用可学习排列直接求解旅行商问题，无需逐步搜索。
Structure As Search: Unsupervised Permutation Learning for Combinatorial Optimization
- 通过连续松弛学习排列矩阵，直接生成最优路径。
- 在无监督条件下性能媲美经典启发式算法。
- 适合研究组合优化与神经网络结构建模的学者。
我们提出一种非自回归框架解决旅行商问题，使解直接从学习到的排列中产生，无需显式搜索。通过将哈密顿环进行相似性变换，模型利用连续松弛逼近排列矩阵。该无监督方法在性能上可与经典启发式算法相媲美，证明了问题内在结构能有效引导组合优化，而无需依赖序列决策。本方法为神经网络直接捕捉并利用组合结构提供了实证支持。
原文摘要 · Abstract (English)
We propose a non-autoregressive framework for the Travelling Salesman Problem where solutions emerge directly from learned permutations, without requiring explicit search. By applying a similarity transformation to Hamiltonian cycles, the model learns to approximate permutation matrices via continuous relaxations. Our unsupervised approach achieves competitive performance against classical heuristics, demonstrating that the inherent structure of the problem can effectively guide combinatorial optimization without sequential decision-making. Our method offers concrete evidence that neural networks can directly capture and exploit combinatorial structure.
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