Solving the Traveling Salesman Problem (TSP) efficiently holds significant value across multiple domains, yet traditional algorithms and learning-based methods struggle to maintain efficiency while achieving high accuracy as the problem scales expand. Despite efficient inferring without any iterative search, neural constructive approaches, commonly starting solvers from a sequence of vertex embeddings for the entire instance, cause terrible computation complexity for large-scale problems due to global and meticulous spatial capture. In this paper, we introduce the General Decomposition and Merging Framework (GDMF), a novel approach enhancing the efficiency of solving large-scale TSP through parallel processes and multi-level representation. GDMF comprises two key steps: First, GDMF decomposes input instances into more tractable sub-units which are then processed in parallel to construct sub-paths, substantially accelerating computational throughput. To effectively generate tours, we integrate the neural network with multi-level features from individual vertices, local grids, and global graph topology, leading to comprehensive perception and potent decisions. Extensive experiments underscore the effectiveness of GDMF in time-critical settings. Notably, GDMF attains a superior computational efficiency, approximately 3–9 times speedup with a comparable optimality gap than the prior efficient method for large-scale TSP. This innovation showcases its potential for real-time decision support in practical applications such as dynamic routing in logistics and crisis management.

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Fusion of Multi-level Information: Solve Large-Scale Traveling Salesman Problem with an Efficient Framework

  • Wenzhao Liu,
  • Congying Han,
  • Tiande Guo,
  • Haoran Li,
  • Zicheng Zhang

摘要

Solving the Traveling Salesman Problem (TSP) efficiently holds significant value across multiple domains, yet traditional algorithms and learning-based methods struggle to maintain efficiency while achieving high accuracy as the problem scales expand. Despite efficient inferring without any iterative search, neural constructive approaches, commonly starting solvers from a sequence of vertex embeddings for the entire instance, cause terrible computation complexity for large-scale problems due to global and meticulous spatial capture. In this paper, we introduce the General Decomposition and Merging Framework (GDMF), a novel approach enhancing the efficiency of solving large-scale TSP through parallel processes and multi-level representation. GDMF comprises two key steps: First, GDMF decomposes input instances into more tractable sub-units which are then processed in parallel to construct sub-paths, substantially accelerating computational throughput. To effectively generate tours, we integrate the neural network with multi-level features from individual vertices, local grids, and global graph topology, leading to comprehensive perception and potent decisions. Extensive experiments underscore the effectiveness of GDMF in time-critical settings. Notably, GDMF attains a superior computational efficiency, approximately 3–9 times speedup with a comparable optimality gap than the prior efficient method for large-scale TSP. This innovation showcases its potential for real-time decision support in practical applications such as dynamic routing in logistics and crisis management.