A Mixed-Curvature based Pre-training Paradigm for Multi-Task Vehicle Routing Solver

Solving various types of vehicle routing problems (VRPs) using a unified neural solver has garnered significant attentions in recent years. Despite their effectiveness, existing neural multi-task solvers often fail to account for the geometric structures inherent in different tasks, which may result in suboptimal performance. To address this limitation, we propose a curvature-aware pre-training framework. Specifically, we leverage mixed-curvature spaces during the feature fusion stage, encouraging the model to capture the underlying geometric properties of each instance. Through extensive experiments, we evaluate the proposed pre-training strategy on existing neural multi-task solvers across a variety of testing scenarios. The results demonstrate that the curvature-aware pre-training approach not only enhances the generalization capabilities of existing neural VRP solvers on synthetic datasets but also improves solution quality on real-world benchmarks.