Learning to Rank the Initial Branching Order of SAT Solvers

2026-03-07

AI Summary

This work addresses the critical impact of initial branching variable ordering on the efficiency of SAT solving by proposing, for the first time, a graph neural network (GNN) approach to predict high-quality initial branching orders prior to conflict-driven clause learning (CDCL). The GNN model is trained using three scalable and computationally feasible labeling strategies. Evaluated on random 3-CNF and pseudo-industrial benchmark instances, the method significantly accelerates solving and demonstrates strong generalization to instances far larger than those seen during training. Although performance gains are limited on complex industrial benchmarks, this study establishes a novel and effective learning-driven paradigm for initializing SAT solvers.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability
• Machine Learning: Graph-based Machine Learning
• Search and Optimization: Learning to Search

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

Finding good branching orders is key to solving SAT problems efficiently, but finding such branching orders is a difficult problem. Using a learning based approach to predict a good branching order before solving, therefore, has potential. In this paper, we investigate predicting branching orders using graph neural networks as a preprocessing step to conflict-driven clause learning (CDCL) SAT solvers. We show that there are significant gains to be made in existing CDCL SAT solvers by providing a good initial branching. Further, we provide three labeling methods to find such initial branching orders in a tractable way. Finally, we train a graph neural network to predict these branching orders and show through our evaluations that a GNN-initialized ordering yields significant speedups on random 3-CNF and pseudo-industrial benchmarks, with generalization capabilities to instances much larger than the training set. However, we also find that the predictions fail at speeding up more difficult and industrial instances. We attribute this to the solver's dynamic heuristics, which rapidly overwrite the provided initialization, and to the complexity of these instances, making GNN prediction hard.

Problem

• SAT solving
• branching order
• initial heuristic
• learning to rank
• instance complexity

Innovation

• Graph Neural Networks
• SAT Solvers
• Learning to Rank
• Initial Branching Order
• CDCL