HEATACO: Heatmap-Guided Ant Colony Decoding for Large-Scale Travelling Salesman Problems

TL;DR

HeatACO introduces a novel heatmap-guided ant colony decoding method for large-scale TSPs, effectively balancing solution quality and computational efficiency by treating heatmaps as soft priors and using global coordination.

Contribution

The paper presents HeatACO, a new probabilistic tour construction approach that leverages heatmaps as soft priors and integrates lightweight global feedback, outperforming existing methods in large-scale TSPs.

Findings

HeatACO achieves near-optimal solutions with minimal computation.

The method outperforms greedy and MCTS-based decoders on large TSP instances.

Heatmap reliability correlates with decoding performance, especially under distribution shifts.

Abstract

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.