Evolving Spatial Weights for Cartographic Synthesis

2026-06-20

AI Summary

This study addresses the reliance on expert-derived weights and the absence of data-driven approaches in multi-thematic geographic layer fusion by proposing GIS-moGA, a novel bi-objective evolutionary framework. For the first time, spatial autocorrelation structure is integrated into a multi-objective genetic algorithm to automatically optimize layer weights by simultaneously maximizing global spatial autocorrelation (Global Moran’s I) and minimizing local spatial heterogeneity (LISA variance). The method employs a queen-contiguity sparse matrix to enhance computational efficiency for large-scale geographic units and uncovers the critical role of high mutation rates in maintaining population diversity. Validated on epidemiological data from 523 spatial units in Araraquara, Brazil, GIS-moGA significantly outperforms the Analytic Hierarchy Process (AHP), yielding a substantially larger Pareto front hypervolume and markedly improved spatial consistency (p < 0.001, Cliff’s delta = 0.87).

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.

Problem

• cartographic synthesis
• spatial autocorrelation
• multi-objective optimization
• geographic decision analysis
• spatial weights

Innovation

• multi-objective evolutionary algorithm
• spatial autocorrelation
• cartographic synthesis
• scalable spatial optimization
• GIS-moGA