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

TL;DR

This paper introduces a universal Graph Neural Network architecture that learns efficient, problem-specific heuristics for solving various Constraint Satisfaction Problems through end-to-end training, outperforming previous neural methods and rivaling traditional heuristics.

Contribution

The paper presents a novel, general GNN-based framework for CSPs that operates on a global search space and can be trained unsupervised, enabling scalable and effective problem-solving across diverse CSPs.

Findings

Outperforms prior neural approaches on CSP benchmarks.

Can handle larger and more complex instances than training data.

Competes with traditional heuristics on challenging CSPs.

Abstract

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.