A GPU-Accelerated Hybrid Method for a Class of Multi-Depot Vehicle Routing Problems

Multi-depot vehicle routing problems (MDVRPs) are prevalent in a variety of practical applications. However, they are computationally challenging to solve due to their inherent complexity. This paper proposes an effective hybrid algorithm for a class of MDVRPs. The algorithm integrates a learning-driven, diversity-controlled route-exchange crossover and a multi-depot-supported feasible-and-infeasible search framework guided by a multi-penalty evaluation function. Two dedicated depot-related local search operators are incorporated to further strengthen the search capability in multi-depot settings. To improve computational efficiency and scalability, an enhanced version of the algorithm is developed that uses a tensor-based GPU acceleration combined with a novel multi-move update strategy. Extensive computational experiments on benchmark instances of three MDVRP variants show that the proposed algorithms are highly competitive with state-of-the-art methods, especially for large-scale instances.