Many combinatorial optimization problems can be phrased in the language of constraint satisfaction problems. We introduce a graph neural network architecture for solving such optimization problems. The architecture is generic; it works for all binary constraint satisfaction problems. Training is unsupervised, and it is sufficient to train on relatively small instances; the resulting networks perform well on much larger instances (at least 10-times larger). We experimentally evaluate our approach for a variety of problems, including Maximum Cut and Maximum Independent Set. Despite being generic, we show that our approach matches or surpasses most greedy and semi-definite programming based algorithms and sometimes even outperforms state-of-the-art heuristics for the specific problems.
@article{arxiv.1909.08387,
title = {Graph Neural Networks for Maximum Constraint Satisfaction},
author = {Jan Toenshoff and Martin Ritzert and Hinrikus Wolf and Martin Grohe},
journal= {arXiv preprint arXiv:1909.08387},
year = {2020}
}