# INViT: A Generalizable Routing Problem Solver with Invariant Nested View Transformer

arXiv: https://arxiv.org/abs/2402.02317 · HTML: https://mlsanity.com/paper/2402.02317/

## Key facts

- Cited by 44 papers in the map (data through 14 Oct 2026).
- Placed in RL for games and combinatorial optimization, one of 15 directions in Deep reinforcement learning methods.
- Builds on 30 of its 45 references that are in the map.
- First posted on arXiv 4 Feb 2024.

## Placed in

- Deep reinforcement learning methods / [RL for games and combinatorial optimization](https://mlsanity.com/deeprl/rl-for-games-and-combinatorial-optimization/)

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

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Playing Atari with Deep Reinforcement Learning](https://mlsanity.com/paper/1312.5602/) (2013)
- [Pointer Networks](https://mlsanity.com/paper/1506.03134/) (2015)
- [Attention, Learn to Solve Routing Problems!](https://mlsanity.com/paper/1803.08475/) (2018)
- [Neural Combinatorial Optimization with Reinforcement Learning](https://mlsanity.com/paper/1611.09940/) (2016)
- [Learning Combinatorial Optimization Algorithms over Graphs](https://mlsanity.com/paper/1704.01665/) (2017)
- [Lipschitz regularity of deep neural networks: analysis and efficient estimation](https://mlsanity.com/paper/1805.10965/) (2018)
- [POMO: Policy Optimization with Multiple Optima for Reinforcement Learning](https://mlsanity.com/paper/2010.16011/) (2020)
- [An Efficient Graph Convolutional Network Technique for the Travelling Salesman Problem](https://mlsanity.com/paper/1906.01227/) (2019)
- [DIFUSCO: Graph-based Diffusion Solvers for Combinatorial Optimization](https://mlsanity.com/paper/2302.08224/) (2023)
- [Generalize a Small Pre-trained Model to Arbitrarily Large TSP Instances](https://mlsanity.com/paper/2012.10658/) (2020)
- [Neural Combinatorial Optimization with Heavy Decoder: Toward Large Scale Generalization](https://mlsanity.com/paper/2310.07985/) (2023)
- [DIMES: A Differentiable Meta Solver for Combinatorial Optimization Problems](https://mlsanity.com/paper/2210.04123/) (2022)
- [Hybrid Genetic Search for the CVRP: Open-Source Implementation and SWAP* Neighborhood](https://mlsanity.com/paper/2012.10384/) (2020)
- [Multi-Decoder Attention Model with Embedding Glimpse for Solving Vehicle Routing Problems](https://mlsanity.com/paper/2012.10638/) (2020)
- [Efficient Active Search for Combinatorial Optimization Problems](https://mlsanity.com/paper/2106.05126/) (2021)
- [Learning the Travelling Salesperson Problem Requires Rethinking Generalization](https://mlsanity.com/paper/2006.07054/) (2020)
- [GLOP: Learning Global Partition and Local Construction for Solving Large-scale Routing Problems in Real-time](https://mlsanity.com/paper/2312.08224/) (2023)
- [Simulation-guided Beam Search for Neural Combinatorial Optimization](https://mlsanity.com/paper/2207.06190/) (2022)
- [Combinatorial Optimization by Graph Pointer Networks and Hierarchical Reinforcement Learning](https://mlsanity.com/paper/1911.04936/) (2019)
- [Towards Omni-generalizable Neural Methods for Vehicle Routing Problems](https://mlsanity.com/paper/2305.19587/) (2023)
- [Learning Generalizable Models for Vehicle Routing Problems via Knowledge Distillation](https://mlsanity.com/paper/2210.07686/) (2022)
- [Towards Generalizable Neural Solvers for Vehicle Routing Problems via Ensemble with Transferrable Local Policy](https://mlsanity.com/paper/2308.14104/) (2023)
- [Unsupervised Learning for Solving the Travelling Salesman Problem](https://mlsanity.com/paper/2303.10538/) (2023)
- [Pointerformer: Deep Reinforced Multi-Pointer Transformer for the Traveling Salesman Problem](https://mlsanity.com/paper/2304.09407/) (2023)
- [H-TSP: Hierarchically Solving the Large-Scale Travelling Salesman Problem](https://mlsanity.com/paper/2304.09395/) (2023)
- [Learning to Solve Routing Problems via Distributionally Robust Optimization](https://mlsanity.com/paper/2202.07241/) (2022)
- [Generalization in Deep RL for TSP Problems via Equivariance and Local Search](https://mlsanity.com/paper/2110.03595/) (2021)
- [Improving Generalization of Deep Reinforcement Learning-based TSP Solvers](https://mlsanity.com/paper/2110.02843/) (2021)
- [Too Big, so Fail? -- Enabling Neural Construction Methods to Solve Large-Scale Routing Problems](https://mlsanity.com/paper/2309.17089/) (2023)

## Built on by (most cited first, 30 of 44)

- [Rethinking Light Decoder-based Solvers for Vehicle Routing Problems](https://mlsanity.com/paper/2503.00753/) (2025)
- [Neural Combinatorial Optimization Algorithms for Solving Vehicle Routing Problems: A Comprehensive Survey with Perspectives](https://mlsanity.com/paper/2406.00415/) (2024)
- [Learning to Reduce Search Space for Generalizable Neural Routing Solver](https://mlsanity.com/paper/2503.03137/) (2025)
- [BOPO: Neural Combinatorial Optimization via Best-anchored and Objective-guided Preference Optimization](https://mlsanity.com/paper/2503.07580/) (2025)
- [MTL-KD: Multi-Task Learning Via Knowledge Distillation for Generalizable Neural Vehicle Routing Solver](https://mlsanity.com/paper/2506.02935/) (2025)
- [Improving Generalization of Neural Combinatorial Optimization for Vehicle Routing Problems via Test-Time Projection Learning](https://mlsanity.com/paper/2506.02392/) (2025)
- [Learning to Insert for Constructive Neural Vehicle Routing Solver](https://mlsanity.com/paper/2505.13904/) (2025)
- [Collaboration! Towards Robust Neural Methods for Routing Problems](https://mlsanity.com/paper/2410.04968/) (2024)
- [Bridging Large Language Models and Optimization: A Unified Framework for Text-attributed Combinatorial Optimization](https://mlsanity.com/paper/2408.12214/) (2024)
- [Rethinking Neural Combinatorial Optimization for Vehicle Routing Problems with Different Constraint Tightness Degrees](https://mlsanity.com/paper/2505.24627/) (2025)
- [URS: A Unified Neural Routing Solver for Cross-Problem Zero-Shot Generalization](https://mlsanity.com/paper/2509.23413/) (2025)
- [Hybrid-Balance GFlowNet for Solving Vehicle Routing Problems](https://mlsanity.com/paper/2510.04792/) (2025)
- [Neural Solver Selection for Combinatorial Optimization](https://mlsanity.com/paper/2410.09693/) (2024)
- [Learning to Segment for Vehicle Routing Problems](https://mlsanity.com/paper/2507.01037/) (2025)
- [Survey on Neural Routing Solvers](https://mlsanity.com/paper/2602.21761/) (2026)
- [Beyond the Heatmap: A Rigorous Evaluation of Component Impact in MCTS-Based TSP Solvers](https://mlsanity.com/paper/2411.09238/) (2024)
- [GELD: A Unified Neural Model for Efficiently Solving Traveling Salesman Problems Across Different Scales](https://mlsanity.com/paper/2506.06634/) (2025)
- [Efficient Neural Combinatorial Optimization Solver for the Min-max Heterogeneous Capacitated Vehicle Routing Problem](https://mlsanity.com/paper/2507.21386/) (2025)
- [Towards Efficient Constraint Handling in Neural Solvers for Routing Problems](https://mlsanity.com/paper/2602.16012/) (2026)
- [LocalEscaper: A Weakly-supervised Framework with Regional Reconstruction for Scalable Neural TSP Solvers](https://mlsanity.com/paper/2502.12484/) (2025)
- [SPACE: Unifying Symmetric and Asymmetric Routing Problems for Generalist Neural Solver](https://mlsanity.com/paper/2605.24484/) (2026)
- [ASAP: Exploiting the Satisficing Generalization Edge in Neural Combinatorial Optimization](https://mlsanity.com/paper/2501.17377/) (2025)
- [Lifelong Learning with Behavior Consolidation for Vehicle Routing](https://mlsanity.com/paper/2509.21765/) (2025)
- [ViTSP: A Vision Language Models Guided Framework for Solving Large-Scale Traveling Salesman Problems](https://mlsanity.com/paper/2509.23465/) (2025)
- [Empowering Targeted Neighborhood Search via Hyper Tour for Large-Scale TSP](https://mlsanity.com/paper/2510.20169/) (2025)
- [Efficient Decoder Scaling Strategy for Neural Routing Solvers](https://mlsanity.com/paper/2603.00430/) (2026)
- [Aligning LLMs with Graph Neural Solvers for Combinatorial Optimization](https://mlsanity.com/paper/2603.27169/) (2026)
- [Rethinking Constraint Awareness for Efficient State Embedding of Neural Routing Solver](https://mlsanity.com/paper/2605.10122/) (2026)
- [Learning with Foresight: Enhancing Neural Routing Policy via Multi-Node Lookahead Prediction](https://mlsanity.com/paper/2605.19975/) (2026)
- [Leveraging Structural Constraints for Diffusion-based Neural TSP Solvers](https://mlsanity.com/paper/2606.09343/) (2026)

## Abstract (arXiv)

Recently, deep reinforcement learning has shown promising results for learning fast heuristics to solve routing problems. Meanwhile, most of the solvers suffer from generalizing to an unseen distribution or distributions with different scales. To address this issue, we propose a novel architecture, called Invariant Nested View Transformer (INViT), which is designed to enforce a nested design together with invariant views inside the encoders to promote the generalizability of the learned solver. It applies a modified policy gradient algorithm enhanced with data augmentations. We demonstrate that the proposed INViT achieves a dominant generalization performance on both TSP and CVRP problems with various distributions and different problem scales.