Title: Beyond the Heatmap: A Rigorous Evaluation of Component Impact in MCTS-Based TSP Solvers
Primary area: other topics in machine learning (i.e., none of the above)
Keywords: Travelling Salesman Problem, Heatmap, Monte Carlo Tree Search, Combinatorial optimization

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: \textbf{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. \textbf{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.

TL;DR: This study shows simple heatmaps and well-tuned MCTS can outperform complex heatmap-based approaches for the Travelling Salesman Problem, advocating for a balanced focus on both learning and search components.