Beyond the Heatmap: A Rigorous Evaluation of Component Impact in MCTS-Based TSP Solvers

2024-11-14

AI Summary

This work investigates the relative impact of heatmap modeling complexity versus Monte Carlo Tree Search (MCTS) configuration on solving the Traveling Salesman Problem (TSP). Through large-scale ablation studies and cross-distribution benchmarking (TSPLIB, GCNN, DIMES), we find that MCTS hyperparameter settings exert significantly greater influence on performance than heatmap architectural sophistication. Motivated by this insight, we propose two key contributions: (1) a parameter-free, distribution-robust heatmap based on k-nearest neighbor (k-NN) structure—eliminating reliance on learned representations; and (2) the first standardized hyperparameter tuning paradigm specifically designed for TSP-MCTS. Empirical results demonstrate that a simple k-NN heatmap, when paired with rigorously optimized MCTS configurations, outperforms state-of-the-art learned heatmap approaches. Our framework enhances method comparability, reproducibility, and evaluation fairness. The implementation is publicly available.

Technology Category

• Search and Optimization: Heuristic Search
• Planning, Routing, and Scheduling: Learning for Planning and Scheduling
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems

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: 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. 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. Our code is available at: https://github.com/LOGO-CUHKSZ/rethink_mcts_tsp.

Problem

• Evaluates impact of heatmap complexity vs MCTS configuration in TSP solvers
• Tests if simple heatmaps with tuned MCTS outperform sophisticated learned ones
• Proposes standardized MCTS tuning for fair heatmap methodology comparisons

Innovation

• Evaluates MCTS configuration impact on TSP solutions
• Uses k-nearest neighbor heatmap with tuned MCTS
• Introduces standardized MCTS hyperparameter tuning pipeline