# Learning the Travelling Salesperson Problem Requires Rethinking Generalization

arXiv: https://arxiv.org/abs/2006.07054 · HTML: https://mlsanity.com/paper/2006.07054/

## Key facts

- Cited by 98 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Jun 2020.

## Built on by (most cited first, 30 of 98)

- [ReEvo: Large Language Models as Hyper-Heuristics with Reflective Evolution](https://mlsanity.com/paper/2402.01145/) (2024)
- [Combinatorial optimization and reasoning with graph neural networks](https://mlsanity.com/paper/2102.09544/) (2021)
- [DIFUSCO: Graph-based Diffusion Solvers for Combinatorial Optimization](https://mlsanity.com/paper/2302.08224/) (2023)
- [Neural Combinatorial Optimization with Heavy Decoder: Toward Large Scale Generalization](https://mlsanity.com/paper/2310.07985/) (2023)
- [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)
- [BQ-NCO: Bisimulation Quotienting for Efficient Neural Combinatorial Optimization](https://mlsanity.com/paper/2301.03313/) (2023)
- [DeepACO: Neural-enhanced Ant Systems for Combinatorial Optimization](https://mlsanity.com/paper/2309.14032/) (2023)
- [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)
- [RouteFinder: Towards Foundation Models for Vehicle Routing Problems](https://mlsanity.com/paper/2406.15007/) (2024)
- [Multi-Task Learning for Routing Problem with Cross-Problem Zero-Shot Generalization](https://mlsanity.com/paper/2402.16891/) (2024)
- [INViT: A Generalizable Routing Problem Solver with Invariant Nested View Transformer](https://mlsanity.com/paper/2402.02317/) (2024)
- [GOAL: A Generalist Combinatorial Optimization Agent Learner](https://mlsanity.com/paper/2406.15079/) (2024)
- [Self-Improvement for Neural Combinatorial Optimization: Sample without Replacement, but Improvement](https://mlsanity.com/paper/2403.15180/) (2024)
- [Neural Algorithmic Reasoning with Causal Regularisation](https://mlsanity.com/paper/2302.10258/) (2023)
- [Towards Better Out-of-Distribution Generalization of Neural Algorithmic Reasoning Tasks](https://mlsanity.com/paper/2211.00692/) (2022)
- [Position: Rethinking Post-Hoc Search-Based Neural Approaches for Solving Large-Scale Traveling Salesman Problems](https://mlsanity.com/paper/2406.03503/) (2024)
- [Neural Combinatorial Optimization Algorithms for Solving Vehicle Routing Problems: A Comprehensive Survey with Perspectives](https://mlsanity.com/paper/2406.00415/) (2024)
- [Visual Reasoning and Multi-Agent Approach in Multimodal Large Language Models (MLLMs): Solving TSP and mTSP Combinatorial Challenges](https://mlsanity.com/paper/2407.00092/) (2024)
- [Neural Algorithmic Reasoning for Combinatorial Optimisation](https://mlsanity.com/paper/2306.06064/) (2023)
- [Distilling Autoregressive Models to Obtain High-Performance Non-Autoregressive Solvers for Vehicle Routing Problems with Faster Inference Speed](https://mlsanity.com/paper/2312.12469/) (2023)
- [SALSA-CLRS: A Sparse and Scalable Benchmark for Algorithmic Reasoning](https://mlsanity.com/paper/2309.12253/) (2023)
- [DISCO: Efficient Diffusion Solver for Large-Scale Combinatorial Optimization Problems](https://mlsanity.com/paper/2406.19705/) (2024)
- [RRNCO: Towards Real-World Routing with Neural Combinatorial Optimization](https://mlsanity.com/paper/2503.16159/) (2025)
- [BPQP: A Differentiable Convex Optimization Framework for Efficient End-to-End Learning](https://mlsanity.com/paper/2411.19285/) (2024)
- [Adversarial Generative Flow Network for Solving Vehicle Routing Problems](https://mlsanity.com/paper/2503.01931/) (2025)
- [An Efficient Diffusion-based Non-Autoregressive Solver for Traveling Salesman Problem](https://mlsanity.com/paper/2501.13767/) (2025)
- [Primal-Dual Neural Algorithmic Reasoning](https://mlsanity.com/paper/2505.24067/) (2025)
- [GDSG: Graph Diffusion-based Solution Generator for Optimization Problems in MEC Networks](https://mlsanity.com/paper/2412.08296/) (2024)

## Abstract (arXiv)

End-to-end training of neural network solvers for graph combinatorial optimization problems such as the Travelling Salesperson Problem (TSP) have seen a surge of interest recently, but remain intractable and inefficient beyond graphs with few hundreds of nodes. While state-of-the-art learning-driven approaches for TSP perform closely to classical solvers when trained on trivially small sizes, they are unable to generalize the learnt policy to larger instances at practical scales. This work presents an end-to-end neural combinatorial optimization pipeline that unifies several recent papers in order to identify the inductive biases, model architectures and learning algorithms that promote generalization to instances larger than those seen in training. Our controlled experiments provide the first principled investigation into such zero-shot generalization, revealing that extrapolating beyond training data requires rethinking the neural combinatorial optimization pipeline, from network layers and learning paradigms to evaluation protocols. Additionally, we analyze recent advances in deep learning for routing problems through the lens of our pipeline and provide new directions to stimulate future research.