AI 中文总结
针对大规模旅行商问题计算昂贵的问题，提出图边稀疏化（GES）方法，整合几何结构与组合优化技术，自适应生成稀疏化图，实验证明该方法能大幅修剪边，保持解与最优值差距小，且泛化能力强。
AI 中文摘要
精确求解大规模旅行商问题（TSP）在计算上成本高昂。研究人员常采用图稀疏化方法提高计算效率。传统方法依赖固定启发式，无法充分利用实例特定结构信息。本文提出图边稀疏化（GES），一种基于学习的欧几里得TSP稀疏化方法。通过整合几何结构信息和组合优化技术，为不同实例自适应生成稀疏化图，显著减小图规模并加速求解。实验表明，在MATILDA数据集上可修剪95%的边，解差距在最优值1%以内。在TSPLIB某些大规模实例上，修剪率超99%，最优性差距低于1%，且具有强泛化能力。
英文摘要
Solving large-scale instances of the Traveling Salesman Problem (TSP) exactly is computationally expensive. Researchers often employ graph sparsification methods to improve computational efficiency. Traditional sparsification methods typically rely on fixed heuristics and fail to fully exploit instance-specific structural information. In this paper, we propose Graph Edge Sparsification (GES), a learning-based sparsification approach for Euclidean TSP. By incorporating geometric structural information and combinatorial optimization technology, our proposed method adaptively generates a sparsification graph for different instances, significantly reducing the graph size and accelerating the solving process. Experimental results demonstrate that our sparsification method can prune up to 95% of edges on the MATILDA dataset, while keeping the solution gap within 1% of the optimal value. Moreover, our approach exhibits strong generalization capability on the TSPLIB benchmark.In some large-scale instances, the pruning rate exceeds 99%, while the optimality gap remains below 1%.
