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Small Shifts, Large Gains: Unlocking Traditional TSP Heuristic Guided-Sampling via Unsupervised Neural Instance Modification

Wei Huang, Hanchen Wang, Dong Wen, Wenjie Zhang

TL;DR

This work tackles the Travelings Salesman Problem by marrying the practicality of traditional deterministic heuristics with guided-sampling via an unsupervised neural instance modifier. By pre-processing the original instance to generate multiple modified variants and running base heuristics on them, TSP-MDF yields multiple candidate tours that, when mapped back, improve solution quality without requiring ground-truth supervision. Key innovations include discretized coordinate offsets, self-imitation learning, and unifying the target output space to stabilize training, all contributing to performance on large-scale benchmarks comparable to neural solvers but with dramatically shorter training times. The framework demonstrates strong generalization to real-world TSPLib instances and offers a scalable, practical alternative for high-quality TSP approximations in resource-constrained settings.

Abstract

The Traveling Salesman Problem (TSP) is one of the most representative NP-hard problems in route planning and a long-standing benchmark in combinatorial optimization. Traditional heuristic tour constructors, such as Farthest or Nearest Insertion, are computationally efficient and highly practical, but their deterministic behavior limits exploration and often leads to local optima. In contrast, neural-based heuristic tour constructors alleviate this issue through guided-sampling and typically achieve superior solution quality, but at the cost of extensive training and reliance on ground-truth supervision, hindering their practical use. To bridge this gap, we propose TSP-MDF, a novel instance modification framework that equips traditional deterministic heuristic tour constructors with guided-sampling capability. Specifically, TSP-MDF introduces a neural-based instance modifier that strategically shifts node coordinates to sample multiple modified instances, on which the base traditional heuristic tour constructor constructs tours that are mapped back to the original instance, allowing traditional tour constructors to explore higher-quality tours and escape local optima. At the same time, benefiting from our instance modification formulation, the neural-based instance modifier can be trained efficiently without any ground-truth supervision, ensuring the framework maintains practicality. Extensive experiments on large-scale TSP benchmarks and real-world benchmarks demonstrate that TSP-MDF significantly improves the performance of traditional heuristics tour constructors, achieving solution quality comparable to neural-based heuristic tour constructors, but with an extremely short training time.

Small Shifts, Large Gains: Unlocking Traditional TSP Heuristic Guided-Sampling via Unsupervised Neural Instance Modification

TL;DR

This work tackles the Travelings Salesman Problem by marrying the practicality of traditional deterministic heuristics with guided-sampling via an unsupervised neural instance modifier. By pre-processing the original instance to generate multiple modified variants and running base heuristics on them, TSP-MDF yields multiple candidate tours that, when mapped back, improve solution quality without requiring ground-truth supervision. Key innovations include discretized coordinate offsets, self-imitation learning, and unifying the target output space to stabilize training, all contributing to performance on large-scale benchmarks comparable to neural solvers but with dramatically shorter training times. The framework demonstrates strong generalization to real-world TSPLib instances and offers a scalable, practical alternative for high-quality TSP approximations in resource-constrained settings.

Abstract

The Traveling Salesman Problem (TSP) is one of the most representative NP-hard problems in route planning and a long-standing benchmark in combinatorial optimization. Traditional heuristic tour constructors, such as Farthest or Nearest Insertion, are computationally efficient and highly practical, but their deterministic behavior limits exploration and often leads to local optima. In contrast, neural-based heuristic tour constructors alleviate this issue through guided-sampling and typically achieve superior solution quality, but at the cost of extensive training and reliance on ground-truth supervision, hindering their practical use. To bridge this gap, we propose TSP-MDF, a novel instance modification framework that equips traditional deterministic heuristic tour constructors with guided-sampling capability. Specifically, TSP-MDF introduces a neural-based instance modifier that strategically shifts node coordinates to sample multiple modified instances, on which the base traditional heuristic tour constructor constructs tours that are mapped back to the original instance, allowing traditional tour constructors to explore higher-quality tours and escape local optima. At the same time, benefiting from our instance modification formulation, the neural-based instance modifier can be trained efficiently without any ground-truth supervision, ensuring the framework maintains practicality. Extensive experiments on large-scale TSP benchmarks and real-world benchmarks demonstrate that TSP-MDF significantly improves the performance of traditional heuristics tour constructors, achieving solution quality comparable to neural-based heuristic tour constructors, but with an extremely short training time.
Paper Structure (33 sections, 22 equations, 5 figures, 6 tables, 1 algorithm)

This paper contains 33 sections, 22 equations, 5 figures, 6 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Works
  3. Preliminary
  4. Proposed Approach: TSP-MDF
  5. TSP-MDF Overview
  6. Basic Design of $f_\theta$
  7. Discretization of Coordinate Offset
  8. Guiding $f_\theta$ with Self-imitation Learning
  9. Unifying Target Output Space across Nodes
  10. Experiments
  11. Experimental Settings
  12. Datasets
  13. Baselines
  14. Evaluation Metrics
  15. Overall Performance
  16. ...and 18 more sections

Figures (5)

  • Figure 1: An example of an optimal tour for a TSP instance.
  • Figure 2: An overview of our TSP-MDF. In the pre-processing stage, we sample multiple modified instances by leveraging a neural-based instance modifier to modify the coordinates of nodes in the original instance. In the tour construction stage, traditional heuristic tour constructors are executed on these modified instances to construct candidate tours, which are then mapped back to the original instance. In the optional instance refinement stage, the modified instance that currently results in the best tour can be further modified to sample new tours.
  • Figure 3: Average tour length reduction of TSP-MDF-enhanced traditional heuristic tour constructors on training TSP instances.
  • Figure 4: Ablation study: average tour length reduction on training TSP instances.
  • Figure 5: An example of TSP-MDF-enhanced heuristic tour constructors on a TSP-500 test instance. Green nodes in the modified instance indicate nodes whose coordinates have been modified.