Structure As Search: Unsupervised Permutation Learning for Combinatorial Optimization

Yimeng Min, Carla P Gomes

Keywords: Travelling Salesman Problem (TSP), Combinatorial Optimization, Unsupervised Learning, Non-Autoregressive Models, Graph Neural Networks (GNNs)

TL;DR: We propose a non-autoregressive, unsupervised framework that learns permutation matrices to solve the Travelling Salesman Problem without explicit search or supervision.

Abstract: We propose a non-autoregressive framework for the Travelling Salesman Problem where solutions emerge directly from learned permutations, without requiring explicit search. By applying a similarity transformation to Hamiltonian cycles, the model learns to approximate permutation matrices via continuous relaxations. Our unsupervised approach achieves competitive performance against classical heuristics, demonstrating that the inherent structure of the problem can effectively guide combinatorial optimization without sequential decision-making.

Submission Number: 3