In recent years, machine learning (ML) has emerged as a promising avenue for addressing optimization problems like the Travelling Salesman Problem (TSP). ML techniques, particularly those involving neural networks and reinforcement learning, have shown potential in learning heuristics and patterns that can guide the search for optimal routes more efficiently. By leveraging data, ML models can improve the quality of solutions and reduce computation time. One notable approach is the use of heat map-based search, where ML models generate heat maps that highlight promising regions of the solution space. These heat maps are then used to focus the search process, potentially enhancing the efficiency and effectiveness of finding optimal or near-optimal solutions [1]. Recently, the authors of paper [2] (referred to as SoftDist) discussed the neural approach and claimed: Our theoretical and experimental analysis raises doubts about the effectiveness of MLbased heat map generation. In support of this, we demonstrate that a simple baseline method can outperform complex ML approaches in heat map generation. Here, however, we show that the authors in SoftDist misconducted the experiments, leading to an unfair comparison and a flawed conclusion.

Recent advancements in solving large-scale traveling salesman problems (TSP) utilize the heatmap-guided Monte Carlo tree search (MCTS) paradigm, where machine learning (ML) models generate heatmaps, indicating the probability distribution of each edge being part of the optimal solution, to guide MCTS in solution finding. However, our theoretical and experimental analysis raises doubts about the effectiveness of ML-based heatmap generation. In support of this, we demonstrate that a simple baseline method can outperform complex ML approaches in heatmap generation. Furthermore, we question the practical value of the heatmap-guided MCTS paradigm. To substantiate this, our findings show its inferiority to the LKH-3 heuristic despite the paradigm's reliance on problem-specific, hand-crafted strategies. For the future, we suggest research directions focused on developing more theoretically sound heatmap generation methods and exploring autonomous, generalizable ML approaches for combinatorial problems. The code is available for review: https://github.com/xyfffff/rethink_mcts_for_tsp.