Graph Neural Networks for Maximum Constraint Satisfaction
This provides a scalable, unsupervised method for solving constraint satisfaction problems, benefiting researchers and practitioners in optimization and AI.
The paper tackles combinatorial optimization problems by introducing a generic graph neural network architecture for binary constraint satisfaction, achieving performance that matches or surpasses many existing algorithms and sometimes outperforms state-of-the-art heuristics on problems like Maximum Cut and Maximum Independent Set.
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.