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.

The neural network based solvers, have emerged as powerful tools for solving various kinds of Vehicle Routing Problems (VRPs). While effective, current neural solvers often overlook a crucial piece of information: the unique geometric structures in the delivery map: whether the delivery points are spread out on a broad area or clustered in a small region with winding roads. These complex patterns can confuse the solver and finally lead into sub-optimal routes.Our research introduces a novel way to pre-train these neural models. We call it "curvature-aware pre-training" because it teaches the model to better perceive the underlying spatial arrangements. By exposing the model to various types of geometric subspaces with adaptive curvatures during its training stage, we enable it to capture the true nature of each instance in a more concrete way. Our experiments show that this new pre-training approach significantly improves existing neural solvers. It helps them perform better on unseen scenarios and find higher-quality, more accurate solutions for both simulated and real-world routing problems.