Strategy-Aware Optimization Modeling with Reasoning LLMs

Abstract: LLMs can generate syntactically valid optimization programs, yet often struggle to reliably choose an effective modeling strategy, leading to incorrect formulations and inefficient solver behavior. We propose SAGE, a strategy-aware framework that makes Modeling Strategy explicit in both data construction and post-training. SAGE builds a solver-verified multi-strategy dataset and trains a student model with supervised fine-tuning followed by Segment-Weighted GRPO using a composite reward over format compliance, correctness, and solver efficiency. Across eight benchmarks spanning synthetic and real-world settings, SAGE improves average pass@1 from 72.7 to 80.3 over the strongest open-source baseline. With multiple generations, SAGE discovers more distinct correct formulations and improves component-level diversity at pass@16 by 19-29%. At the largest scale, SAGE produces more compact constraint systems with 14.2% fewer constraints than the baseline, consistent with solver-efficient modeling. Overall, these results show that making Modeling Strategy explicit improves automated optimization modeling. Code is available at https://github.com/rachhhhing/SAGE.