# Vision-Assisted Foundation Model for Solving Multi-Task Vehicle Routing Problems

arXiv: https://arxiv.org/abs/2606.10431 · HTML: https://mlsanity.com/paper/2606.10431/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 35 of its 53 references that are in the map.
- First posted on arXiv 9 Jun 2026.

## Builds on (most cited first, 30 of 35)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [FlashAttention: Fast and Memory-Efficient Exact Attention with IO-Awareness](https://mlsanity.com/paper/2205.14135/) (2022)
- [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)
- [An Efficient Graph Convolutional Network Technique for the Travelling Salesman Problem](https://mlsanity.com/paper/1906.01227/) (2019)
- [Cross-Modal Self-Attention Network for Referring Image Segmentation](https://mlsanity.com/paper/1904.04745/) (2019)
- [Diffusion models as plug-and-play priors](https://mlsanity.com/paper/2206.09012/) (2022)
- [DIFUSCO: Graph-based Diffusion Solvers for Combinatorial Optimization](https://mlsanity.com/paper/2302.08224/) (2023)
- [Learning Improvement Heuristics for Solving Routing Problems](https://mlsanity.com/paper/1912.05784/) (2019)
- [What Makes Multi-modal Learning Better than Single (Provably)](https://mlsanity.com/paper/2106.04538/) (2021)
- [A Review of Sparse Expert Models in Deep Learning](https://mlsanity.com/paper/2209.01667/) (2022)
- [Neural Combinatorial Optimization with Heavy Decoder: Toward Large Scale Generalization](https://mlsanity.com/paper/2310.07985/) (2023)
- [MFAS: Multimodal Fusion Architecture Search](https://mlsanity.com/paper/1903.06496/) (2019)
- [Learning to Search Feasible and Infeasible Regions of Routing Problems with Flexible Neural k-Opt](https://mlsanity.com/paper/2310.18264/) (2023)
- [MVMoE: Multi-Task Vehicle Routing Solver with Mixture-of-Experts](https://mlsanity.com/paper/2405.01029/) (2024)
- [RouteFinder: Towards Foundation Models for Vehicle Routing Problems](https://mlsanity.com/paper/2406.15007/) (2024)
- [PyVRP: a high-performance VRP solver package](https://mlsanity.com/paper/2403.13795/) (2023)
- [Multi-Task Learning for Routing Problem with Cross-Problem Zero-Shot Generalization](https://mlsanity.com/paper/2402.16891/) (2024)
- [GOAL: A Generalist Combinatorial Optimization Agent Learner](https://mlsanity.com/paper/2406.15079/) (2024)
- [Deep Multi-modal Fusion of Image and Non-image Data in Disease Diagnosis and Prognosis: A Review](https://mlsanity.com/paper/2203.15588/) (2022)
- [Deep Reinforcement Learning for Electric Vehicle Routing Problem with Time Windows](https://mlsanity.com/paper/2010.02068/) (2020)
- [Cross-Problem Learning for Solving Vehicle Routing Problems](https://mlsanity.com/paper/2404.11677/) (2024)
- [Majority Vote of Diverse Classifiers for Late Fusion](https://mlsanity.com/paper/1404.7796/) (2014)
- [An Overview and Experimental Study of Learning-based Optimization Algorithms for Vehicle Routing Problem](https://mlsanity.com/paper/2107.07076/) (2021)
- [Contrastive Registration for Unsupervised Medical Image Segmentation](https://mlsanity.com/paper/2011.08894/) (2020)
- [A concise guide to existing and emerging vehicle routing problem variants](https://mlsanity.com/paper/1906.06750/) (2019)
- [Road Network Representation Learning with the Third Law of Geography](https://mlsanity.com/paper/2406.04038/) (2024)

## Built on by (most cited first, 1 of 1)

- [Hyper Algorithm Design Agent: Evolving Learnable Optimizer from Zero](https://mlsanity.com/paper/2609.35328/) (2026)

## Abstract (arXiv)

Multi-task vehicle routing problems play a critical role in enhancing efficiency across various industries and service sectors. These problems consist of multiple variants that optimize routing costs while meeting diverse customer constraints. Existing multi-task VRP solvers solely utilize a graph-based modality, limiting their ability to address variants with multiple constraints. As a format to represent complex semantics, vision modality shows great potential for encoding diverse VRP constraints. This motivates us to learn patch-level semantics from the vision images, and then integrate them into a graph-based model to solve various VRP variants simultaneously. However, directly applying this approach to multi-task VRPs presents three challenges: 1) existing VRP images lack constraint representations, which are essential for multi-task VRPs, 2) the fixed receptive field of individual patches cannot effectively accommodate varying requirements across tasks, and 3) imbalanced pixel distribution among constraints may cause the model to overlook constraints with fewer pixels. In this paper, we propose a vision-assisted foundation model (VaFM) to address these challenges. In the vision modality, input images tailored to all constraints are encoded by a convolutional neural network. The obtained patch embeddings are fused with graph-based nodes to generate solutions, with an auxiliary task designed to address the pixel-imbalanced issue. The performance of VaFM is evaluated across 16 different VRP variants. The experimental results demonstrate the superiority of VaFM over state-of-the-art methods, especially for variants with complex constraints.