## 1 Introduction
[PERSON] and [PERSON] proposed a hybrid model that predicts short-term demand for an HSR by combining singular spectrum analysis, a convolutional neural network (CNN), and support vector regression [27]. [PERSON] et al. developed a hybrid approach combining the ensemble empirical mode decomposition (EEMD) and gray support vector machine (GSVM) for the short-term prediction of HSR flows [28]. When planning and constructing a new railway line or station, the influencing factors of demand become the variables for long-term demand forecasting. [PERSON] et al. proposed several factors affecting long-term passenger flow in rail transit, constructing a prediction model based on a class neural network [29]. [PERSON] et al. focused on investigating the relationship between the built environment around the station and its passenger flow, developing a passenger flow prediction model using a multilayer perceptron (MLP) that could be applied to new railway stations without historical passenger flow data [30]. [PERSON] et al. used mathematical and neural network methods to predict metro passenger flow based on land use around stations [31]. [PERSON] et al. divided a city into multiple regions with similar internal traffic properties and a moderate spatial size to obtain more accurate factors affecting passenger flow, proposing a new prediction model based on the fuzzy processing method and Xgboost [32]. [PERSON] et al. proposed a passenger flow prediction model based on station attributes affecting passenger flow regularity and predicted the passenger flow of a new line or station using its own attributes [33]. [PERSON] et al. presented a new system with deterministic and probabilistic forecasting capacities based on residual component disposing for HSR demand forecasting [34]. Using long-distance elasticities, [PERSON] investigated the prediction performance of two state-of-the-art Swedish HSR demand-forecasting models: the nested logit-based Sampers long-distance model and the newly developed Box-Cox transformation-based model [35]. Thus, a large number of researchers are engaged in this topic on all continents. The optimal strategy algorithm has been widely used not only academically but also practically in railway trip assignment models [36; 37]. This algorithm assigns origin-destination (O/D) trips to the route that minimizes passenger travel time among various route options. The procedure is as follows [38]:  
1. Define a departure node (station or stop);
2. Move to and board the vehicle that arrives first at the departure node among the competing routes;
3. Get off at the intermediate node (station or stop) that was determined according to the optimal strategy;
4. End if the passenger arrives at their destination; otherwise, define the alighting node as the departure node and repeat from step 1. This approach is limited when simulating access trip patterns from each zone to diverse railway stations because this algorithm is based on an all-or-nothing trip assignment approach assigning all trips to only one railway station that minimizes the generalized cost. [PERSON] et al. proposed a practical procedure that automatically calibrates and validates large-scale transit assignments based on the optimal strategy [36]. They used smart card data and adopted a particle swarm optimization (PSO) algorithm as an optimization technique. [PERSON] and [PERSON] [39] and [PERSON] et al. [40] improved the optimal strategy algorithm to simulate congestion and delay by considering capacity constraints in the optimal strategy, but they did not overcome other limitations. There are many access modes to HSR stations, and those selected by passengers will vary depending on the preferred access modes in a zone. Furthermore, in an HSR trip, the proportion of access time compared with in-vehicle time in the total travel time is higher than that of other public transportation. Therefore, it is necessary to develop a trip assignment algorithm that can reflect the diverse passenger preferences for accessibility to HSR stations.