arXiv AI July 15, 2026 By Ke Sun, Xinyuan Zhang, Xinwu Qian

Connected by Construction: Learning Tractable Near-Tour Marginals for Traveling Salesman Problems

arXiv:2607. 12127v1 Announce Type: new Abstract: Learning-based methods for the traveling salesman problem (TSP) are often evaluated through the tours produced after decoding or search, but the learned object itself frequently lives in a surrogate space such as heatmaps, assignments, construction policies, or search-guidance scores.

Summary generated by The Flow from the publisher's feed. The full article lives at arXiv AI.

arXiv AI

Jun 9

Leveraging Structural Constraints for Diffusion-based Neural TSP Solvers

arXiv:2606. 09343v1 Announce Type: new Abstract: Neural combinatorial optimization has recently achieved strong results on the Euclidean Traveling Salesman Problem (TSP) using generative models such as diffusion and consistency models.

By Micka\"el Basson (CRIStAL, Scool), Philippe Preux (CRIStAL, Scool)

diffusion

arXiv AI

Jun 9

IDEQ -- Improving Diffusion Models for the Traveling Salesman Problem (TSP) by Leveraging the Structure of the Solution Space

arXiv:2412. 13858v2 Announce Type: replace Abstract: We investigate diffusion models to solve the Traveling Salesman Problem.

By Mickael Basson, Philippe Preux

diffusion benchmarks

arXiv AI

Jul 7

Graph Neural Networks are Heuristics

arXiv:2601. 13465v4 Announce Type: replace Abstract: Graph neural networks are usually treated as auxiliaries for combinatorial optimization: they imitate algorithms, guide search, or supply scores to classical procedures.

By Yimeng Min, Carla P. Gomes

arXiv AI

Aug 11

DualCert: A Solver for the Traveling Salesman Problem with Constraint-Coupled Learning

arXiv:2608. 09042v1 Announce Type: new Abstract: Large traveling salesman problem (TSP) instances require a solver to allocate limited computation while preserving the validity of its outputs.

By Yancheng Song, Yongzhi Qi, Wei Qi, Zuo-Jun Max Shen

arXiv AI

Jul 20

GeoRouteNet: A Geometry-Aware Non-Autoregressive Neural Solver for the Euclidean Traveling Salesman Problem

arXiv:2606. 22776v2 Announce Type: replace-cross Abstract: Non-autoregressive neural solvers amortize computation across traveling salesman problem (TSP) instances, but models trained on random Euclidean instances can degrade when the number or spatial distribution of nodes changes.

By Xiang Li

reinforcement-learning

arXiv AI

Jul 28

Understanding Human-like Solutions in Combinatorial Optimization via Learning and Search

arXiv:2607. 23854v1 Announce Type: new Abstract: Humans often find good solutions to combinatorial optimization problems that are computationally hard even for advanced computer algorithms.

By Haijiang Yan, Jian-Qiao Zhu, Liqiang Huang, Ming Meng

reinforcement-learning fine-tuning

Related stories

Leveraging Structural Constraints for Diffusion-based Neural TSP Solvers

IDEQ -- Improving Diffusion Models for the Traveling Salesman Problem (TSP) by Leveraging the Structure of the Solution Space

Graph Neural Networks are Heuristics

DualCert: A Solver for the Traveling Salesman Problem with Constraint-Coupled Learning

GeoRouteNet: A Geometry-Aware Non-Autoregressive Neural Solver for the Euclidean Traveling Salesman Problem

Understanding Human-like Solutions in Combinatorial Optimization via Learning and Search