LLM-Guided Graph Generation for Structure-Based Local Improvement Methods
Researchers built an automatic pipeline that prompts an LLM to produce a graph generator mapping MiniZinc problem instances to uniform weighted graphs, where nodes represent decision variables and edges represent constraint relationships. These graphs guide a structure-based local improvement framework (SLIM) in variable selection and configuration selection. Evaluation on 20 MiniZinc competition problems showed algorithm selection achieves a 39.5% average problem-weighted win rate against a one-shot Gurobi baseline, more than doubling the best single configuration.
A new method uses LLMs to automatically generate problem-agnostic graph representations for combinatorial optimization problems in MiniZinc format. The generated graphs capture variable-constraint relationships and enable a structure-based local improvement framework (SLIM) to perform variable selection and configuration selection. In experiments across 20 MiniZinc competition problems, the approach achieved a 39.5% average problem-weighted win rate against a one-shot Gurobi baseline, more than doubling the best single configuration.
The pipeline leverages LLM prompting with semantic guidelines to generate a graph generator, producing uniform weighted graphs for any instance of a problem type. This enables extraction of shared graph features for configuration selection, suggesting a novel use of LLMs for automated representation learning in combinatorial optimization. The reported win rate indicates the graph-based variable selection can significantly outperform a strong mathematical programming solver baseline.
This research demonstrates a practical path for applying LLMs to improve solver performance on constraint programming and optimization problems without domain-specific feature engineering. The MiniZinc format compatibility suggests potential integration with existing modeling tools and solvers, which could lower the barrier for using advanced local improvement methods in industrial scheduling, routing, and resource allocation.
For enterprises using combinatorial optimization, this approach could reduce the need for manual tuning of solver parameters and variable selection heuristics, potentially improving solution quality or reducing solve times. The problem-agnostic nature may enable a single tool to handle diverse optimization tasks, lowering development and maintenance costs.
Next observable signals include follow-up papers applying the pipeline to additional problem classes, open-source release of the graph generator and SLIM framework, and comparisons with other LLM-based optimization approaches. If the method generalizes, it may influence solver configuration tools and hybrid LLM-solver systems.