[Objectives] The quality of the leisure environment is a critical factor influencing residents' leisure experiences and participation, and it is closely related to the vitality of urban areas and economic development. Therefore, exploring how environmental quality influences the vitality of leisure space is crucial for promoting urban development. [Methods] A human-centered approach is adopted to construct a research framework for exploring the relationship between leisure environment quality and leisure space vitality based on image-text fusion perception. Online review texts and street view images are used to comprehensively perceive the leisure environment quality of the city. Natural language processing and semantic segmentation techniques are used to assess the leisure environment quality, while mobile signaling data is utilized to quantitatively measure the vitality of leisure spaces through user trajectory semantic modeling. Finally, using an Optimal Parameter-based Geographical Detector (OPGD), an in-depth analysis is conducted on the impact mechanisms of individual leisure environment quality factors and their interactions with the vitality of leisure spaces at global and local spatial scales in Nanjing. [Results] The findings reveal that: (1) The spatial distribution of leisure space vitality exhibits a "single-core-multi-center" pattern. The vitality in the main urban area is concentrated around the Xinjiekou commercial district, while Jiangbei District forms a "three-point" pattern with interactions between the two ends and the center. In the Xianlin area, high-vitality zones are distributed around the university town, while in the Dongshan area, they are located along the Shuanglong Avenue corridor. (2) On a macro scale, the leisure space vitality of Nanjing is indirectly dominated by economic levels. On a local scale, the influence of 14 leisure environment quality factors on leisure space vitality demonstrates significant regional heterogeneity. However, in municipal and district-level core areas with high leisure space vitality, the effects of these environmental quality factors are all significant. (3) The formation mechanism of leisure space vitality in Nanjing is closely related to regional geographical location, population density and composition, and economic income levels. [Conclusions] The analysis of Nanjing indicates that the exploration of leisure environment quality through image-text fusion perception enhances the systematic and comprehensive understanding of the factors influencing leisure space vitality and its mechanisms. This provides a scientific basis for optimizing the quality of the urban leisure environment and enhancing the vitality of leisure space.

[Objectives] Forests, as the backbone of terrestrial ecosystems, play crucial roles in climate regulation and soil and water conservation. Among the many threats to forests, the impact of forest fires is becoming increasingly severe. Analyzing the factors influencing forest fires is essential for preventing forest fires and formulating relevant strategies. [Methods] This study focuses on China, using multi-source data related to fires, vegetation, climate, topography, and human activities to analyze the spatial heterogeneity of forest fire driving forces from multiple perspectives. [Results] The findings reveal that: (1) At a global scale, the spatial distribution of forest fires is most influenced by FVC, with an explanatory power of 0.130 2, while climate factors exert a relatively strong influence. The interaction between driving factors is enhanced, and forest fire occurrence results from the combined influence of multiple factors. Moreover, a nonlinear relationship and impact threshold exist between these driving factors and the probability of forest fire occurrence. (2) At a local scale, climate and vegetation serve as key driving factors behind forest fires, significantly explaining their spatial distribution across different zones. Temperature is the most influential factor in the Cold Temperate Needle-leaf Forest region, the Temperate Coniferous and Broad-leaved Mixed Forest region, and the Alpine Vegetation of the Tibetan Plateau region, with explanatory powers of 0.313, 0.41, and 0.052, respectively. In contrast, wind speed is the dominant factor in the Warm Temperate Broad-leaved Forest region, with an explanatory power of 0.279. [Conclusions] The primary driving factors and their interactions vary across different regions, quantitatively confirming the spatial heterogeneity of forest fire driving forces. This research contributes to a national-scale understanding of forest fire drivers and fire hazard distribution in China, assisting policymakers in designing fire management strategies to mitigate potential fire risks.

[Objectives] Deep Convolutional Neural Networks (DCNNs) have been successfully applied to semantic segmentation of high-resolution remote sensing images. However, such images often exhibit large intra-class variance, small inter-class variance, and significant variations in target scale. Convolutional operations struggle to handle these complexities due to their localized nature. While Transformer-based methods offer powerful global information modeling capabilities, they are less effective at capturing local information. The combination of Convolutional Neural Networks and Transformers is widely used, yet optimizing these strategies for more effective feature integration remains a challenge. Additionally, many existing models focus on multilevel and multiscale feature extraction but fail to fully account for diverse target types and scales in high-resolution remote sensing images. [Methods] To address these challenges, this paper proposes a dual-path high-resolution remote sensing image segmentation algorithm for enhanced multi-scale target perception, utilizing an asymmetric dual encoder structure based on DCNN and Transformer. First, a Scalable Channel Spatial Pyramid module is introduced, leveraging deep convolution to dynamically extract fused multi-channel information while maintaining a large receptive field, enhancing the model's ability to capture multiscale features. Second, a Multiscale Feature Enhanced Transformer module is proposed, incorporating feature anchor preprocessing to provide spatial induction bias information. Additionally, a learnable cosine similarity matrix is constructed within the self-attention mechanism, guiding the module to focus on target features of varying scales while reducing redundant information interference. Finally, a Bilateral Feature-Guided Fusion module is constructed to facilitate fusion and information exchange between different-scale features across both branches through an attention mechanism. [Results] Comparative and ablation experiments were conducted on the Vaihingen and Potsdam datasets. The proposed model achieved 83.29% mean Intersection over Union, 90.65% mean F1 score, and 91.69% Overall Accuracy on the Vaihingen dataset, and 73.29% mean Intersection over Union, 83.98% mean F1 score, and 88.47% Overall Accuracy on the Postdam dataset. Compared to the best baseline method, the proposed model improved mIoU by 0.76% on the Vaihingen dataset and 1.42% on the Potsdam dataset. Additionally, a comparison of model complexity and segmentation performance showed that DMFPNet achieves the best balance between floating-point computation capacity, parameter efficiency, and segmentation performance. [Conclusions] In summary, the proposed model demonstrates strong performance and high segmentation accuracy in addressing the complex challenges of high-resolution remote sensing image semantic segmentation, including large intra-class and inter-class variance and variable target scales.

The greater food approach sets forth elevated requisites and novel benchmarks for the advancement of conceptualization, expansion of connotations, transformation of objectives, and evolution of strategies in the governance of non-grain conversion of cultivated land. A reevaluation of "Non-grain Conversion" of cultivated land governance through the greater food approach not only aids in rectifying the imbalance in food supply and demand, but also establishes a fundamental underpinning for national security assurance. Findings reveal that: (1) The crux of "Non-grain Conversion" of cultivated land under the greater food approach lies not in the dichotomy of "grain" versus "non-grain" but rather in the judicious allocation of diverse food categories within the framework of the greater food approach. (2) The greater food approach and "Non-grain Conversion" of cultivated land governance in the theoretical logic of the fundamental goal and value orientation consistency, theoretical origin and practice to follow the same origin, determines the two in the practical logic of interaction and linkage, embracing the greater food approach serves as the guiding ethos for "Non-grain Conversion" of cultivated land governance, constituting the bedrock and avenue for enacting the greater food approach. (3) Governance of "Non-grain Conversion" of cultivated land under the greater food approach encounters challenges such as lagging adjustments in planting structures, an inverted significance of grain and income gradients, simultaneous existence of production bottlenecks and wastage, as well as incongruences between universally applicable rectification measures and localized idiosyncrasies. (4) Proposals encompass five overarching strategies for systematized governance of "Non-grain Conversion" of cultivated land oriented towards the greater food approach, focusing on the preservation of grain within land, crops, techniques, losses, and policies. Grounded in the multifaceted demands and holistic outlook of the greater food approach, the optimization of governance strategies proffers invaluable insights for the theoretical refinement and practical exploration of "Non-grain Conversion" of cultivated land governance amidst the backdrop of a multidimensional transformation in the agricultural and food system.

[Objectives] Accurate and reliable daily Satellite Precipitation Products (SPPs) are essential data sources for meteorological and hydrological research. However, existing daily SPPs often fail to capture local precipitation details accurately and exhibit substantial errors in certain regions, resulting in unclear precipitation spatial characterization and low prediction accuracy. [Methods] To address these limitations, this study proposes SHW-Stacking, a weighted stacking method designed to enhance the quality of daily SPPs by accurately capturing spatial heterogeneity in precipitation. The method first integrates feature importance and nonlinear correlations for adaptive feature selection. It then employs Gaussian mixture clustering to delineate homogeneous subregions that reflect spatial heterogeneity of daily precipitation. Finally, a weighted stacking machine learning model fuses SPP data with gauge observations to generate high-accuracy precipitation estimates. [Results] Using daily IMERG precipitation data from China between 2016 and 2020, SHW-Stacking was rigorously compared against a traditionally partitioned categorical gradient boosting model (TC-CatBoost), five classical machine learning algorithms (CatBoost, LightGBM, XGBoost, RF, and ELM), and the original SPP. Results show that SHW-Stacking consistently outperforms all benchmarks across multiple temporal scales, accurately reconstructing the spatial distribution of observed precipitation. Specifically, it reduces the Mean Absolute Error (MAE) by at least 4.6%, 3.1%, and 2.7% at daily, seasonal, and annual scales, respectively, while improving the Kling-Gupta Efficiency (KGE) by a minimum of 3.4%, 1.9%, and 2.0% at the corresponding scales. Notably, SHW-Stacking demonstrates superior performance in capturing precipitation events exceeding 1 mm/day. Furthermore, clustering-based spatial partitioning emerged as the second most influential factor after IMERG data, ranking as the top and second-most significant contributor in 39.6% and 33.9% of cases, respectively. This highlights the critical role of spatial heterogeneity characterization in precipitation fusion. [Conclusions] In summary, SHW-Stacking effectively captures local precipitation details and accurately characterizes spatial precipitation distribution, providing a promising approach for refined precipitation data production.

The institution of territorial spatial governance for 'integrated mountains, rivers, forests, fields, lakes, grassland and deserts' is a direction for exploring ecological civilisation and is crucial for China to modernise its governance systems and capacity. This paper analyses the core concepts and theoretical logic of territorial spatial governance and analyses its governance problems and realisation bases. It explores the appropriate ways forward for the specific institutional construction. The main conclusions are as follows: (1) The current governance problems are that the ecological feedback of the governance object needs to be taken seriously, the coordination and linkage of the governance subject is still a problem, along with the fact the synergy and empowerment of the governance system is not yet in place. (2) It is necessary to respond to the demand for modernisation of the national governance system and capacity in the context of China's natural ecology, taking into account fairness and efficiency, and integrating security and development, yet to define the basis of the realisation of the governance subject and the governance system. (3) We should carry out the construction of territorial spatial governance institutions for 'integrated mountains, rivers, forests, fields, lakes and grasses' in three aspects, namely, the governance object, governance subject and governance system.

[Objectives] The 3D model reconstruction of buildings based on a model-driven approach using airborne LiDAR building point clouds relies on fitting the building point cloud to predefined geometric primitives. However, due to the uneven density and noise in the building point cloud, errors often arise in structural details during the primitive fitting process, leading to reduced reconstruction accuracy. To address this issue, this study proposes a 3D model reconstruction method for airborne LiDAR building point clouds based on sequential quadratic programming and elevation step correction. [Methods] First, a primitive library containing classical roof structures is established, including simple roofs, complex roofs, and steep roofs. An adjacency matrix is constructed by incorporating the adjacency relationships and ridge properties between roof patches. The best-matching primitives are then selected from the primitive library based on the adjacency matrix. Next, the shape parameters of the selected primitives are optimized using the sequential quadratic programming algorithm to achieve a globally optimal fitting state. The initial 3D model is then generated. To further enhance accuracy, the relative position of the building models and the roof point clouds in 3D space is refined through translation and rotation, reducing the relative distance deviation and improving the fitting precision. Finally, the City Geography Markup Language (CityGML) is used to store the reconstructed 3D building models, ensuring clear structure and correct topology, which facilitates the visual representation of reconstruction results. [Results] Ten sets of classical building point clouds from the 3D Building dataset were selected for the 3D model reconstruction experiment. The proposed method was compared with existing reconstruction approaches based on the same model-driven framework, and classical accuracy evaluation matrics were used for quantitative analysis. The average objective function value for the selected experimental data was 0.32 m, which is 0.03 m higher than the comparison method, indicating improved accuracy. The horizontal average deviation between the reconstructed building elements and the building point cloud was 0.10 m, while the vertical average deviation was 0.04 m. [Conclusions] In summary, the optimal shape parameters, obtained through the sequential quadratic programming algorithm, enable the construction of 3D building models with complete topology and regular shapes. Additionally, the elevation step correction, which utilizes the average point spacing of the roof point cloud as the step length, effectively enhances the reconstruction accuracy of 3D building models.

Agricultural ecosystem accounting is an important support for understanding the sustainability of agricultural production, the health of the ecological environment, and the quality and safety of agricultural products. Currently, there are three international standards for agricultural ecosystem accounting: the System of Environmental-Economic Accounting for Agriculture, Forestry and Fisheries (SEEA-AFF), the System of Environmental-Economic Accounting-Ecosystem Accounting (SEEA-EA2021), and The Economics of Ecosystems and Biodiversity for Agriculture & Food (TEEB-AgriFood). Based on these three international standards, some countries have carried out agricultural ecosystem accounting. This article first reviews the development process of the three international standards, and compares them from six aspects: theoretical basis, accounting perspective, accounting object, accounting scope, classification standard, and account expression. Secondly, the international practices of agricultural ecosystem accounting are summarized from the overall situation and practical experience. Finally, combined with the current situation of agricultural ecosystem accounting in China, policy recommendations for agricultural ecosystem accounting in China are proposed.

[Objectives] Existing semantic change detection methods fail to fully utilize local and global features in very high-resolution images and often overlook the spatial-temporal dependencies between bi-temporal remote sensing images, resulting in inaccurate land cover classification results. Additionally, the detected change regions suffer from boundary ambiguity, leading to low consistency between the detected and actual boundaries. [Methods] To address these issues, inspired by the Vision State Space Model (VSSM) with long-sequence modeling capabilities, we propose a semantic change detection network, CVS-Net, which combines Convolutional Neural Networks (CNNs) and VSSM. CVS-Net effectively leverages the local feature extraction capability of CNNs and the long-distance dependency modeling ability of VSSM. Furthermore, we embed a bi-directional spatial-temporal feature modeling module based on VSSM into CVS-Net to guide the network in capturing spatial-temporal change relations. Finally, we introduce a boundary-aware reinforcement branch to enhance the model's performance in boundary localization. [Results] We validate the proposed method on the SECOND and Fuzhou GF2 (FZ-SCD) datasets and compare it with five state-of-the-art methods: HRSCD.str4, Bi-SRNet, ChangeMamba, ScanNet, and TED. Comparative experiments demonstrate that our method outperforms these existing approaches, achieving a Sek of 23.95% and mIoU of 72.89% on the SECOND dataset, and a Sek of 23.02% and mIoU of 72.60% on the FZ-SCD dataset. In ablation experiments, as the proposed modules were progressively added, the SeK improved to 21.26%, 23.04%, and 23.95%, respectively, demonstrating the effectiveness of each module. Notably, compared with CNN-based, Transformer-based, and Mamba-based feature extractors,the proposed CNN-VSS feature extractor achieved the highest Sek, mIoU and Fscd, indicating its robust feature extraction capability and effective balance between local and global feature representation. Additionally, ST-SS2D improved the Sek score by 1.19% on average compared to other spatial-temporal modeling methods, effectively capturing the spatial-temporal dependencies of bi-temporal features and enhancing the model's ability to infer potential feature changes. Furthermore, the proposed edge-enhancement branch improved the consistency between detected and actual boundaries, achieving a consistency degree of 92.97%. [Conclusions] The proposed method significantly improves both the attribute and geometric accuracy of semantic change detection, providing technical references and data support for sustainable urban development and land resource management.

[Objectives] Inconsistencies between contour lines and rivers are a common challenge in updating and maintaining geospatial databases. Most existing studies focus on single-line rivers, with few addressing double-line rivers. To address this gap, this study proposes a method for detecting and resolving inconsistencies between contour lines and double-line rivers by analyzing their morphological features. [Methods] First, the DTW algorithm is used to establish a mapping relationship between the target nodes on both sides of the river's shoreline, and the Morphing transform is applied to extract the centerline of the double-line river. Second, contour valley points are identified based on bending feature parameters, and approximate valley lines are extracted using the DTW algorithm. Third, using the centerline of the double-line river as a reference, comprehensive judgment rules are established to assess inconsistencies between valley points and double-line rivers, as well as between valley lines and double-line rivers. Finally, the detected inconsistencies are corrected through contour transformation, river displacement, and contour collaborative transformation. Additionally, an affine transformation is applied to resolve cases where local contour lines fall into the water. [Results] This study conducts experiments in three different terrain areas. After correction, all valley points are positioned within the double-line river, and the average path difference between the valley line and the double-line river is significantly reduced. The overall average path differences corrected using contour similarity transformation combined with collaborative transformation are 2.417, 0.033, and 2.783 m, respectively. The overall average path differences corrected using river displacement combined with contour collaborative transformation are 2.667, 0.057, and 0.042 m, respectively, all of which remain within the consistency threshold. [Conclusions] This study thoroughly explores the morphological characteristics of contour lines and double-line rivers, enabling effective detection and correction of inconsistencies. By expanding the research scope of spatial relationship consistency between contour lines and rivers, this study contributes to the high-quality integration and fusion of multi-source geographic spatial data.

[Objectives] The quality of training samples significantly impacts model performance and prediction accuracy. In regions with limited sample data, the small number of samples and their uneven spatial distribution may prevent the model from effectively learning the features of disaster-inducing factors. This increases the risk of overfitting and ultimately affects the accuracy of model predictions. Therefore, it is crucial to collect and optimize training samples based on regional characteristics. [Methods] To address this issue, this study proposes a sampling optimization method for training samples. The method combines the Prototype Sampling (PBS) approach for selecting landslide-positive samples with an unsupervised clustering model for training sample selection. This results in a screened and expanded positive sample dataset and an objectively extracted negative sample dataset, forming an optimized training sample dataset. Subsequently, the Random Forest (RF) and Support Vector Machine (SVM) models, which are well suited for handling small sample data, were employed to construct a landslide susceptibility evaluation model. Comparative experiments were conducted using Raw Data (RD), a dataset with only Data Augmentation (DA), and the optimized dataset. Model prediction performance was assessed using metrics such as the Area Under the Curve (AUC). Additionally, the frequency ratio method was applied to optimize the results of landslide susceptibility zoning. Finally, a case study was conducted in Putian City, where landslide sample data is relatively scarce, to verify the effectiveness and generalization capability of the proposed sampling optimization method. [Results] The results indicate that models trained on the SO dataset achieved AUC improvements of 10.69% and 18.23% compared to those trained on the RD and DA datasets, respectively, demonstrating a significant enhancement in predictive performance. This suggests that selecting and expanding positive samples while objectively extracting negative samples can improve model accuracy and mitigate the overfitting problem during training. Furthermore, the frequency ratio analysis revealed that the SO-RF model achieved higher frequency ratios in regions with extremely high and high susceptibility than the SO-SVM model, indicating that SO-RF is more suitable for evaluating landslide susceptibility in regions with limited landslide sample data, such as Putian City. [Conclusions] The proposed training sample optimization approach, combined with machine learning evaluation methods, demonstrates high applicability and accuracy. Therefore, the findings of this study provide valuable insights into machine learning-based sampling strategies for landslide susceptibility assessment.

[Objectives] Building group patterns are a crucial component of urban structure and function, and their automatic recognition remains a key challenge in urban planning, analysis, and regional cartographic generalization. Existing research on building group pattern classification tends to be simplistic and specific, often overlooking the application of domain knowledge. To address this gap, this study proposes an automatic classification method for building group patterns that integrates domain knowledge. [Methods] First, driven by the need for multi-scale representation and cartographic generalization of buildings, building group patterns are classified into three categories—regular, mixed, and irregular—based on their distribution hierarchy within a block. A dataset is then constructed and annotated accordingly. Next, a Dual Positive Projection Graph (DPRG) and its node similarity feature description are designed, drawing from principles of visual cognition and traditional rule-based algorithms used in similarity judgment. Finally, a Graph Sample and Aggregate (GraphSAGE) network is introduced to develop an automatic classification model for building group patterns, leveraging data-driven learning to enhance classification capabilities. [Results] Experimental results show that DPRG outperforms commonly used neighbor graphs and their dual graph structures, achieving a test set accuracy of 91.2%, which is 9.0% higher than existing methods. Additionally, it attains 98.4% binary classification accuracy for distinguishing between regular and irregular patterns. Compared to GCN and GAT models, the proposed model improves classification accuracy by 3.6% and 4.6%, respectively. [Conclusions] The model demonstrates excellent classification accuracy for both regular and irregular patterns, as well as strong differentiation of ambiguous mixed patterns. The classification results have also been validated through application testing and analysis.

[Objectives] The similarity computation of multi-scale planar building groups has important applications in scene similarity retrieval, pattern recognition and matching, and map synthesis. However, traditional geometric methods can only extract low-dimensional building features when computing similarity, and their weight settings are highly subjective. Existing deep learning methods rarely consider spatial relationships between buildings and primarily obtain contextual information at the graph-level, often overlooking differences in finer details. To address these issues, this paper proposes a similarity computation method for multi-scale planar building groups that incorporates spatial relationships and SimGNN (Similarity Computation via Graph Neural Networks). By comparing geometric features and spatial relationship features of two building groups using both graph-level and fine-grained node-level strategies, the method calculates their similarity value. [Methods] First, experienced cartographers divide two vector maps of different scales into several building groups within the same area based on geographical features such as streets and rivers, ensuring that both datasets fully cover all buildings in the region. When the scale decreases, some buildings are merged or removed, leading to an inconsistent number of nodes in the graph structure of the two groups. To address this, pseudo-building data is added at the centroid positions of missing buildings, ensuring a "1:1" correspondence between the two groups. Their graph structures are then constructed using a minimum spanning tree. Next, the geometric features of each building and spatial relationship features, including topological, directional, and distance relationships, are extracted to form feature vectors. Finally, the graph structures and feature vectors are input into the SimGNN similarity computation model. The model processes the data at both the graph-level and the node-level to obtain overall similarity and node-level similarity between the two groups. [Results] Experimental results show that, compared to existing methods, the proposed model, by integrating geometric and spatial relationship features, produces similarity results that align more closely with human spatial cognition. Additionally, the model can reflect the nuanced differences between building groups through node-level similarity, significantly improving the accuracy of similarity computation across different scales. [Conclusions] The proposed model enhances the rationality and reliability of spatial data processing methods, including similarity retrieval, recognition, matching of building groups, and cartographic synthesis.

[Objectives] Urban road network selection is a critical research area in map generalization, aimed at simplifying map data by extracting key roads. Feature selection plays a crucial role in determining the accuracy of road network selection. However, with the continuous introduction of new feature indicators, selecting features scientifically has become an urgent challenge. [Methods] To address this issue, this study introduces the SHAP (SHapley Additive exPlanations) framework, a machine learning interpretability approach, into feature selection analysis for road network selection. The study is based on vector road network data at scales of 1:250 000 and 1:1 000 000, where a dataset is constructed by computing feature indicators. Two supervised learning models, XGBoost and LightGBM, were employed for training, and their performances were comparatively evaluated using accuracy, precision, recall, and ROC-AUC metrics. Finally, the SHAP framework was utilized to interpret the features from three perspectives: feature similarity, feature influence direction, and feature importance. This study focuses on seven common features: length, class, degree, betweenness centrality, closeness centrality, traffic flow, and number of POIs around roads. [Results] The experimental results indicate that, in terms of feature similarity, there is a strong correlation among topological features, whereas the similarity between mumber of POIs around roads and other features is relatively weak. Regarding the direction of feature influence, mumber of POIs around roads and traffic flow exhibit more unstable influence directions, while high values of the other features generally contribute positively to the model. In terms of feature importance, class is the most critical feature in nonlinear models, followed by length and traffic flow. In linear models, class remains the most important feature, but the significance of degree, betweenness centrality, and closeness centrality increases significantly. The study further applies the weight results from this paper to select the road network and compares the selection results with standard data. The experimental results show high consistency with the standard data. [Conclusions] This paper provides a novel approach for analyzing feature importance in road network selection and offers valuable insights for feature selection and weighting in the road network selection process.

[Objectives] Facility location problems have been widely applied in public service facility planning. Mainstream location problems typically aim to optimize objectives such as facility cost, travel cost, or customer coverage, often neglecting spatial equality. Delivering quality services in an efficient and equitable manner is critical to the general public. While some location models consider spatial equality, balancing service efficiency and equality in location problems remains both theoretically and practically challenging. In addition to spatial efficiency and equality, the cost of supply is also a key factor in service planning. This paper aims to formulate a Cost-Efficient and Equitable Facility Location Problem (CEEFLP) that simultaneously balances facility cost, spatial efficiency, and spatial equality. [Methods] The CEEFLP incorporates two objective functions: minimizing the total facility cost to optimize service supply costs and minimizing the aggregation of travel distance and distance semi-variance to balance spatial efficiency and spatial equality. The CEEFLP can be transformed into a single-objective location problem by converting the cost objective into a facility cost constraint. This transformation allows the problem to be efficiently solved using a Mixed-Integer Programming (MIP) optimizer or heuristic algorithms. To solve the CEEFLP, a heuristic algorithm based on Iterative Local Search (ILS) was designed, incorporating several key techniques: A fast node interchange method to improve the current solution, multiple solution perturbation methods to escape local optimum, a population of elite and diverse solutions to explore the solution space, and a set-covering procedure to identify better solutions. [Results] The effectiveness of the CEEFLP and the performance of the ILS algorithm were tested using four well-known benchmark instances and ten well-designed test instances. Pareto-optimal solutions for the CEEFLP were obtained by solving the single-objective problem with multiple parameter sets. Experimental results demonstrate that the proposed model effectively balances facility cost, travel cost, and spatial equality in location solutions. When the cost of supply is considered, the CEEFLP outperforms both the efficiency-oriented PMP and the equality-oriented MDELP. Two key findings emerge from the Pareto-optimal solutions: Increasing the facility cost budget can simultaneously reduce travel costs and improve spatial equality. Once the facility cost budget is determined, all spatial equality indicators can be improved with only a slight increase in mean travel distance. [Conclusions] The CEEFLP provides a set of Pareto-optimal solutions for selecting cost-efficient and equitable facility locations, making it a valuable tool for public service planning applications.

[Objectives] Understanding whether Large Language Models (LLMs) possess spatial cognitive abilities and how to quantify them are critical research questions in the fields of large language models and geographic information science. However, there is currently a lack of systematic evaluation methods and standards for assessing the spatial cognitive abilities of LLMs. Based on an analysis of existing LLM characteristics, this study develops a comprehensive evaluation standard for spatial cognition in large language models. Ultimately, it establishes a testing standard framework, SRT4LLM, along with standardized testing processes to evaluate and quantify spatial cognition in LLMs. [Methods] The testing standard is constructed along three dimensions: spatial object types, spatial relations, and prompt engineering strategies in spatial scenarios. It includes three types of spatial objects, three categories of spatial relations, and three prompt engineering strategies, all integrated into a standardized testing process. The effectiveness of the SRT4LLM standard and the stability of the results are verified through multiple rounds of testing on eight large language models with different parameter scales. Using this standard, the performance scores of different LLMs are evaluated under progressively improved prompt engineering strategies. [Results] The geometric complexity of input spatial objects influences the spatial cognition of LLMs. While different LLMs exhibit significant performance variations, the scores of the same model remain stable. As the geometric complexity of spatial objects and the complexity of spatial relations increase, LLMs' accuracy in judging three spatial relations decreases by only 7.2%, demonstrating the robustness of the test standard across different scenarios. Improved prompt engineering strategies can partially enhance LLM's spatial cognitive Question-Answering (Q&A) performance, with varying degrees of improvement across different models. This verifies the effectiveness of the standard in analyzing LLMs' spatial cognitive abilities. Additionally, Multiple rounds of testing on the same LLM indicate that the results are convergent, and score differences between different LLMs exhibit a stable distribution. [Conclusions] SRT4LLM effectively measures the spatial cognitive abilities of LLMs and serves as a standardized evaluation tool. It can be used to assess LLMs' spatial cognition and support the development of native geographic large models in future research.