Structure As Search: Unsupervised Permutation Learning for Combinatorial Optimization

TL;DR

This paper introduces an unsupervised, non-autoregressive neural framework that learns to generate solutions for the Traveling Salesman Problem directly from permutation structures, bypassing explicit search procedures.

Contribution

It presents a novel permutation-based learning approach that captures combinatorial structure without supervision or sequential decision-making.

Findings

Achieves competitive results against classical heuristics.

Demonstrates neural networks can directly model combinatorial structures.

Provides evidence for structure-guided optimization without explicit search.

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. Our method offers concrete evidence that neural networks can directly capture and exploit combinatorial structure.