Large language models (LLMs) can translate natural-language optimization problems into solver-ready formulations, but direct code generation is brittle: schema, indexing, and semantic errors can cause compilation failures, infeasible models, or incorrect objectives, while iterative repair, search, and multi-agent workflows increase inference cost. We present IR2Solve, an intermediate-representation-first autoformulation pipeline that uses a single semantic LLM call to produce a schema-constrained ModelIR, followed by two deterministic stages: verification and IR-to-solver compilation. ModelIR explicitly represents sets, parameters, variables, objectives, and constraints using restricted Python-like expression strings. A concrete scalar-constraint convention represents finite per-index constraint families as individual entries, reducing free-index and implicit-quantification errors while simplifying downstream verification and compilation. Across six cleaned optimization benchmarks, IR2Solve achieves strong objective correctness and remains competitive with recent optimization-modeling systems. A controlled ablation on 153 IndustryOR and ComplexLP instances shows sequential gains from the structured IR interface, the scalar-constraint instruction, and deterministic verification. On a matched ten-instance cost panel, IR2Solve uses one semantic call per instance, whereas Chain-of-Experts and SAC-Opt use 8 and 39 calls per instance and consume 3.3 and 22.9 times the token volume of IR2Solve, respectively. These results show that structured intermediate representations, combined with deterministic post-generation processing, provide a practical accuracy-cost trade-off for LLM-based optimization autoformulation.
Large language models (LLMs) increasingly translate natural-language optimization problems into executable solver code. Yet for constraint-dense operations research (OR) problems, existing data-filtering and training pipelines largely rely on objective-equivalence signals such as differential testing and answer agreement, which a program can pass while adding spurious constraints or silently omitting required ones, whenever those constraints are non-binding on the tested instance. We propose constraint injection, which uses feasible probes to expose spurious over-constraint and one-constraint-violating probes to reveal silent constraint omission. Combined with differential testing, it forms a dual verifier. We instantiate and evaluate it on vehicle routing problems (VRPs), a representative constraint-dense combinatorial optimization testbed with coupled operational constraints. We develop VRPCoder, an 8B end-to-end model that translates natural-language VRP scenarios into Gurobi scripts, together with an expert-verified VRP benchmark suite covering 21 variants. The verifier is reused as a rejection-sampling filter during data synthesis and as a per-rollout reward in group relative policy optimization (GRPO). Across four VRP benchmarks, VRPCoder-GRPO reaches 93\% average Pass@1, outperforms Gemini-3.1-Pro Preview on three benchmarks, exceeds Claude-Sonnet-4.5 by 28 average points, and surpasses prior OR-LLMs by 78 average points.