EvoOptiGraph: Weakness-Driven Coevolution via Graph-Based Structural Generation for Optimization Modeling
For researchers and practitioners automating optimization modeling, this work provides a closed-loop coevolution framework that demonstrably improves LLM performance on MILP tasks.
EvoOptiGraph addresses the lack of structural diversity and static data generation in LLM-based optimization modeling by co-evolving data and model via graph-based evolutionary operators and weakness-driven reinforcement learning. It achieves significant improvements in accuracy, executability, and generalization over larger models and baselines on six public datasets.
Automating optimization modeling from natural language with large language models (LLMs) faces two key challenges. First, training corpora lack structural diversity. Second, data generation pipelines remain static and decoupled from model learning. To address these challenges, we propose EvoOptiGraph, a novel framework where data and model co-evolve, driven by model weaknesses. EvoOptiGraph represents each mixed-integer linear program (MILP) as an attributed bipartite graph and applies validity-preserving evolutionary operators to generate structurally diverse instances. The evolved graphs are converted into solver code and natural language via deterministic compilation and verified back-translation. Training proceeds in two stages: supervised fine-tuning (SFT) on an initial dataset, followed by reinforcement learning with verifiable rewards (RLVR), where graph-derived weakness signals guide the generation of new instances targeting the model's failures. This forms a closed loop that continuously updates the training distribution. Empirical results on six public datasets show that EvoOptiGraph significantly outperforms larger generalist models, agentic methods, and specialized baselines in accuracy, executability, and generalization. These results demonstrate that targeted data-model coevolution is an effective strategy for improving LLMs on optimization modeling tasks.