Heatmap-based non-autoregressive solvers for large-scale Travelling Salesman Problems output dense edge-probability scores, yet final performance largely hinges on the decoder that must satisfy degree-2 constraints and form a single Hamiltonian tour. Greedy commitment can cascade into irreparable mistakes at large $N$, whereas MCTS-guided local search is accurate but compute-heavy and highly engineered. We instead treat the heatmap as a soft edge prior and cast decoding as probabilistic tour construction under feasibility constraints, where the key is to correct local mis-rankings via inexpensive global coordination. Based on this view, we introduce HeatACO, a plug-and-play Max-Min Ant System decoder whose transition policy is softly biased by the heatmap while pheromone updates provide lightweight, instance-specific feedback to resolve global conflicts; optional 2-opt/3-opt post-processing further improves tour quality. On TSP500/1K/10K, using heatmaps produced by four pretrained predictors, HeatACO+2opt achieves gaps down to 0.11%/0.23%/1.15% with seconds-to-minutes CPU decoding for fixed heatmaps, offering a better quality--time trade-off than greedy decoding and published MCTS-based decoders. Finally, we find the gains track heatmap reliability: under distribution shift, miscalibration and confidence collapse bound decoding improvements, suggesting heatmap generalisation is a primary lever for further progress.

翻译：基于热图的大规模旅行商问题非自回归求解器输出密集的边概率分数，但最终性能在很大程度上取决于必须满足度数为2约束并形成单一哈密顿回路的解码器。贪心承诺策略在大规模$N$下可能引发不可修复的级联错误，而MCTS引导的局部搜索虽精确但计算繁重且高度工程化。为此，我们将热图视为软边先验，并将解码建模为可行性约束下的概率性回路构建过程，其核心在于通过低成本的全局协调来修正局部排序错误。基于这一视角，我们提出HeatACO——一种即插即用的最大最小蚁群系统解码器，其转移策略受热图软性偏置，同时信息素更新提供轻量级、实例特定的反馈以解决全局冲突；可选的2-opt/3-opt后处理进一步优化回路质量。在TSP500/1K/10K数据集上，使用四种预训练预测器生成的热图，HeatACO+2opt在仅需秒至分钟级CPU解码时间（固定热图）的情况下，将最优解差距降至0.11%/0.23%/1.15%，相比贪心解码与已发表的基于MCTS的解码器提供了更优的质量-时间权衡。最后，我们发现性能提升与热图可靠性密切相关：在分布偏移下，校准偏差与置信度坍缩会限制解码改进，这表明热图泛化能力是推动后续进展的主要杠杆。