Learning Unified Graph and Language Representations for SMT Algorithm Selection

LLM-Guided Graph Generation for Structure-Based Local Improvement Methods

Large neighborhood search normally selects a random subset of decision variables for iterative optimization. To efficiently solve various problems, researchers tend to design variable selection strategies that take into account structural features across different domains. In this paper, we build an automatic pipeline that is problem-agnostic to all problems in the MiniZinc format. By prompting an LLM with our semantic guidelines, we guide the LLM to produce a graph generator that maps any instance of a problem type to a uniform weighted graph, where nodes represent decision variables and edges represent constraint relationships. These problem-agnostic graphs guide our structure-based local improvement (SLIM) framework for variable selection. Meanwhile, the weighted graph enables all problem instances to share the same generic graph representation, from which the same graph features can be extracted and used for configuration selection. We evaluated our pipeline on instances across 20 MiniZinc competition problems, finding that algorithm selection achieves a 39.6% average problem-weighted win rate against a one-shot Gurobi baseline, more than doubling the best single configuration (19.3%). A post-hoc configuration and a feature ablation indicate a headroom of up to 44.0%, demonstrating that LLM-based semantic generation enables effective automated structure and feature extraction for constraint optimization.

SAT Solver Selection: Move Beyond Handcrafted Features

Boolean Satisfiability (SAT) Problem is a cornerstone in computer science and artificial intelligence, underpinning numerous applications. Since no single SAT solver dominates all problem instances, SAT Solver Selection (SSS) leverages machine learning to dynamically choose the most effective algorithm. However, traditional SSS methods rely on handcrafted features, which are computationally expensive and require extensive domain expertise. To address this challenge, we propose an end-to-end approach for handcrafted Feature-Free SAT Solver Selection, called F2S3. This approach transforms problem instances into graph data, employing the Correlation Refinement Factor Graph to maintain higher-order structural properties and node relationships. The Dual-Proximity Graph Representation is then utilized to enhance the graph features and project them into low-dimensional vectors. Finally, the Sensitive-Associative Cascade Forest is applied to select the optimal SAT solver through classification. This method effectively captures the structural complexity of graph data, eliminates the need for handcrafted features, and improves feature representation in the low-dimensional space. Experiments conducted on the ASlib database dataset demonstrate that this method consistently outperforms state-of-the-art SSS approaches, achieving higher gap values while requiring less computation time compared to other manually computed features.

Poster: Neural Network-Based SAT Solver Selection Using Instance Features

OptGraph: Large Language Models Enhanced Evolutionary Optimization Via Graph Retrieval-Augmented Generation

OptGraph is the first optimization agentic workflow that introduces graph retrieval-augmented generation (GraphRAG) and first constructs reusable experience as a typed graph, capturing the relationships among modeling patterns, problem formalization, implementation details, and error corrections.

PALSAT: Deep Cooperation of Unit Propagation and Local Search in Incomplete SAT Solving

Evolution-Aware MSA Reasoning for Subsampling via Factor Graphs

Experiments show that AP-REASONER outperforms baseline subsamplers on structure-sensitive downstream tasks and enables controllable recovery of alternative protein conformations, highlighting the value of modeling MSA subsampling as a controllable optimization problem, where factor-graph reasoning offers an effective alternative to heuristic selection.