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

2026-08-13

AI Summary

This work addresses the limited generality of traditional large neighborhood search methods, which rely on manually designed variable selection strategies. The authors propose a problem-agnostic automated pipeline that leverages large language models (LLMs) to generate unified weighted graphs from semantic prompts—where nodes represent decision variables and edges encode constraint relationships—to guide variable selection within the Structured Local Improvement Method (SLIM) framework. This approach requires no domain-specific knowledge and automatically extracts structural features to configure optimization algorithms for any MiniZinc problem. Evaluated on 20 MiniZinc Challenge instances, the method achieves an average win rate of 39.5%, substantially outperforming the best single algorithm configuration (19.3%); further ablation-based refinements improve this to 44.0%.

Abstract

Large neighborhood search normally selects a random subset of decision variables for iterative optimization. For efficiently solving different problems, researchers tend to design variable selection strategies by taking into account structural features from 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 framework (SLIM) in 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 39.5% average problem-weighted win rate against a one-shot Gurobi baseline, more than doubling the best single configuration (19.3%). Configuration and feature ablation boost the performance further to 44.0%, demonstrating that LLM-based semantic generation enables effective automated structure extraction and feature extraction for constraint optimization.

Problem

• large neighborhood search
• structure-based optimization
• constraint optimization
• problem-agnostic representation
• variable selection

Innovation

• LLM-guided graph generation
• structure-based local search
• problem-agnostic optimization
• constraint programming
• algorithm configuration