Evolving Spatial Weights for Cartographic Synthesis
Authors: Gesiel R. Lopes, Roberto F. da Silva, Mellina Yamamura, Sergio H. V. L. de Mattos, Antonio M. Saraiva, Alexandre C. B. Delbem, Eric K. Tokuda
Organizations: Institute of Mathematics and Computer Sciences, University of Sao Paulo, Sao Carlos, Brazil · Biosystems Engineering Department, University of Sao Paulo, Piracicaba, Brazil · Department of Nursing, Federal University of Sao Carlos, Sao Carlos, Brazil · Department of Hydrobiology, Federal University of Sao Carlos, Sao Carlos, Brazil · Polytechnic School, University of Sao Paulo, Sao Paulo, Brazil
Abstract
The integration of multiple thematic data layers into a single composite map, known as the cartographic synthesis problem, is typically addressed through expert-driven weighting schemes. This study presents a multi-objective formulation of cartographic synthesis grounded in spatial autocorrelation structure. We develop a bi-objective evolutionary framework, GIS-moGA, that estimates layer weights by simultaneously maximizing global spatial structure, measured by Global Moran's I, and minimizing local spatial heterogeneity, measured by the variance of Local Indicators of Spatial Association (LISA). Because naive evaluation of spatial relationships requires O(N^2) operations, direct computation becomes impractical for larger datasets. We address this challenge by exploiting the 97.7% sparsity of queen contiguity matrices, reducing effective complexity to O(N k) and enabling scalable municipal-level analysis. The framework is evaluated on a high-dimensional spatial epidemiology dataset with N = 523 units from Araraquara, Brazil. A 64-scenario experimental design is used to examine evolutionary behavior across parameter settings. Results show that higher mutation rates are important for maintaining population diversity and preventing premature convergence in spatially autocorrelated fitness landscapes, where crossover operators can disrupt geographically coherent structures. Compared with expert-derived Analytic Hierarchy Process baselines, the resulting Pareto fronts show substantial hypervolume gains and significant improvements in spatial coherence (p < 0.001, Cliff's delta = 0.87). These findings provide a systematic and scalable framework for data-driven geographic multi-criteria decision analysis.
We analyze an algorithm for assigning weights prior to scalarization in discrete multi-objective problems arising from data analysis. The algorithm evolves weights (interpreted as the relevance of features) by a replicator-type dynamic on the standard simplex, with update indices computed from a normalized data matrix. We prove that the resulting sequence converges globally to a unique interior equilibrium, yielding non-degenerate limiting weights.
Aris Daniilidis, Alberto Domínguez Corella, Philipp Wissgott
We present IOAH3 (Importance-Oriented Adaptive H3 partitioning), a computational method for constructing data-driven spatial partitions of geo-referenced observation domains. Standard approaches to spatial aggregation adopt fixed areal units, such as administrative boundaries or uniform hexagonal grids at a single resolution, without regard to the informational content of the underlying observations in each region. This leads to the well-known modifiable areal unit problem: statistical and inferential results depend on the arbitrary choice of partition, and spatially concentrated phenomena are averaged out in coarse cells that obscure fine-scale structure. IOAH3 addresses this by constructing an adaptive partition in three stages: multi-source feature extraction and importance scoring via principal component analysis over road density, POI density, building density, and terrain roughness signals, with population and flood-hazard data entering as auxiliary inputs to cell filtering and spatial smoothness; spatial cell selection via Markov Random Field graph-cut optimisation, which jointly maximises per-cell importance while enforcing spatial contiguity; and data-driven hierarchical refinement of high-importance regions to finer H3 resolution levels, with neighbour-propagated support to avoid isolated fine-resolution islands. The resulting partitions serve as input to spatial inference pipelines and provide a principled resolution of the partition-sensitivity problem prior to any modelling step.
Spatial understanding is crucial for foundation models (FMs), and maps have long helped humans organize and reason about geographic information. This study examines whether choropleth maps remain useful for machine spatial understanding when models can directly process structured geodata. We introduce ChoroplethMap-Bench, a controlled benchmark containing 2,400 synthetic choropleth maps, corresponding GeoJSON data, and 12,000 questions across five cognitive dimensions: Identify, Spatial Recognition, Compare, Rank, and Delineate. We evaluate 22 open-source and proprietary models under three input conditions: Data Only, Map Only, and Data + Map. The results show that maps substantially improve spatial reasoning, especially when combined with symbolic data and for tasks requiring higher-level understanding of spatial patterns. We further analyze the effects of map type, color hue, and spatial structure, as well as prompting strategies, language, geographic context, decoding settings, classification methods, and response stability. Overall, the Data + Map condition achieves the strongest performance, demonstrating that maps remain valuable external representations for foundation model spatial reasoning.