A Q-Learning-Assisted Evolutionary Optimization Method for Solving the Capacitated Vehicle Routing Problem

The Capacitated Vehicle Routing Problem (CVRP) is a classic combinatorial optimization problem in logistics and distribution, with significant theoretical and practical importance. To address the limitations of traditional evolutionary algorithms—particularly their use of fixed operator selection and simplistic search strategies—this paper proposes a Q-learning-based evolutionary algorithm (QEA). By incorporating a reinforcement learning mechanism, the QEA adaptively selects among multiple neighborhood search operators, effectively balancing global exploration and local exploitation. In addition, a novel insertion-based crossover operator and a set of diverse neighborhood search strategies are designed to further enhance solution quality and search efficiency. Experimental results on a variety of standard CVRP benchmark instances show that the QEA demonstrates a superior performance and strong robustness, significantly outperforming several representative state-of-the-art algorithms for solving the CVRP. These results confirm the effectiveness and practical value of the proposed method.