Beyond the Heatmap: A Rigorous Evaluation of Component Impact in MCTS-Based TSP Solvers

TL;DR

This work critically evaluates the Heatmap + Monte Carlo Tree Search approach for the Travelling Salesman Problem, challenging the notion that heatmap complexity is the principal driver of performance. It demonstrates that careful MCTS configuration can dominate solver quality and that a simple, parameter-free $k$-nearest neighbor heatmap (GT-Prior) can rival or exceed more sophisticated heatmaps when paired with optimized search. By introducing a streamlined MCTS hyperparameter tuning pipeline and using SHAP to quantify parameter importance, the paper provides a rigorous, fair framework for comparing heatmap methods across multiple TSP scales and distributions, including TSPLIB benchmarks. The findings advocate a balanced integration of learning and search components, highlighting GT-Prior’s generalization and practical appeal for scalable, robust TSP solvers, with code available at the provided repository.

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 $k$-nearest neighbor structure of TSP instances, when coupled with an optimally tuned MCTS, can match or surpass the performance of more sophisticated, learned heatmaps, demonstrating robust generalizability on problem scale and distribution shift. To facilitate rigorous and fair evaluations in future research, we introduce a streamlined pipeline for standardized MCTS hyperparameter tuning. Collectively, these findings challenge the prevalent assumption that heatmap complexity is the primary determinant of performance, advocating instead for a balanced integration and comprehensive evaluation of both learning and search components within this paradigm. Our code is available at: https://github.com/LOGO-CUHKSZ/rethink_mcts_tsp.

Figures (8)

• Figure 1: Beeswarm plots of SHAP values for three different heatmaps. MD: Max_Depth, MCN: Max_Candidate_Num, H: Param_H, UH: Use_Heatmap. Each dot represents a feature's SHAP value for one instance, indicating its impact on the TSP solution length. The x-axis shows SHAP value magnitude and direction, while the y-axis lists features. Vertical stacking indicates similar impacts across instances. Wider spreads suggest greater influence and potential nonlinear effects. Dot color represents the corresponding feature value.
• Figure 2: Box plots of the optimality gap (%) for various heatmap sources, scales and MCTS settings.
• Figure 3: Empirical distribution of $k$-nearest neighbor selection in optimal TSP tours
• Figure 4: Beeswarm plots of SHAP values for six methods across different TSP sizes.
• Figure 5: Beeswarm plots of SHAP values for the UTSP heatmap across different TSP sizes.