Unsupervised Learning for Quadratic Assignment

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.