The Travelling Salesman Problem (TSP) remains a fundamental challenge in combinatorial optimization, inspiring diverse algorithmic strategies. This paper revisits the "heatmap + Monte Carlo Tree Search (MCTS)" paradigm that has recently gained traction for learning-based TSP solutions. Within this framework, heatmaps encode the likelihood of edges forming part of the optimal tour, and MCTS refines this probabilistic guidance to discover optimal solutions. Contemporary approaches have predominantly emphasized the refinement of heatmap generation through sophisticated learning models, inadvertently sidelining the critical role of MCTS. Our extensive empirical analysis reveals two pivotal insights: 1) The configuration of MCTS strategies profoundly influences the solution quality, demanding meticulous tuning to leverage their full potential; 2) Our findings demonstrate that a rudimentary and parameter-free heatmap, derived from the intrinsic k-nearest nature of TSP, can rival or even surpass the performance of complicated heatmaps, with strong generalizability across various scales. Empirical evaluations across various TSP scales underscore the efficacy of our approach, achieving competitive results. These observations challenge the prevailing focus on heatmap sophistication, advocating a reevaluation of the paradigm to harness both components synergistically. The Travelling Salesman Problem (TSP) stands as a quintessential challenge in combinatorial optimization, drawing considerable interest from both theoretical and applied research communities. As a problem characterized by NP-hardness, the TSP has become a benchmark for evaluating the efficacy of novel algorithmic strategies in determining optimal or near-optimal solutions efficiently (Applegate et al., 2009). It has significant practical applications in domains such as logistics, transportation, manufacturing, and telecommunications, where finding efficient routes is crucial for minimizing costs and improving efficiency (Helsgaun, 2017; Nagata & Kobayashi, 2013). Recent advancements in machine learning have inspired a fresh wave of methodologies for tackling the TSP, particularly through the lens of the "heatmap + Monte Carlo Tree Search (MCTS)" paradigm.

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.