game theory, Section 4 designs an adaptive hybrid solving algorithm combining GA and SAA, Section 5 is devoted to the case study based on real data, and Section 6 concludes the paper.