Rethinking the "Heatmap + Monte Carlo Tree Search" Paradigm for Solving Large Scale TSP

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.