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Position: Rethinking Post-Hoc Search-Based Neural Approaches for Solving Large-Scale Traveling Salesman Problems

Yifan Xia, Xianliang Yang, Zichuan Liu, Zhihao Liu, Lei Song, Jiang Bian

TL;DR

The work interrogates the efficacy of ML-generated heatmaps guiding post-hoc MCTS for large-scale TSPs, showing that a simple baseline, SoftDist, can exceed many complex heatmap approaches in both solution quality and speed. It demonstrates that the heatmap-guided MCTS paradigm underperforms traditional heuristics like LKH-3 under identical resources, prompting a rethink of surrogate losses and training-test alignment. A new Score metric is proposed to quantify relative efficiency versus LKH-3, revealing sizable practical gaps. The paper advocates theory-backed heatmap methods and explores end-to-end autonomous ML approaches for combinatorial optimization to better balance performance and generalizability.

Abstract

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.

Position: Rethinking Post-Hoc Search-Based Neural Approaches for Solving Large-Scale Traveling Salesman Problems

TL;DR

The work interrogates the efficacy of ML-generated heatmaps guiding post-hoc MCTS for large-scale TSPs, showing that a simple baseline, SoftDist, can exceed many complex heatmap approaches in both solution quality and speed. It demonstrates that the heatmap-guided MCTS paradigm underperforms traditional heuristics like LKH-3 under identical resources, prompting a rethink of surrogate losses and training-test alignment. A new Score metric is proposed to quantify relative efficiency versus LKH-3, revealing sizable practical gaps. The paper advocates theory-backed heatmap methods and explores end-to-end autonomous ML approaches for combinatorial optimization to better balance performance and generalizability.

Abstract

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.
Paper Structure (40 sections, 6 equations, 6 figures, 5 tables)

This paper contains 40 sections, 6 equations, 6 figures, 5 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Supervised Learning
  4. Unsupervised Learning
  5. Reinforcement Learning
  6. Preliminaries
  7. Problem Definition
  8. Heatmap Generation
  9. Monte Carlo Tree Search
  10. Initialization.
  11. $k$-opt Search.
  12. Backpropagation.
  13. Proposed Baseline
  14. Motivation
  15. SoftDist Baseline
  16. ...and 25 more sections

Figures (6)

  • Figure 1: Relative performance comparison of ML-based methods with and without SoftDist. Inference Latency represents the heatmap generation time, with lower being better. Solution Quality represents the effectiveness of TSP solutions generated through MCTS guided by the heatmaps, with higher being better.
  • Figure 2: Heatmap-Guided MCTS Phases.
  • Figure 3: SoftDist-Guided MCTS Phases.
  • Figure 4: Performance of MCTS under default settings for TSP-500, TSP-1000, and TSP-10000.
  • Figure 4: Coarsened grid search results for SoftDist temperature settings.
  • ...and 1 more figures