## 4 Discussion and Conclusions
### Conclusions  
With the fast expansion of urban infrastructure and the continual upgrading of the urban public transportation network system, it is becoming increasingly important to give the optimal travel plan to travelers in restricted networks. This study proposes an improved A* algorithm for the optimal path analysis of the restricted networks to suit the demands of travelers regarding the transfer of public transportation networks. Furthermore, as urban satellite towns develop and the concept of low-carbon travel is implemented, the proliferation of P&R transfer parking lots and the demand for transfer travel in hybrid networks are on the rise. Based on the improved A* algorithm for path analysis of restricted networks, an A* algorithm for path analysis of hybrid networks is developed to fulfill the transfer travel demands of travelers combining private cars and public transportation. The following highlights are the properties of the improved A* algorithm proposed in this paper:  
1. The algorithm takes into account the diverse travel requirements of travelers, incorporating factors such as transfer numbers, travel time, and travel costs. A multivariate heuristic function is proposed to determine the priority of nodes during the node expansion operation. Finally, the optimal travel plan is determined by carefully addressing the various demands of travelers. 2. The heap and search tree methods are introduced in the key step of the A* algorithm of expanding node operations, considerably improving the operational efficiency of the algorithm and achieving a better user experience. Figure 14: The example of the algorithm in Amap: (**a**). Case 1; (**b**). Case 2. 3. The spatial topological relationship between the public transportation stations and the road centerline network is established by determining the subordinate relationship between the stations and the centerline within a specified buffer zone. Thus, the topological relationship between the restricted and the unrestricted networks are formed, providing the essential data foundation for the implementation of the algorithm for path analysis of hybrid networks. As a result, the algorithm effectively addresses the transfer demand between private cars and public transportation. 4. During the algorithm design process, buffer search is incorporated into the node expansion method. This allows the algorithm to calculate the demand for transfers between various forms of public transportation lines, such as rail transit, bus lines, airport express lines, ferry lines, tourist lines, trans, suburban special lines, and others. 5. Currently, the wave of digital innovation and the integration of the sharing economy has been gradually changing the way people live and travel, such as the successive popularization and promotion of bike sharing, which provides more convenient options for people to travel [45]. This is particularly significant for such a cosmopolitan city like Shanghai, where bike sharing can address the last kilometer problem, providing a valuable supplement in public transportation travel. In future research, it is hoped that the bike-sharing-related data (parking points, electronic fences, vehicle service providers, etc.) can be integrated into the algorithm to provide more refined travel choices for travelers according to their preferences and more accurate positioning. The improved A* algorithm proposed in this paper primarily addresses the optimal path analysis issue in restricted networks and hybrid networks. It solves the P&R transfer problem from private cars to public transportation in hybrid networks. In the future, commercial e-navigation maps, such as Amap, are expected to incorporate corresponding P&R travel path search navigation services for the combination of private cars and public transport to meet the growing demand for P&R travel. Additionally, with the popularity and promotion of shared bicycles in recent years, the use of shared bicycles for public transportation has become increasing convenience for travelers.