# Collaboration! Towards Robust Neural Methods for Routing Problems

arXiv: https://arxiv.org/abs/2410.04968 · HTML: https://mlsanity.com/paper/2410.04968/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 73 of its 93 references that are in the map.
- First posted on arXiv 7 Oct 2024.

## Builds on (most cited first, 30 of 73)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [Universal and Transferable Adversarial Attacks on Aligned Language Models](https://mlsanity.com/paper/2307.15043/) (2023)
- [Jailbroken: How Does LLM Safety Training Fail?](https://mlsanity.com/paper/2307.02483/) (2023)
- [Theoretically Principled Trade-off between Robustness and Accuracy](https://mlsanity.com/paper/1901.08573/) (2019)
- [Pointer Networks](https://mlsanity.com/paper/1506.03134/) (2015)
- [Robustness May Be at Odds with Accuracy](https://mlsanity.com/paper/1805.12152/) (2018)
- [Ensemble Adversarial Training: Attacks and Defenses](https://mlsanity.com/paper/1705.07204/) (2017)
- [Universal Adversarial Triggers for Attacking and Analyzing NLP](https://mlsanity.com/paper/1908.07125/) (2019)
- [Attention, Learn to Solve Routing Problems!](https://mlsanity.com/paper/1803.08475/) (2018)
- [Machine Learning for Combinatorial Optimization: a Methodological Tour d'Horizon](https://mlsanity.com/paper/1811.06128/) (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)
- [Robust Adversarial Reinforcement Learning](https://mlsanity.com/paper/1703.02702/) (2017)
- [Adversarial Attacks on Neural Networks for Graph Data](https://mlsanity.com/paper/1805.07984/) (2018)
- [POMO: Policy Optimization with Multiple Optima for Reinforcement Learning](https://mlsanity.com/paper/2010.16011/) (2020)
- [Certifying Some Distributional Robustness with Principled Adversarial Training](https://mlsanity.com/paper/1710.10571/) (2017)
- [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)
- [DIFUSCO: Graph-based Diffusion Solvers for Combinatorial Optimization](https://mlsanity.com/paper/2302.08224/) (2023)
- [Improving Adversarial Robustness via Promoting Ensemble Diversity](https://mlsanity.com/paper/1901.08846/) (2019)
- [Learning a SAT Solver from Single-Bit Supervision](https://mlsanity.com/paper/1802.03685/) (2018)
- [Geometry-aware Instance-reweighted Adversarial Training](https://mlsanity.com/paper/2010.01736/) (2020)
- [Learning to Perform Local Rewriting for Combinatorial Optimization](https://mlsanity.com/paper/1810.00337/) (2018)
- [Disentangling Adversarial Robustness and Generalization](https://mlsanity.com/paper/1812.00740/) (2018)
- [Learning Improvement Heuristics for Solving Routing Problems](https://mlsanity.com/paper/1912.05784/) (2019)
- [Generalize a Small Pre-trained Model to Arbitrarily Large TSP Instances](https://mlsanity.com/paper/2012.10658/) (2020)
- [Understanding and Mitigating the Tradeoff Between Robustness and Accuracy](https://mlsanity.com/paper/2002.10716/) (2020)
- [Neural Combinatorial Optimization with Heavy Decoder: Toward Large Scale Generalization](https://mlsanity.com/paper/2310.07985/) (2023)

## Built on by (most cited first, 9 of 9)

- [BOPO: Neural Combinatorial Optimization via Best-anchored and Objective-guided Preference Optimization](https://mlsanity.com/paper/2503.07580/) (2025)
- [TuneNSearch: a hybrid transfer learning and local search approach for solving vehicle routing problems](https://mlsanity.com/paper/2503.12662/) (2025)
- [Chain-of-Context Learning: Dynamic Constraint Understanding for Multi-Task VRPs](https://mlsanity.com/paper/2603.01667/) (2026)
- [Latent Guided Sampling for Combinatorial Optimization](https://mlsanity.com/paper/2506.03672/) (2025)
- [Adversarial Instance Generation and Robust Training for Neural Combinatorial Optimization with Multiple Objectives](https://mlsanity.com/paper/2601.01665/) (2026)
- [Rethinking Efficiency in Neural Combinatorial Optimization: Batched Preference Optimization with Mamba](https://mlsanity.com/paper/2602.20730/) (2026)
- [FiLMMeD: Feature-wise Linear Modulation for Cross-Problem Multi-Depot Vehicle Routing](https://mlsanity.com/paper/2604.28102/) (2026)
- [LINC: Decoupling Local Consequence Scoring from Hidden Matching in Constructive Neural Routing](https://mlsanity.com/paper/2605.06332/) (2026)
- [RAISE: LLM-based Automated Heuristic Design with Robust Adversary Instance Search](https://mlsanity.com/paper/2606.31801/) (2026)

## Abstract (arXiv)

Despite enjoying desirable efficiency and reduced reliance on domain expertise, existing neural methods for vehicle routing problems (VRPs) suffer from severe robustness issues -- their performance significantly deteriorates on clean instances with crafted perturbations. To enhance robustness, we propose an ensemble-based Collaborative Neural Framework (CNF) w.r.t. the defense of neural VRP methods, which is crucial yet underexplored in the literature. Given a neural VRP method, we adversarially train multiple models in a collaborative manner to synergistically promote robustness against attacks, while boosting standard generalization on clean instances. A neural router is designed to adeptly distribute training instances among models, enhancing overall load balancing and collaborative efficacy. Extensive experiments verify the effectiveness and versatility of CNF in defending against various attacks across different neural VRP methods. Notably, our approach also achieves impressive out-of-distribution generalization on benchmark instances.