# CAMP: Collaborative Attention Model with Profiles for Vehicle Routing Problems

arXiv: https://arxiv.org/abs/2501.02977 · HTML: https://mlsanity.com/paper/2501.02977/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Jan 2025.

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

- [Rethinking Light Decoder-based Solvers for Vehicle Routing Problems](https://mlsanity.com/paper/2503.00753/) (2025)
- [Learning to Solve the Min-Max Mixed-Shelves Picker-Routing Problem via Hierarchical and Parallel Decoding](https://mlsanity.com/paper/2502.10233/) (2025)
- [Chain-of-Context Learning: Dynamic Constraint Understanding for Multi-Task VRPs](https://mlsanity.com/paper/2603.01667/) (2026)
- [USPR: Learning a Unified Solver for Profiled Routing](https://mlsanity.com/paper/2505.05119/) (2025)
- [Learning with Foresight: Enhancing Neural Routing Policy via Multi-Node Lookahead Prediction](https://mlsanity.com/paper/2605.19975/) (2026)
- [Multi-Action Self-Improvement for Neural Combinatorial Optimization](https://mlsanity.com/paper/2510.12273/) (2025)
- [Vehicle-as-Prompt: A Unified Deep Reinforcement Learning Framework for Heterogeneous Fleet Vehicle Routing Problem](https://mlsanity.com/paper/2604.05195/) (2026)
- [LaT: LLM-as-Trainer for Multi-Task Vehicle Routing Solvers](https://mlsanity.com/paper/2607.17708/) (2026)

## Abstract (arXiv)

The profiled vehicle routing problem (PVRP) is a generalization of the heterogeneous capacitated vehicle routing problem (HCVRP) in which the objective is to optimize the routes of vehicles to serve client demands subject to different vehicle profiles, with each having a preference or constraint on a per-client basis. While existing learning methods have shown promise for solving the HCVRP in real-time, no learning method exists to solve the more practical and challenging PVRP. In this paper, we propose a Collaborative Attention Model with Profiles (CAMP), a novel approach that learns efficient solvers for PVRP using multi-agent reinforcement learning. CAMP employs a specialized attention-based encoder architecture to embed profiled client embeddings in parallel for each vehicle profile. We design a communication layer between agents for collaborative decision-making across profiled embeddings at each decoding step and a batched pointer mechanism to attend to the profiled embeddings to evaluate the likelihood of the next actions. We evaluate CAMP on two variants of PVRPs: PVRP with preferences, which explicitly influence the reward function, and PVRP with zone constraints with different numbers of agents and clients, demonstrating that our learned solvers achieve competitive results compared to both classical state-of-the-art neural multi-agent models in terms of solution quality and computational efficiency. We make our code openly available at https://github.com/ai4co/camp.