Combination-of-Experts with Knowledge Sharing for Cross-Task Vehicle Routing Problems

Recent neural methods have shown promise in generalizing across various vehicle routing problems (VRPs). These methods adopt either a fully-shared dense model across all VRP tasks (i.e., variants) or a mixture-of-experts model that assigns node embeddings within each task instance to different experts. However, they both struggle to generalize from training tasks with basic constraints to out-of-distribution (OOD) tasks involving unseen constraint combinations and new basic constraints, as they overlook the fact that each VRP task is defined by a combination of multiple basic constraints. To address this, this paper proposes a novel model, combination-of-experts with knowledge sharing (CoEKS), which leverages the structural characteristic of VRP tasks. CoEKS enhances generalization to constraint combinations via two complementary components: a combination-of-experts architecture enabling flexible combinations via prior assignment of constraint-specific experts, and a knowledge sharing strategy strengthening generalization via automatic learning of transferable general knowledge across constraints. Moreover, CoEKS allows new experts to be plugged into the trained model for rapid adaptation to new constraints. Experiments demonstrate that CoEKS outperforms state-of-the-art methods on in-distribution tasks and delivers greater gains on OOD tasks, including unseen constraint combinations (relative improvement of 12\% over SOTA) and new constraints (25\% improvement).