# Learning to Solve Vehicle Routing Problems with Time Windows through Joint Attention

arXiv: https://arxiv.org/abs/2006.09100 · HTML: https://mlsanity.com/paper/2006.09100/

## Key facts

- Cited by 29 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Jun 2020.

## Built on by (most cited first, 29 of 29)

- [NeuroLKH: Combining Deep Learning Model with Lin-Kernighan-Helsgaun Heuristic for Solving the Traveling Salesman Problem](https://mlsanity.com/paper/2110.07983/) (2021)
- [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)
- [GOAL: A Generalist Combinatorial Optimization Agent Learner](https://mlsanity.com/paper/2406.15079/) (2024)
- [PolyNet: Learning Diverse Solution Strategies for Neural Combinatorial Optimization](https://mlsanity.com/paper/2402.14048/) (2024)
- [Learning to Handle Complex Constraints for Vehicle Routing Problems](https://mlsanity.com/paper/2410.21066/) (2024)
- [Neural Combinatorial Optimization Algorithms for Solving Vehicle Routing Problems: A Comprehensive Survey with Perspectives](https://mlsanity.com/paper/2406.00415/) (2024)
- [An Overview and Experimental Study of Learning-based Optimization Algorithms for Vehicle Routing Problem](https://mlsanity.com/paper/2107.07076/) (2021)
- [Learning to Control Local Search for Combinatorial Optimization](https://mlsanity.com/paper/2206.13181/) (2022)
- [Learning to Solve Vehicle Routing Problems: A Survey](https://mlsanity.com/paper/2205.02453/) (2022)
- [Neural Deconstruction Search for Vehicle Routing Problems](https://mlsanity.com/paper/2501.03715/) (2025)
- [Joint Attention for Multi-Agent Coordination and Social Learning](https://mlsanity.com/paper/2104.07750/) (2021)
- [MODRL/D-EL: Multiobjective Deep Reinforcement Learning with Evolutionary Learning for Multiobjective Optimization](https://mlsanity.com/paper/2107.07961/) (2021)
- [PARCO: Parallel AutoRegressive Models for Multi-Agent Combinatorial Optimization](https://mlsanity.com/paper/2409.03811/) (2024)
- [Too Big, so Fail? -- Enabling Neural Construction Methods to Solve Large-Scale Routing Problems](https://mlsanity.com/paper/2309.17089/) (2023)
- [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)
- [Deep Reinforcement Learning for Demand Driven Services in Logistics and Transportation Systems: A Survey](https://mlsanity.com/paper/2108.04462/) (2021)
- [Large Neighborhood Search based on Neural Construction Heuristics](https://mlsanity.com/paper/2205.00772/) (2022)
- [Neuro CROSS exchange: Learning to CROSS exchange to solve realistic vehicle routing problems](https://mlsanity.com/paper/2206.02771/) (2022)
- [RP-DQN: An application of Q-Learning to Vehicle Routing Problems](https://mlsanity.com/paper/2104.12226/) (2021)
- [Solving the Traveling Salesperson Problem with Precedence Constraints by Deep Reinforcement Learning](https://mlsanity.com/paper/2207.01443/) (2022)
- [Recurrent State Encoders for Efficient Neural Combinatorial Optimization](https://mlsanity.com/paper/2509.05084/) (2025)
- [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)
- [Learning to Search for Vehicle Routing with Multiple Time Windows](https://mlsanity.com/paper/2505.23098/) (2025)
- [LaT: LLM-as-Trainer for Multi-Task Vehicle Routing Solvers](https://mlsanity.com/paper/2607.17708/) (2026)
- [Smart routes: a system for development and comparison of algorithms for solving vehicle routing problems with realistic constraints](https://mlsanity.com/paper/2608.14140/) (2026)
- [Deep Reinforcement Learning solution for pickup and delivery routing problems with time window and capacity constraints](https://mlsanity.com/paper/2608.14156/) (2026)
- [JAMPR+/L2D: scalable neural heuristic for constrained vehicle routing problems in dynamic environment](https://mlsanity.com/paper/2609.26275/) (2026)
- [Depot-Closed Multi-Component Construction for Neural Vehicle Routing](https://mlsanity.com/paper/2609.35066/) (2026)

## Abstract (arXiv)

Many real-world vehicle routing problems involve rich sets of constraints with respect to the capacities of the vehicles, time windows for customers etc. While in recent years first machine learning models have been developed to solve basic vehicle routing problems faster than optimization heuristics, complex constraints rarely are taken into consideration. Due to their general procedure to construct solutions sequentially route by route, these methods generalize unfavorably to such problems. In this paper, we develop a policy model that is able to start and extend multiple routes concurrently by using attention on the joint action space of several tours. In that way the model is able to select routes and customers and thus learns to make difficult trade-offs between routes. In comprehensive experiments on three variants of the vehicle routing problem with time windows we show that our model called JAMPR works well for different problem sizes and outperforms the existing state-of-the-art constructive model. For two of the three variants it also creates significantly better solutions than a comparable meta-heuristic solver.