# A Deep Reinforcement Learning Algorithm Using Dynamic Attention Model for Vehicle Routing Problems

arXiv: https://arxiv.org/abs/2002.03282 · HTML: https://mlsanity.com/paper/2002.03282/

## Key facts

- Cited by 30 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Feb 2020.

## Built on by (most cited first, 30 of 30)

- [DIFUSCO: Graph-based Diffusion Solvers for Combinatorial Optimization](https://mlsanity.com/paper/2302.08224/) (2023)
- [DIMES: A Differentiable Meta Solver for Combinatorial Optimization Problems](https://mlsanity.com/paper/2210.04123/) (2022)
- [Efficient Active Search for Combinatorial Optimization Problems](https://mlsanity.com/paper/2106.05126/) (2021)
- [Deep Policy Dynamic Programming for Vehicle Routing Problems](https://mlsanity.com/paper/2102.11756/) (2021)
- [BQ-NCO: Bisimulation Quotienting for Efficient Neural Combinatorial Optimization](https://mlsanity.com/paper/2301.03313/) (2023)
- [Learning Generalizable Models for Vehicle Routing Problems via Knowledge Distillation](https://mlsanity.com/paper/2210.07686/) (2022)
- [Neural Combinatorial Optimization Algorithms for Solving Vehicle Routing Problems: A Comprehensive Survey with Perspectives](https://mlsanity.com/paper/2406.00415/) (2024)
- [Analytics and Machine Learning in Vehicle Routing Research](https://mlsanity.com/paper/2102.10012/) (2021)
- [An Overview and Experimental Study of Learning-based Optimization Algorithms for Vehicle Routing Problem](https://mlsanity.com/paper/2107.07076/) (2021)
- [Efficient Meta Neural Heuristic for Multi-Objective Combinatorial Optimization](https://mlsanity.com/paper/2310.15196/) (2023)
- [Learning to Solve Vehicle Routing Problems: A Survey](https://mlsanity.com/paper/2205.02453/) (2022)
- [Attention, Filling in The Gaps for Generalization in Routing Problems](https://mlsanity.com/paper/2207.07212/) (2022)
- [A Deep Reinforcement Learning Approach for the Meal Delivery Problem](https://mlsanity.com/paper/2104.12000/) (2021)
- [Solving Dynamic Graph Problems with Multi-Attention Deep Reinforcement Learning](https://mlsanity.com/paper/2201.04895/) (2022)
- [A deep learning Attention model to solve the Vehicle Routing Problem and the Pick-up and Delivery Problem with Time Windows](https://mlsanity.com/paper/2212.10399/) (2022)
- [Beyond the Heatmap: A Rigorous Evaluation of Component Impact in MCTS-Based TSP Solvers](https://mlsanity.com/paper/2411.09238/) (2024)
- [LMask: Learn to Solve Constrained Routing Problems with Lazy Masking](https://mlsanity.com/paper/2505.17938/) (2025)
- [Where the Action is: Let's make Reinforcement Learning for Stochastic Dynamic Vehicle Routing Problems work!](https://mlsanity.com/paper/2103.00507/) (2021)
- [Deep-Steiner: Learning to Solve the Euclidean Steiner Tree Problem](https://mlsanity.com/paper/2209.09983/) (2022)
- [Recurrent State Encoders for Efficient Neural Combinatorial Optimization](https://mlsanity.com/paper/2509.05084/) (2025)
- [Edge Rewiring Goes Neural: Boosting Network Resilience without Rich Features](https://mlsanity.com/paper/2110.09035/) (2021)
- [Sample-Efficient, Exploration-Based Policy Optimisation for Routing Problems](https://mlsanity.com/paper/2205.15656/) (2022)
- [Combining Constructive and Perturbative Deep Learning Algorithms for the Capacitated Vehicle Routing Problem](https://mlsanity.com/paper/2211.13922/) (2022)
- [Multi-Start Team Orienteering Problem for UAS Mission Re-Planning with Data-Efficient Deep Reinforcement Learning](https://mlsanity.com/paper/2303.01963/) (2023)
- [Using Reinforcement Learning for the Three-Dimensional Loading Capacitated Vehicle Routing Problem](https://mlsanity.com/paper/2307.12136/) (2023)
- [Symmetry-preserving graph attention network to solve routing problems at multiple resolutions](https://mlsanity.com/paper/2310.15543/) (2023)
- [Learn to Solve Vehicle Routing Problems ASAP: A Neural Optimization Approach for Time-Constrained Vehicle Routing Problems with Finite Vehicle Fleet](https://mlsanity.com/paper/2411.04777/) (2024)
- [LRM-1B: Towards Large Routing Model](https://mlsanity.com/paper/2507.03300/) (2025)
- [An End-to-End Deep Reinforcement Learning Approach for Solving the Traveling Salesman Problem with Drones](https://mlsanity.com/paper/2511.05265/) (2025)
- [Optimizing Nursing Care Taxi Dispatch Leveraging Integer Linear Programming Solvers and Machine Learning](https://mlsanity.com/paper/2606.29725/) (2026)

## Abstract (arXiv)

Recent researches show that machine learning has the potential to learn better heuristics than the one designed by human for solving combinatorial optimization problems. The deep neural network is used to characterize the input instance for constructing a feasible solution incrementally. Recently, an attention model is proposed to solve routing problems. In this model, the state of an instance is represented by node features that are fixed over time. However, the fact is, the state of an instance is changed according to the decision that the model made at different construction steps, and the node features should be updated correspondingly. Therefore, this paper presents a dynamic attention model with dynamic encoder-decoder architecture, which enables the model to explore node features dynamically and exploit hidden structure information effectively at different construction steps. This paper focuses on a challenging NP-hard problem, vehicle routing problem. The experiments indicate that our model outperforms the previous methods and also shows a good generalization performance.