用进化算法自动优化地图合成权重，提升空间一致性与可扩展性。
Evolving Spatial Weights for Cartographic Synthesis
- 基于空间自相关构建双目标优化框架，同时最大化全局集聚与最小化局部差异。
- 在523个区县数据上，相比专家方法显著提升空间连贯性（p<0.001）。
- 利用邻接矩阵稀疏性实现高效计算，支持大规模城市级制图分析。
将多个主题数据层整合为单一综合地图的制图合成问题，传统上依赖专家赋权。本文提出基于空间自相关结构的多目标制图合成框架，开发了双目标进化算法GIS-moGA，通过同时最大化全局空间结构（以全局莫兰指数衡量）和最小化局部空间异质性（以局部关联指标方差衡量）来估计各层权重。由于直接计算空间关系需O(N²)复杂度，对大数据不适用。本文利用97.7%稀疏的皇后邻接矩阵特性，将有效复杂度降至O(Nk)，实现可扩展的市级分析。在巴西阿拉拉夸拉市523个单元的高维空间流行病学数据集上，通过64种情景实验评估演化行为。结果表明，较高突变率有助于维持种群多样性，防止在具有空间自相关的适应度景观中过早收敛；而交叉操作可能破坏地理一致结构。相较于专家制定的层次分析法基线，所得帕累托前沿表现出显著的超体积增益及空间一致性提升（p < 0.001，Cliff's delta = 0.87）。研究为数据驱动的地理多准则决策分析提供了系统且可扩展的框架。
原文摘要 · Abstract (English)
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.
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