IR2Solve: Structured Intermediate Representations for Cost-Efficient Optimization Autoformulation

• URL: http://arxiv.org/abs/2608.02641v1
• Date: Fri, 31 Jul 2026 13:36:26 GMT
• Title: IR2Solve: Structured Intermediate Representations for Cost-Efficient Optimization Autoformulation
• Abstract summary: Large language models (LLMs) can translate natural-language optimization problems into solver-ready formulations, but direct code generation is brittle.<n>We present IR2, an intermediate-representation-first autoformulation pipeline that uses a single semantic call to produce a schema-constrained ModelIR.<n>A concrete scalar-constraint convention represents finite per-index constraint families as individual entries, reducing free-index and implicit-quantification errors.
• Score: 15.520617657780578
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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