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

2026-01-31

AI Summary

This work proposes TSP-MDF, a novel framework that integrates unsupervised neural networks with classical heuristics to address the limitations of existing approaches for the Traveling Salesman Problem (TSP). Traditional heuristics often stagnate in local optima due to their deterministic nature, while current neural heuristics rely on supervised training and incur substantial computational costs. TSP-MDF circumvents these issues by fine-tuning instance node coordinates to generate a diverse solution space, guiding classical heuristics—such as Farthest or Nearest Insertion—to sample solutions on the perturbed instance, which are then mapped back to the original problem via inverse coordinate transformation. Requiring no ground-truth labels, this method endows traditional heuristics with guided sampling capabilities, achieving solution quality on large-scale and real-world TSP benchmarks comparable to state-of-the-art neural heuristics, yet at a significantly lower training cost.

Technology Category

• Search and Optimization: Heuristic Search
• Machine Learning: Unsupervised & Self-Supervised Learning
• Planning, Routing, and Scheduling: Learning for Planning and Scheduling

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

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.

Problem

• Traveling Salesman Problem
• heuristic
• guided-sampling
• unsupervised learning
• combinatorial optimization

Innovation

• instance modification
• unsupervised learning
• guided sampling
• TSP heuristics
• combinatorial optimization