Beyond the Heatmap: A Rigorous Evaluation of Component Impact in MCTS-Based TSP Solvers
Xuanhao Pan, Chenguang Wang, Chaolong Ying, Ye Xue, Tianshu Yu
TL;DR
This paper critically evaluates the impact of heatmap complexity versus MCTS configuration in TSP solvers, showing that simple heatmaps with proper tuning can outperform complex ones, emphasizing the importance of MCTS tuning.
Contribution
It introduces a standardized pipeline for MCTS hyperparameter tuning and demonstrates that simple, parameter-free heatmaps can match or outperform complex learned heatmaps in TSP solving.
Findings
MCTS configuration significantly affects solution quality.
Simple heatmaps based on k-nearest neighbors perform well with tuned MCTS.
Proper MCTS tuning is crucial for fair comparison and optimal performance.
Abstract
The ``Heatmap + Monte Carlo Tree Search (MCTS)'' paradigm has recently emerged as a prominent framework for solving the Travelling Salesman Problem (TSP). While considerable effort has been devoted to enhancing heatmap sophistication through advanced learning models, this paper rigorously examines whether this emphasis is justified, critically assessing the relative impact of heatmap complexity versus MCTS configuration. Our extensive empirical analysis across diverse TSP scales, distributions, and benchmarks reveals two pivotal insights: 1) The configuration of MCTS strategies significantly influences solution quality, underscoring the importance of meticulous tuning to achieve optimal results and enabling valid comparisons among different heatmap methodologies. 2) A rudimentary, parameter-free heatmap based on the intrinsic -nearest neighbor structure of TSP instances, when coupled…
Peer Reviews
Decision·ICLR 2026 Poster
This is a very nice paper that investigates an angle mostly ignored by the literature. The results nicely support the conclusions the authors come to, and suggest that research efforts should be focused in a different direction for more impact. The paper complements the existing literature very nicely. The proposed GT-Prior is, to the best of my knowledge, novel and seems to work very well in practice. It would be interesting to investigate to what extent it differs from heatmaps learned in oth
None major.
1. This paper is written in an accessible manner, offering a clear explanation of the ``MCTS`` method implemented in ``Att-GCN``, and provides a thorough analysis of how each MCTS parameter influences the solution. 2. This paper conducts sufficient generalization tests across different distributions and scales, including experiments on ``TSPLIB``.
1. The authors state that ``The underlying assumption is often that heatmap sophistication directly translates to superior solution quality``, yet they provide no experiments to substantiate this claim. They lack analytical experiments to compare the heatmaps produced by different methods, such using greedy strategy. 2. It can be inferred from ``Table 1`` and the sentence ``The Time_Limit for MCTS was set to 0.1 for TSP-500 and TSP-1000, and 0.01 for TSP-10000`` that the authors run MCTS in par
- The paper systematically assesses the "Heatmap + MCTS" paradigm for large-scale TSP, isolating and quantifying each component's impact. - The work challenges a key assumption: that more complex heatmap models always improve TSP solver performance. With a well-tuned baseline, it shows that optimizing MCTS often matters more than increasing heatmap sophistication. - A parameter-free k-nearest neighbor heatmap (GT-Prior) matches or outperforms complex learned heatmaps when paired with optimized M
- Scope: The analysis, experiments, and proposed GT-Prior heatmap are specialized to the Euclidean TSP. It remains unclear whether the insights transfer to other TSP variants (non-Euclidean, with constraints) or different combinatorial optimization problems (e.g., VRP, graph matching). - Dependency on optimal solutions: GT-Prior construction relies on empirical distributions extracted from near-optimal solutions. In scenarios where such solutions are expensive or unavailable—a typical motivation
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Taxonomy
TopicsOptimization and Packing Problems
MethodsFocus · Heatmap