Learning to Solve Weighted Maximum Satisfiability with a Co-Training Architecture

TL;DR

This paper introduces SplitGNN, a novel GNN-based approach with a co-training architecture and a new graph representation, significantly improving solution quality and speed for weighted MaxSAT problems, especially on large, complex instances.

Contribution

The paper presents SplitGNN, a new GNN architecture with a co-training framework and edge-splitting factor graph, advancing MaxSAT solving capabilities and generalization.

Findings

Achieves 3x faster convergence than other GNNs.

Outperforms modern heuristic MaxSAT solvers on large, complex benchmarks.

Demonstrates strong generalization across diverse instances.

Abstract

Wepropose SplitGNN, a graph neural network (GNN)-based approach that learns to solve weighted maximum satisfiabil ity (MaxSAT) problem. SplitGNN incorporates a co-training architecture consisting of supervised message passing mech anism and unsupervised solution boosting layer. A new graph representation called edge-splitting factor graph is proposed to provide more structural information for learning, which is based on spanning tree generation and edge classification. To improve the solutions on challenging and weighted instances, we implement a GPU-accelerated layer applying efficient score calculation and relaxation-based optimization. Exper iments show that SplitGNN achieves 3* faster convergence and better predictions compared with other GNN-based ar chitectures. More notably, SplitGNN successfully finds solu tions that outperform modern heuristic MaxSAT solvers on much larger and harder weighted MaxSAT benchmarks, and demonstrates exceptional generalization abilities on diverse structural instances.