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We propose a universal Graph Neural Network architecture which can be trainedas an end-2-end search heuristic for any Constraint Satisfaction Problem (CSP).Our architecture can be trained unsupervised with policy gradient descent togenerate problem specific heuristics for any CSP in a purely data drivenmanner. The approach is based on a novel graph representation for CSPs that isboth generic and compact and enables us to process every possible CSP instancewith one GNN, regardless of constraint arity, relations or domain size. Unlikeprevious RL-based methods, we operate on a global search action space and allowour GNN to modify any number of variables in every step of the stochasticsearch. This enables our method to properly leverage the inherent parallelismof GNNs. We perform a thorough empirical evaluation where we learn heuristicsfor well known and important CSPs from random data, including graph coloring,MaxCut, 3-SAT and MAX-k-SAT. Our approach outperforms prior approaches forneural combinatorial optimization by a substantial margin. It can compete with,and even improve upon, conventional search heuristics on test instances thatare several orders of magnitude larger and structurally more complex than thoseseen during training.

One Model, Any CSP: Graph Neural Networks as Fast Global Search Heuristics for Constraint Satisfaction