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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.

Data-Driven Robust Optimization for Solving the Heterogeneous Vehicle Routing Problem with Customer Demand Uncertainty