One Model, Any CSP: Graph Neural Networks as Fast Global Search Heuristics for Constraint Satisfaction
This provides a fast, data-driven solution for solving diverse CSPs like graph coloring and SAT, with potential applications in optimization and AI, though it builds incrementally on existing GNN and RL techniques.
The authors tackled the problem of developing a universal heuristic for constraint satisfaction problems (CSPs) by proposing a Graph Neural Network architecture trained unsupervised, which outperformed prior neural methods and matched or improved upon conventional heuristics on larger, more complex test instances.
We propose a universal Graph Neural Network architecture which can be trained as an end-2-end search heuristic for any Constraint Satisfaction Problem (CSP). Our architecture can be trained unsupervised with policy gradient descent to generate problem specific heuristics for any CSP in a purely data driven manner. The approach is based on a novel graph representation for CSPs that is both generic and compact and enables us to process every possible CSP instance with one GNN, regardless of constraint arity, relations or domain size. Unlike previous RL-based methods, we operate on a global search action space and allow our GNN to modify any number of variables in every step of the stochastic search. This enables our method to properly leverage the inherent parallelism of GNNs. We perform a thorough empirical evaluation where we learn heuristics for well known and important CSPs from random data, including graph coloring, MaxCut, 3-SAT and MAX-k-SAT. Our approach outperforms prior approaches for neural combinatorial optimization by a substantial margin. It can compete with, and even improve upon, conventional search heuristics on test instances that are several orders of magnitude larger and structurally more complex than those seen during training.