A Surrogate-Assisted Bi-Level Evolutionary Algorithm for Multi-Depot Vehicle Routing Problems With Uncertain Demand

The Multi-depot Vehicle Routing Problem with Uncertain Demand (MD-VRPUD) can be modeled as a bi-level optimization problem (BLOP), because it requires both assigning customers to different depots and determining the routes for servicing customers, where the optimization of these two parts is coupled with each other. Although the bi-level evolutionary algorithm is a fitting approach for tackling the MD-VRPUD, its nested structure often leads to computational inefficiency. To this end, this paper tailors a surrogate-assisted bi-level evolutionary algorithm (SABLEA) to achieve highly efficient nested algorithms tailored for solving the MD-VRPUD. To deal with the combinatorial property of MD-VRPUD, two groups of continuous features are first extracted to help the surrogate model to effectively distinguish the superiority and inferiority of schemes. Then, a management strategy is designed to adaptively build the surrogate models in different subspaces so as to alleviate the performance bottleneck faced by the model. Finally, an adaptive computing resource allocation strategy is integrated into the lower-level optimization, to allocate more resources to promising customer assignment schemes, enabling the discovery of better routes and improving the overall accuracy of models. The comprehensive experimental results demonstrate the effectiveness of the SABLEA in handling MD-VRPUD, outperforming four existing algorithms in terms of both computational efficiency and solution quality.