Learning-Aided Neighborhood Search for Vehicle Routing Problems

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.