Learning-Aided Neighborhood Search for Vehicle Routing Problems

• Published in: IEEE transactions on pattern analysis and machine intelligence Vol. 47; no. 7; pp. 5930 - 5944
• Main Authors: Guo, Tong, Mei, Yi, Zhang, Mengjie, Zhao, Haoran, Cai, Kaiquan, Du, Wenbo
• Format: Journal Article
• Language: English
• Published: United States IEEE 01.07.2025
• Subjects: adaptive operator selection; Benchmark testing; Convolutional neural networks; Decision making; Feature extraction; Heuristic algorithms; Logistics; Optimization; reinforcement learning; Routing; Search problems; variable neighborhood search; Vehicle routing
• ISSN: 0162-8828; 1939-3539; 2160-9292; 1939-3539
• DOI: 10.1109/TPAMI.2025.3554669

The Vehicle Routing Problem (VRP) is a classic optimization problem with diverse real-world applications. The neighborhood search has emerged as an effective approach, yielding high-quality solutions across different VRPs. However, most existing studies exhaustively explore all considered neighborhoods with a pre-fixed order, leading to an inefficient search process. To address this issue, this paper proposes a Learning-aided Neighborhood Search algorithm (LaNS) that employs a cutting-edge multi-agent reinforcement learning-driven adaptive operator/neighborhood selection mechanism to achieve efficient routing for VRP. Within this framework, two agents serve as high-level instructors, collaboratively guiding the search direction by selecting perturbation/improvement operators from a pool of low-level heuristics. Furthermore, to equip the agents with comprehensive information for learning guidance knowledge, we have developed a new informative state representation. This representation transforms the spatial route structures into an image-like tensor, allowing us to extract spatial features using a convolutional neural network. Comprehensive evaluations on diverse VRP benchmarks, including the capacitated VRP (CVRP), multi-depot VRP (MDVRP) and cumulative multi-depot VRP with energy constraints, demonstrate LaNS's superiority over the state-of-the-art neighborhood search methods as well as the existing learning-guided neighborhood search algorithms.