Graph Neural Networks for Maximum Constraint Satisfaction

Frontiers in Artificial Intelligence, vol. 3, pp. 580607

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.

Authors 4

1. Jan Tönshoff Aachen Chair of Computer Science 7 (Logic and Theory of Discrete Systems) Department of Computer Science

   RWTH Aachen University

   Affiliation as printed

   Chair of Computer Science 7 (Logic and Theory of Discrete Systems), Department of Computer Science, RWTH Aachen University, Aachen, Germany

2. Martin Ritzert Aachen Chair of Computer Science 7 (Logic and Theory of Discrete Systems) Department of Computer Science

   RWTH Aachen University

   Affiliation as printed

   Chair of Computer Science 7 (Logic and Theory of Discrete Systems), Department of Computer Science, RWTH Aachen University, Aachen, Germany

3. Hinrikus Wolf Aachen Chair of Computer Science 7 (Logic and Theory of Discrete Systems) Department of Computer Science

   RWTH Aachen University

   Affiliation as printed

   Chair of Computer Science 7 (Logic and Theory of Discrete Systems), Department of Computer Science, RWTH Aachen University, Aachen, Germany

4. Martin Grohe Aachen Chair of Computer Science 7 (Logic and Theory of Discrete Systems) Department of Computer Science

   RWTH Aachen University

   Affiliation as printed

   Chair of Computer Science 7 (Logic and Theory of Discrete Systems), Department of Computer Science, RWTH Aachen University, Aachen, Germany