Rethinking the "Heatmap + Monte Carlo Tree Search'' Paradigm for Solving Large Scale TSP
Keywords: Travelling Salesman Problem, Heatmap, Monte Carlo Tree Search, Combinatorial optimization, k-nearest neighbor
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.
Abstract: 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: \textbf{1}) The configuration of MCTS strategies profoundly influences the solution quality, demanding meticulous tuning to leverage their full potential; \textbf{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.
Primary Area: other topics in machine learning (i.e., none of the above)
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Submission Number: 1305
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