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Learning for routing: A guided review of recent developments and future directions

Fangting Zhou, Attila Lischka, Balazs Kulcsar, Jiaming Wu, Morteza Haghir Chehreghani, Gilbert Laporte

TL;DR

This paper addresses the challenge of applying machine learning to routing problems, notably the Traveling Salesman Problem and the Vehicle Routing Problem, by proposing a taxonomy that splits ML-based routing methods into construction-based and improvement-based families, with exact-algorithm-based methods integrated as hybrids. It surveys a large corpus (2016–2025) of 253 articles, synthesizing architectures (MLPs, GNNs, RNNs, Transformers), learning formulations (SL, USL, RL), and the use of LLMs, and it maps these methods to practical routing contexts including VRP variants and multi-modal settings. The authors contribute a structured framework, a performance-oriented synthesis of methods, a data realism critique with a proposed synthetic data generator, and a benchmarking blueprint to standardize evaluation across studies. They also present a forward-looking research agenda aligned with UN Sustainable Development Goals, emphasizing resilience, multi-objective optimization, cross-domain generalization, industry applicability, and safety/ethics in ML-driven routing. Overall, the work serves as a comprehensive guide bridging traditional OR techniques and modern ML approaches, guiding researchers toward scalable, robust, and practically impactful routing solutions.

Abstract

This paper reviews the current progress in applying machine learning (ML) tools to solve NP-hard combinatorial optimization problems, with a focus on routing problems such as the traveling salesman problem (TSP) and the vehicle routing problem (VRP). Due to the inherent complexity of these problems, exact algorithms often require excessive computational time to find optimal solutions, while heuristics can only provide approximate solutions without guaranteeing optimality. With the recent success of machine learning models, there is a growing trend in proposing and implementing diverse ML techniques to enhance the resolution of these challenging routing problems. We propose a taxonomy categorizing ML-based routing methods into construction-based and improvement-based approaches, highlighting their applicability to various problem characteristics. This review aims to integrate traditional OR methods with state-of-the-art ML techniques, providing a structured framework to guide future research and address emerging VRP variants.

Learning for routing: A guided review of recent developments and future directions

TL;DR

This paper addresses the challenge of applying machine learning to routing problems, notably the Traveling Salesman Problem and the Vehicle Routing Problem, by proposing a taxonomy that splits ML-based routing methods into construction-based and improvement-based families, with exact-algorithm-based methods integrated as hybrids. It surveys a large corpus (2016–2025) of 253 articles, synthesizing architectures (MLPs, GNNs, RNNs, Transformers), learning formulations (SL, USL, RL), and the use of LLMs, and it maps these methods to practical routing contexts including VRP variants and multi-modal settings. The authors contribute a structured framework, a performance-oriented synthesis of methods, a data realism critique with a proposed synthetic data generator, and a benchmarking blueprint to standardize evaluation across studies. They also present a forward-looking research agenda aligned with UN Sustainable Development Goals, emphasizing resilience, multi-objective optimization, cross-domain generalization, industry applicability, and safety/ethics in ML-driven routing. Overall, the work serves as a comprehensive guide bridging traditional OR techniques and modern ML approaches, guiding researchers toward scalable, robust, and practically impactful routing solutions.

Abstract

This paper reviews the current progress in applying machine learning (ML) tools to solve NP-hard combinatorial optimization problems, with a focus on routing problems such as the traveling salesman problem (TSP) and the vehicle routing problem (VRP). Due to the inherent complexity of these problems, exact algorithms often require excessive computational time to find optimal solutions, while heuristics can only provide approximate solutions without guaranteeing optimality. With the recent success of machine learning models, there is a growing trend in proposing and implementing diverse ML techniques to enhance the resolution of these challenging routing problems. We propose a taxonomy categorizing ML-based routing methods into construction-based and improvement-based approaches, highlighting their applicability to various problem characteristics. This review aims to integrate traditional OR methods with state-of-the-art ML techniques, providing a structured framework to guide future research and address emerging VRP variants.

Paper Structure

This paper contains 49 sections, 5 equations, 6 figures, 19 tables.

Table of Contents

  1. Introduction
  2. Machine learning background
  3. Neural network architectures
  4. Multilayer perceptrons (MLPs)
  5. Graph neural networks (GNNs)
  6. Recurrent neural networks (RNNs)
  7. Transformers
  8. Comparison of neural architectures
  9. Learning formulations
  10. Supervised learning (SL)
  11. Unsupervised learning (USL)
  12. Reinforcement learning (RL)
  13. Comparison of learning formulations
  14. Large language models
  15. Overview of machine learning methods
  16. ...and 34 more sections

Figures (6)

  • Figure 1: Proposed classification for ML methods for routing
  • Figure 2: Incremental Methods - A trained model iteratively builds a solution.
  • Figure 3: One-Shot Methods - A trained model predicts an intermediate result, which helps find a solution.
  • Figure 4: $2$-opt visualized.
  • Figure 5: Subproblem-Based Method.
  • ...and 1 more figures