# Unsupervised Learning for Quadratic Assignment

arXiv: https://arxiv.org/abs/2503.20001 · HTML: https://mlsanity.com/paper/2503.20001/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 21 references that are in the map.
- First posted on arXiv 25 Mar 2025.

## Builds on (most cited first, 6 of 6)

- [Pointer Networks](https://mlsanity.com/paper/1506.03134/) (2015)
- [Neural Combinatorial Optimization with Reinforcement Learning](https://mlsanity.com/paper/1611.09940/) (2016)
- [An Efficient Graph Convolutional Network Technique for the Travelling Salesman Problem](https://mlsanity.com/paper/1906.01227/) (2019)
- [Unsupervised Learning for Solving the Travelling Salesman Problem](https://mlsanity.com/paper/2303.10538/) (2023)
- [HoTPP Benchmark: Are We Good at the Long Horizon Events Forecasting?](https://mlsanity.com/paper/2406.14341/) (2024)
- [Learning Solution-Aware Transformers for Efficiently Solving Quadratic Assignment Problem](https://mlsanity.com/paper/2406.09899/) (2024)

## Abstract (arXiv)

We introduce PLUME search, a data-driven framework that enhances search efficiency in combinatorial optimization through unsupervised learning. Unlike supervised or reinforcement learning, PLUME search learns directly from problem instances using a permutation-based loss with a non-autoregressive approach. We evaluate its performance on the quadratic assignment problem, a fundamental NP-hard problem that encompasses various combinatorial optimization problems. Experimental results demonstrate that PLUME search consistently improves solution quality. Furthermore, we study the generalization behavior and show that the learned model generalizes across different densities and sizes.