HeatACO: A Heatmap-Guided Max--Min Ant System for Large-Scale Travelling Salesman Problems

Non-autoregressive neural solvers predict an edge-confidence heatmap for the Travelling Salesman Problem (TSP) in one forward pass, but a decoder must still produce a feasible Hamiltonian cycle. As instance size grows, this stage must reconcile a quadratic number of edge scores with global tour constraints. Greedy edge merging is fast and deterministic but produces low-quality tours, whereas Monte Carlo Tree Search (MCTS) over k-opt moves recovers better tours at high computational cost and requires predictor-specific tuning. We propose HeatACO, a predictor-agnostic heatmap-to-tour decoder. Its key is a capped, degree-aware evidence factor that integrates a fixed heatmap into a Max--Min Ant System (MMAS). The factor rewards only edge confidence beyond a node's tour-degree capacity, and its strength is scaled automatically from the pheromone dynamic range, allowing one configuration to decode heatmaps from different predictors without retraining or per-predictor tuning. Across four heatmap sources, HeatACO produces higher-quality solutions in less decoding time than the MCTS baseline on TSP500, TSP1K and TSP10K. Against matched standard MMAS baselines with the same search budget, heatmap guidance improves construction for all four predictors at both scales and remains beneficial with local search. HeatACO also transfers competitively to several distribution shifts and the asymmetric TSP (ATSP). Our post-hoc analysis identifies measurable heatmap properties associated with the observed performance variation.