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

2025-06-30

AI Summary

For NP-hard routing optimization problems—such as the Traveling Salesman Problem (TSP) and Vehicle Routing Problem (VRP)—exact algorithms suffer from prohibitive computational complexity, while traditional heuristics lack optimality guarantees. This paper presents a systematic survey of machine learning (ML) applications in routing optimization and proposes a unified “constructive–improvement” taxonomy that integrates operations research models with deep learning (supervised and reinforcement learning), constructive heuristics, and local search techniques. Its key contributions are threefold: (i) the first structured, ML-driven classification framework for routing algorithms; (ii) a principled integration pathway bridging classical optimization and data-driven methods; and (iii) enhanced modeling and efficient solution capabilities for novel VRP variants. The work establishes a scalable theoretical foundation and practical paradigm for intelligent routing decision-making systems. (136 words)

Technology Category

• Planning, Routing, and Scheduling: Learning for Planning and Scheduling
• Machine Learning: Optimization
• Search and Optimization: Learning to Search

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Security and Privacy: Security and privacy of machine learning and AI applications

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.

Problem

• Applying ML to solve NP-hard routing problems
• Integrating traditional OR with ML techniques
• Addressing computational complexity in TSP and VRP

Innovation

• ML techniques for NP-hard routing problems
• Taxonomy for ML-based routing methods
• Integration of OR and ML methods