带有二维装箱约束车辆路径问题的知识驱动强化学习求解

Logistics distribution efficiency and cost optimization are among the core challenges in manufacturing supply chain management, with related problems often modeled as vehicle routing problems. For fragile goods such as home appliances, which cannot be stacked and must be laid flat during transportation, this practical constraint is incorporated by adding two-dimensional loading constraints to the traditional vehicle routing model, forming the capacitated vehicle routing problem with two-dimensional loading constraints (2L-CVRP). This problem integrates both route planning and two-dimensional packing subproblems, characterized by strong constraints and multi-extreme combinatorial optimization. Traditional exact algorithms and heuristic methods face limitations in solving large-scale instances due to high time consumption and low efficiency, making them inadequate for dynamic demands with real-time changes in customer locations and requirements.To address these rapid-solving challenges, this paper designs a knowledge-driven reinforcement learning algorithm based on the collaboration of reinforcement learning and variable neighborhood search, aiming to optimize the total travel distance in the 2L-CVRP. First, an Actor-Critic reinforcement learning framework based on attention mechanisms and pointer networks is developed, using travel distance as the reward. Within this framework, multiple heuristic algorithms are employed to handle packing constraints and improve infeasible solutions, generating initial vehicle routes. Subsequently, an efficient problem-knowledge-driven variable neighborhood search strategy is designed to refine the initial route sequences obtained from the end-to-end network. In terms of simulation experiments, the proposed algorithm is validated on classical 2L-CVRP benchmark sets. Experimental results demonstrate that compared to classical heuristic methods, the proposed algorithm reduces the travel distance by 21.52% on small-scale instances and updates the best-known solutions for 50% of large-scale instances. Moreover, the proposed algorithm significantly outperforms comparative algorithms in solving speed, with advantages becoming more pronounced in large-scale cases, verifying its high efficiency in solving the 2L-CVRP.