Learning the Satisfiability of Pseudo-Boolean Problem with Graph Neural Networks

Minghao Liu, Fan Zhang, Pei Huang, Shuzi Niu, Feifei Ma, Jian Zhang

Abstract: Graph Neural Network (GNN) has shown great power on many practical tasks in the past few years. It is also considered to be a potential technique in bridging the gap between machine learning and symbolic reasoning. Experimental investigations have also shown that some $$\mathcal {NP}$$ -Hard constraint satisfaction problems can be well learned by the GNN models. In this paper, a GNN-based classification model to learn the satisfiability of pseudo-Boolean (PB) problem is proposed. After constructing the bipartite graph representation, a two-phase message passing process is executed. Experiments on 0–1 knapsack and weighted independent set problems show that the model can effectively learn the features related to the problem distribution and satisfiability. As a result, competitive prediction accuracy has been achieved with some generalization to larger-scale problems. The studies indicate that GNN has great potential in solving constraint satisfaction problems with numerical coefficients.