The spatial optimization method between combinatorial optimization problems and GIS has many geographical applications. The p-center problem is a classic NP-hard location modeling problem, which has essential applications in many real-world scenarios, such as urban facility locations (ambulances, fire stations, pipelines maintenance centers, police stations, etc.). This study implements two methods to solve this problem: an exact algorithm and an approximate algorithm. Exact algorithms can get the optimal solution to the problem, but they are inefficient and time-consuming. The approximate algorithm can give the sub-optimal solution of the problem in polynomial time, which has high efficiency, but the accuracy of the solution is closely related to the initialization center point. We propose a new paradigm that combines a graph convolution network and greedy algorithm to solve the p-center problem through direct training and realize that the efficiency is faster than the exact algorithm. The accuracy is superior to the heuristic algorithm. We generate a large amount of p-center problems by the Erdos–Renyi graph, which can generate instances in many real problems. Experiments show that our method can compromise between time and accuracy and affect the solution of p-center problems.

The ability to quickly calculate or query the shortest path distance between nodes on a road network is essential for many real-world applications. However, the traditional graph traversal shortest path algorithm methods, such as Dijkstra and Floyd–Warshall, cannot be extended to large-scale road networks, or the traversal speed on large-scale networks is very slow, which is computational and memory intensive. Therefore, researchers have developed many approximate methods, such as the landmark method and the embedding method, to speed up the processing time of graphs and the shortest path query. This study proposes a new method based on landmarks and embedding technology, and it proposes a multilayer neural network model to solve this problem. On the one hand, we generate distance-preserving embedding for each node, and on the other hand, we predict the shortest path distance between two nodes of a given embedment. Our approach significantly reduces training time costs and is able to approximate the real distance with a relatively low Mean Absolute Error (MAE). The experimental results on a real road network confirm these advantages.

With the development of ecological civilization construction, urban planning and development in China have entered a phase in which optimizing and constructing ecological spaces is required. As a national livable city, Xuchang has experienced rapid economic development in recent years, leading to significant urban expansion that has impacted the layout of ecological space networks in the central urban area and its surroundings. Therefore, identifying and optimizing the spatial layout of ecological corridors in Xuchang City are crucial for ecological development and park city construction. This study utilizes multisource geospatial data to identify and extract ecological corridors in the central urban area of Xuchang City. Ecological resistance and gravity models are employed to identify and verify that the primary ecological corridor pattern in Xuchang City is situated in Weidu District, which is a central urban area. Finally, 11 main ecological corridors in the central urban area are delineated. In response to the identification of ecological corridors, this study integrates spatial analysis methods and text analysis methods to evaluate the characteristics of urban ecological corridors. The results indicate that Xudu Park extends outward, serving as the hub of the ecological network, and that West Lake Park and Luming Lake Park form the core of the urban park system. Finally, based on the spatial relationships, ecological benefits, and citizen experience of each ecological corridor and the green parks it traverses, strategies for optimizing the layout of urban ecological corridors are proposed.

Calculating the availability of bicycles and racks is a traditional method for detecting imbalance usage in a public bicycle system (PBS). However, for bike-sharing systems in Asian countries, which have compact layouts and larger system scales, an alternative docking station may be found within walking distance. In this paper, we proposed a synthetic and spatial-explicit approach to discover the imbalance usage by using the Hangzhou public bicycle system as an example. A spatial filter was used to remove the false-alarm docking stations and to obtain true imbalance areas of interest (AOI), where the system operation department installs more stations or increases the capacity of existing stations. In addition, sub-nearest neighbor analysis was adopted to determine the average distance between stations, resulting in an average station spacing of 190 m rather than 15.5 m, which can reflect the nonbiased service level of Hangzhou’s public bicycle systems. Our study shows that neighboring stations are taken into account when analyzing PBSs that use a staggered or face-to-face layout, and our method can reduce the number of problematic stations that need to be reallocated by about 92.81%.