Soft Parameter Sharing Model for Cross-Problem Generalization in Vehicle Routing Problems

Neural Combinatorial Optimization (NCO) has achieved remarkable performance in solving individual Vehicle Routing Problems (VRPs) by leveraging attention mechanisms. However, when generalizing across different problems, these methods perform poorly because the hard parameter sharing models they adopted are unable to capture the commonalities and peculiarities of different problems. To address this limitation, we propose a novel multi-task NCO method called the Soft Parameter Sharing Model (SPSM) that incorporates multiple independent attention modules and a gating network. SPSM allows the model to learn both universal patterns and individualized requirements without explicitly designating any module as shared or task-specific. When solving a specific VRP, the gating network may decide the importance of the characteristics learned by each attention module. Additionally, we adopt the maximum entropy reinforcement learning to maintain the diversity of the model in the training process, which can prevent the model from being greedy for some dominant tasks or only for the training tasks. Experimental results demonstrate that SPSM significantly enhances zero-shot generalization performance across ten unseen VRP variants and real-world benchmark instances. Our code is available at https://github.com/ftwangyang/SPSM.