# SHIELD: Multi-task Multi-distribution Vehicle Routing Solver with Sparsity and Hierarchy

arXiv: https://arxiv.org/abs/2506.08424 · HTML: https://mlsanity.com/paper/2506.08424/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Jun 2025.

## Built on by (most cited first, 8 of 8)

- [Multi-Task Vehicle Routing Solver via Mixture of Specialized Experts under State-Decomposable MDP](https://mlsanity.com/paper/2510.21453/) (2025)
- [Survey on Neural Routing Solvers](https://mlsanity.com/paper/2602.21761/) (2026)
- [Enhancing Cross-Problem Vehicle Routing via Federated Learning](https://mlsanity.com/paper/2604.10652/) (2026)
- [FiLMMeD: Feature-wise Linear Modulation for Cross-Problem Multi-Depot Vehicle Routing](https://mlsanity.com/paper/2604.28102/) (2026)
- [WeCon: An Efficient Weight-Conditioned Neural Solver for Multi-Objective Combinatorial Optimization Problems](https://mlsanity.com/paper/2605.22876/) (2026)
- [Deft Scheduling of Dynamic Cloud Workflows with Varying Deadlines via Mixture-of-Experts](https://mlsanity.com/paper/2606.01162/) (2026)
- [RAISE: LLM-based Automated Heuristic Design with Robust Adversary Instance Search](https://mlsanity.com/paper/2606.31801/) (2026)
- [LaT: LLM-as-Trainer for Multi-Task Vehicle Routing Solvers](https://mlsanity.com/paper/2607.17708/) (2026)

## Abstract (arXiv)

Recent advances toward foundation models for routing problems have shown great potential of a unified deep model for various VRP variants. However, they overlook the complex real-world customer distributions. In this work, we advance the Multi-Task VRP (MTVRP) setting to the more realistic yet challenging Multi-Task Multi-Distribution VRP (MTMDVRP) setting, and introduce SHIELD, a novel model that leverages both sparsity and hierarchy principles. Building on a deeper decoder architecture, we first incorporate the Mixture-of-Depths (MoD) technique to enforce sparsity. This improves both efficiency and generalization by allowing the model to dynamically select nodes to use or skip each decoder layer, providing the needed capacity to adaptively allocate computation for learning the task/distribution specific and shared representations. We also develop a context-based clustering layer that exploits the presence of hierarchical structures in the problems to produce better local representations. These two designs inductively bias the network to identify key features that are common across tasks and distributions, leading to significantly improved generalization on unseen ones. Our empirical results demonstrate the superiority of our approach over existing methods on 9 real-world maps with 16 VRP variants each.