# A deep learning Attention model to solve the Vehicle Routing Problem and the Pick-up and Delivery Problem with Time Windows

arXiv: https://arxiv.org/abs/2212.10399 · HTML: https://mlsanity.com/paper/2212.10399/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 18 references that are in the map.
- First posted on arXiv 20 Dec 2022.

## Builds on (most cited first, 9 of 9)

- [Pointer Networks](https://mlsanity.com/paper/1506.03134/) (2015)
- [Attention, Learn to Solve Routing Problems!](https://mlsanity.com/paper/1803.08475/) (2018)
- [POMO: Policy Optimization with Multiple Optima for Reinforcement Learning](https://mlsanity.com/paper/2010.16011/) (2020)
- [Reinforcement Learning for Solving the Vehicle Routing Problem](https://mlsanity.com/paper/1802.04240/) (2018)
- [Heterogeneous Attentions for Solving Pickup and Delivery Problem via Deep Reinforcement Learning](https://mlsanity.com/paper/2110.02634/) (2021)
- [A Deep Reinforcement Learning Algorithm Using Dynamic Attention Model for Vehicle Routing Problems](https://mlsanity.com/paper/2002.03282/) (2020)
- [Learning to Solve Vehicle Routing Problems with Time Windows through Joint Attention](https://mlsanity.com/paper/2006.09100/) (2020)
- [Fast Approximate Solutions using Reinforcement Learning for Dynamic Capacitated Vehicle Routing with Time Windows](https://mlsanity.com/paper/2102.12088/) (2021)
- [Solving the Traveling Salesperson Problem with Precedence Constraints by Deep Reinforcement Learning](https://mlsanity.com/paper/2207.01443/) (2022)

## Built on by (most cited first, 4 of 4)

- [Pivoting Retail Supply Chain with Deep Generative Techniques: Taxonomy, Survey and Insights](https://mlsanity.com/paper/2403.00861/) (2024)
- [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)
- [A Coalition Game for On-demand Multi-modal 3D Automated Delivery System](https://mlsanity.com/paper/2412.17252/) (2024)
- [JAMPR+/L2D: scalable neural heuristic for constrained vehicle routing problems in dynamic environment](https://mlsanity.com/paper/2609.26275/) (2026)

## Abstract (arXiv)

SNCF, the French public train company, is experimenting to develop new types of transportation services by tackling vehicle routing problems. While many deep learning models have been used to tackle efficiently vehicle routing problems, it is difficult to take into account time related constraints. In this paper, we solve the Capacitated Vehicle Routing Problem with Time Windows (CVRPTW) and the Capacitated Pickup and Delivery Problem with Time Windows (CPDPTW) with a constructive iterative Deep Learning algorithm. We use an Attention Encoder-Decoder structure and design a novel insertion heuristic for the feasibility check of the CPDPTW. Our models yields results that are better than best known learning solutions on the CVRPTW. We show the feasibility of deep learning techniques for solving the CPDPTW but witness the limitations of our iterative approach in terms of computational complexity.