This paper introduces TuneNSearch, a hybrid transfer learning and local search approach for addressing diverse variants of the vehicle routing problem (VRP). Our method uses reinforcement learning to generate high-quality solutions, which are subsequently refined by an efficient local search procedure. To ensure broad adaptability across VRP variants, TuneNSearch begins with a pre-training phase on the multi-depot VRP (MDVRP), followed by a fine-tuning phase to adapt it to other problem formulations. The learning phase utilizes a Transformer-based architecture enhanced with edge-aware attention, which integrates edge distances directly into the attention mechanism to better capture spatial relationships inherent to routing problems. We show that the pre-trained model generalizes effectively to single-depot variants, achieving performance comparable to models trained specifically on single-depot instances. Simultaneously, it maintains strong performance on multi-depot variants, an ability that models pre-trained solely on single-depot problems lack. For example, on 100-node instances of multi-depot variants, TuneNSearch outperforms a model pre-trained on the CVRP by 44%. In contrast, on 100-node instances of single-depot variants, TuneNSearch performs similar to the CVRP model. To validate the effectiveness of our method, we conduct extensive computational experiments on public benchmark and randomly generated instances. Across multiple CVRPLIB datasets, TuneNSearch consistently achieves performance deviations of less than 3% from the best-known solutions in the literature, compared to 6-25% for other neural-based models, depending on problem complexity. Overall, our approach demonstrates strong generalization to different problem sizes, instance distributions, and VRP formulations, while maintaining polynomial runtime complexity despite the integration of the local search algorithm.

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