Automatically discovering heuristics in a complex SAT solver with large language models

2025-07-30

AI Summary

Modern SAT solvers suffer from architectural complexity, difficulty in manual optimization, and limitations of existing automated configuration methods—particularly their reliance on hand-crafted search spaces and modest performance gains. To address these challenges, this paper proposes an LLM-driven framework for automatic heuristic discovery. Our approach comprises three key contributions: (1) a modular SAT solver architecture explicitly designed for large language models, decoupling heuristic components to enable fine-grained intervention; (2) an unsupervised prompt optimization mechanism that dynamically adapts prompts to elicit high-quality, domain-specific heuristics from the LLM; and (3) an efficient search strategy integrating pre-search exploration with evolutionary algorithms to accelerate heuristic discovery. Evaluated across diverse benchmark suites, our method achieves a 50% speedup over baseline solvers, outperforms the current state-of-the-art (SOTA) by 30%, and exceeds parameter-tuned SOTA configurations by 20% on average.

Technology Category

• Search and Optimization: Heuristic Search
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Machine Learning: Large Multimodal Models (LMMs)

Application Category

• Search and Retrieval-Augmented AI: Search Tool Learning with LLM: Teaching LLMs to invoke search and make use of retrieved information
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• User Modeling, Personalization and Recommendation: Large Language Models (LLM) for user modeling and recommendation

Abstract

Satisfiability problem (SAT) is a cornerstone of computational complexity with broad industrial applications, and it remains challenging to optimize modern SAT solvers in real-world settings due to their intricate architectures. While automatic configuration frameworks have been developed, they rely on manually constrained search spaces and yield limited performance gains. This work introduces a novel paradigm which effectively optimizes complex SAT solvers via Large Language Models (LLMs), and a tool called AutoModSAT is developed. Three fundamental challenges are addressed in order to achieve superior performance: (1) LLM-friendly solver: Systematic guidelines are proposed for developing a modularized solver to meet LLMs' compatibility, emphasizing code simplification, information share and bug reduction; (2) Automatic prompt optimization: An unsupervised automatic prompt optimization method is introduced to advance the diversity of LLMs' output; (3) Efficient search strategy: We design a presearch strategy and an EA evolutionary algorithm for the final efficient and effective discovery of heuristics. Extensive experiments across a wide range of datasets demonstrate that AutoModSAT achieves 50% performance improvement over the baseline solver and achieves 30% superiority against the state-of-the-art (SOTA) solvers. Moreover, AutoModSAT attains a 20% speedup on average compared to parameter-tuned alternatives of the SOTA solvers, showcasing the enhanced capability in handling complex problem instances. This work bridges the gap between AI-driven heuristics discovery and mission-critical system optimization, and provides both methodological advancements and empirically validated results for next-generation complex solver development.

Problem

• Optimizing complex SAT solvers using Large Language Models
• Automating heuristic discovery without manual search constraints
• Enhancing solver performance and speed via AI-driven methods

Innovation

• LLM-friendly modularized SAT solver design
• Unsupervised automatic prompt optimization method
• Presearch and EA evolutionary algorithm strategy