Instance Evidence Matters: Tool-Integrated LLM Reasoning for Data-Informed Optimization Formulation

Large language models (LLMs) for optimization modeling typically treat instance data as values to be bound to a formulation inferred from problem descriptions. Yet instance data can play a more fundamental role: when interpreted under problem semantics, their structural and numerical properties become instance evidence that can directly inform formulation decisions, affecting both model correctness and solver efficiency. We introduce **InForm** (**IN**stance-informed **FORM**ulation), a tool-integrated framework that progressively acquires and uses such evidence during optimization formulation. Rather than analyzing the entire instance upfront, InForm interleaves formulation reasoning with targeted tool calls, acquiring decision-relevant evidence before the corresponding formulation decisions are finalized. Its formulation-oriented tools transform raw instance data into mathematically meaningful evidence, while experience retrieval provides reusable guidance for translating recurring evidence patterns into local formulation decisions. Across four large-scale OR benchmarks, InForm achieves 84.1% average formulation accuracy, outperforming the strongest baseline by 6.8 percentage points, and improving 16.2 percentage points on MIPLIB-NL against base LLM. InForm also yields 1.07$\times$–2.18$\times$ solver-time improvements on commonly correct instances. These results show that instance data should not merely instantiate an optimization model: the evidence they reveal can actively shape how the model is formulated.