Abstract
This paper proposes a Q-learning-driven butterfly optimization algorithm (QLBOA) by integrating the Q-learning mechanism of reinforcement learning into the butterfly optimization algorithm (BOA). In order to improve the overall optimization ability of the algorithm, enhance the optimization accuracy, and prevent the algorithm from falling into a local optimum, the Gaussian mutation mechanism with dynamic variance was introduced, and the migration mutation mechanism was also used to enhance the population diversity of the algorithm. Eighteen benchmark functions were used to compare the proposed method with five classical metaheuristic algorithms and three BOA variable optimization methods. The QLBOA was used to solve the green vehicle routing problem with time windows considering customer preferences. The influence of decision makers' subjective preferences and weight factors on fuel consumption, carbon emissions, penalty cost, and total cost are analyzed. Compared with three classical optimization algorithms, the experimental results show that the proposed QLBOA has a generally superior performance.