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GAT-Metas: GeoAI-based metaheuristic framework for solving combinatorial optimization problems
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DOI：10.1007/s10109-026-00499-2.png)
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Abstract
En 中文
Traditional spatial optimization problems such as the maximal coverage location problem and the p-median problem are NP-hard, which makes it difficult to obtain optimal solutions in general. To address this computational difficulty, metaheuristics have been widely deployed. However, they usually operate in spatially blind contexts that do not explicitly account for geographic structures, tending to converge to suboptimal solutions. This study proposes a new hybrid framework named GAT-Metas that integrates a Graph Attention Network (GAT) with metaheuristics to overcome these limitations. GAT-Metas trains GATs in a supervised proxy prediction task to learn an interpretable map of spatial potential. The learned spatial potential is then used to probabilistically bias both initial solution construction and neighborhood search within the metaheuristic and remains fixed during each metaheuristic run. We validate the framework using synthesized grid instances and a case study on optimal placement of shared e-scooter parking zones in Seoul. The experiments show that the GAT-SA and GAT-TS outperform their purely random-initialized counterparts and, for some large instances, even time-limited commercial Mixed-integer Programming baselines, yielding statistically significant improvements and more stable solutions. By combining deep learning’s pattern recognition ability with the exploratory power of classical optimization methods, the GAT-Metas offers a methodological advance for solving complex urban siting problems more effectively, reliably, and interpretably.
Keywords:
GAT-Metas
Spatial optimization
Graph attention network
Graph neural network
Metaheuristics
Micro-mobility
Shared e-scooters
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