[论文解读] HEATACO: Heatmap-Guided Ant Colony Decoding for Large-Scale Travelling Salesman Problems

Bo-Cheng Lin, Yi Mei+1 more|arXiv (Cornell University)|Jan 26, 2026

Vehicle Routing Optimization Methods被引用 0

一句话总结

HeatACO 将热力图边 confidences 视为软先验，并使用 Max–Min Ant System 解码器结合信息素反馈，在大规模下（多达 10K 节点）产生可行解的 TSP 线路，提供强劲的质量与时间权衡。

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.

研究动机与目标

• Motivate decoding for large-scale heatmap-based TSP solvers where the heatmap provides edge confidences.
• Develop a modular, scalable decoder that respects degree-2 and subtour constraints while leveraging heatmaps.
• Offer a lightweight alternative to MCTS-based or greedy decoders with competitive quality under practical budgets.
• Analyze how heatmap reliability and distribution shift affect decoding performance and provide practical tuning guidance.

提出的方法

• Introduce HeatACO, a Max–Min Ant System (MMAS) decoder that treats the heatmap as a multiplicative prior in transition probabilities.
• Bias MMAS sampling with a heatmap-based factor tilde{H}_{ij} derived from H, using a gamma exponent to control guidance strength (p_{i→j} ∝ (τ_{ij})^{α}(η_{ij})^{β}(tilde{H}_{ij})^{γ}).
• Construct sparse candidate lists from the heatmap (with distance-based fallbacks for connectivity) and optionally apply 2-opt/3-opt local improvement after decoding.
• Keep heatmap predictor f_{θ} fixed; pheromone updates provide lightweight, instance-specific global feedback to resolve conflicts.
• Optionally perform 2-opt/3-opt to tighten tours and reinforce pheromones with improved solutions.]
• research_questions: [

实验结果

研究问题

• RQ1 How can a heatmap-based edge prior be integrated into a scalable, feasible-tour decoder without relying on heavy search?
• RQ2 To what extent does heatmap-guided MMAS decode large-scale TSPs efficiently while maintaining high solution quality?
• RQ3 How do heatmap strength and calibration affect the decoding performance and robustness under distribution shift?
• RQ4 What is the impact of optional local search (2-opt/3-opt) on final tour quality and runtime?

主要发现

• HeatACO converts the same heatmaps into high-quality tours under practical CPU budgets, achieving gaps of 0.11%–1.27% on TSP500/1K/10K with seconds-to-minutes of decoding time.
• Compared with greedy decoding, HeatACO offers substantially better quality under similar budgets, and with 2-opt, often outperforms published MCTS-guided decoding within comparable or smaller budgets.
• Heatmap guidance speeds time-to-quality, especially on large instances (TSP10K), by biasing sampling toward high-probability edges while pheromones correct global conflicts.
• The method is robust when heatmaps preserve meaningful edge rankings, but miscalibration and distribution shift (OOD) can limit gains, highlighting heatmap generalisation as a key lever.
• A coarse gamma parameter (γ) controls the balance between heatmap following and exploration, with entropy-based or heuristic rules guiding selection when labels are unavailable.
• Ablations show that heatmap prior improves over vanilla MMAS, and 2-opt/3-opt can significantly tighten results, with 3-opt offering further gains at higher compute cost.