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

Fangting Zhou; Attila Lischka; Balázs Kulcsár; Jiaming Wu; Morteza Haghir Chehreghani; Gilbert Laporte

doi:10.1016/j.tre.2025.104278

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

Fangting Zhou, Attila Lischka, Balázs Kulcsár, Jiaming Wu, Morteza Haghir Chehreghani, Gilbert Laporte

Chalmers University of Technology

Research output: Contribution to journal › Article › peer-review

2 Citations (SciVal)

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.

Original language	English
Article number	104278
Journal	Transportation Research Part E: Logistics and Transportation Review
Volume	202
Early online date	11 Jul 2025
DOIs	https://doi.org/10.1016/j.tre.2025.104278
Publication status	Published - 31 Oct 2025

Bibliographical note

Publisher Copyright:
© 2025 The Authors

Data Availability Statement

The authors are unable or have chosen not to specify which data has been used.

Acknowledgements

The authors would like to thank the anonymous reviewers for their thoughtful and constructive comments on the draft. While some of the feedback presented challenges, it greatly contributed to enhancing the quality of the paper. The authors also thank Dr. Okan Arslan for his kind suggestions during the revision process.

Funding

This work was supported by the European Commission, Swedish Energy Agency, and VINNOVA through the project E-LaaS (F-ENUAC-2022-0003) and project ERGODIC (F-DUT-2022-0078). The partial support of the Chalmers University of Technology is herewith acknowledged via the project COLLECT. Finally, the project LEAR: Robust LEArning methods for electric vehicle route selection sponsored by the Swedish Electromobility Center is also acknowledged. The authors would like to thank the anonymous reviewers for their thoughtful and constructive comments on the draft. While some of the feedback presented challenges, it greatly contributed to enhancing the quality of the paper. The authors also thank Dr. Okan Arslan for his kind suggestions during the revision process.

Funders	Funder number
Chalmers Tekniska Högskola
European Commission
Swedish Electromobility Center
Energimyndigheten
VINNOVA	F-ENUAC-2022-0003, F-DUT-2022-0078

Keywords

Combinatorial optimization
Machine learning
Reinforcement learning
Routing problems
Traveling salesman problem
Vehicle routing problem

ASJC Scopus subject areas

Business and International Management
Civil and Structural Engineering
Transportation

Access to Document

10.1016/j.tre.2025.104278Licence: CC BY

Cite this

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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.",

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AU - Chehreghani, Morteza Haghir

AU - Laporte, Gilbert

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

Abstract

Bibliographical note

Data Availability Statement

Acknowledgements

Funding

Keywords

ASJC Scopus subject areas

Access to Document

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Cite this