In practice, the parameters of the vehicle routing problem are uncertain, which is called the uncertain vehicle routing problem (UVRP). Therefore, a data-driven robust optimization approach to solve the heterogeneous UVRP is studied. The uncertain parameters of customer demand are introduced, and the uncertain model is established. The uncertain model is transformed into a robust model with adjustable parameters. At the same time, we use a least-squares data-driven method combined with historical data samples to design a function of robust adjustable parameters related to the maximum demand, demand range, and given vehicle capacity to optimize the robust model. We improve the deep Q-learning-based reinforcement learning algorithm for the fleet size and mix vehicle routing problem to solve the robust model. Through test experiments, it is proved that the robust optimization model can effectively reduce the number of customers affected by the uncertainty, greatly improve customer satisfaction, and effectively reduce total cost and demonstrate that the improved algorithm also exhibits good performance.
With the increasing proportion of the logistics industry in the economy, the study of the vehicle routing problem has practical significance for economic development. Based on the vehicle routing problem (VRP), the customer presence probability data are introduced as an uncertain random parameter, and the VRP model of uncertain customers is established. By optimizing the robust uncertainty model, combined with a data-driven kernel density estimation method, the distribution feature set of historical data samples can then be fitted, and finally, a distributed robust vehicle routing model for uncertain customers is established. The Q-learning algorithm in reinforcement learning is introduced into the high-level selection strategy using the hyper-heuristic algorithm, and a hyper-heuristic algorithm based on the Q-learning algorithm is designed to solve the problem. Compared with the certain method, the distributed robust model can effectively reduce the total cost and the robust conservatism while ensuring customer satisfaction. The improved algorithm also has good performance.
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