LLMs Synthesize Feature Extractors for Algorithm Selection

Selecting the optimal algorithm for constraint satisfaction problems often hinges on extracting features that accurately represent the problem's underlying structure. Traditionally, designing these feature extractors demands significant domain expertise and becomes a bottleneck when new problem classes emerge. A novel automated method leverages Large Language Models (LLMs) to overcome this challenge. This approach employs an LLM agent within an iterative check-fix-verify loop to synthesize executable Python scripts. These scripts function as interpretable, problem-specific feature extractors. Given a high-level problem description and an instance, the LLM agent generates code that constructs a typed graph representation and computes structural properties such as graph density, variable clustering, and constraint tightness. Evaluations across three combinatorial problems (vehicle routing, car sequencing, fixed-length error-correcting codes) demonstrated the effectiveness of these synthesized extractors. They consistently led to algorithm selectors that outperformed both expert-curated features and advanced transformer-based variants, achieving significant accuracy gains. The key benefit is the automation of a previously manual, expert-intensive process, while maintaining inspectability of the generated features.