AUTHOR=Tönshoff Jan , Ritzert Martin , Wolf Hinrikus , Grohe Martin TITLE=Graph Neural Networks for Maximum Constraint Satisfaction JOURNAL=Frontiers in Artificial Intelligence VOLUME=3 YEAR=2021 URL=https://www.frontiersin.org/journals/artificial-intelligence/articles/10.3389/frai.2020.580607 DOI=10.3389/frai.2020.580607 ISSN=2624-8212 ABSTRACT=

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.