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This paper introduces Execution-Verified Optimization Modeling (EVOM), a reinforcement learning framework that uses a mathematical programming solver as a deterministic verifier to train LLMs for optimization modeling. EVOM generates solver-specific code from natural language problems, executes it, and converts the execution outcomes into scalar rewards for training via GRPO and DAPO, eliminating the need for process-level supervision. Results across multiple datasets and solvers (Gurobi, OR-Tools, COPT) demonstrate that EVOM matches or exceeds the performance of process-supervised SFT, enables zero-shot solver transfer, and facilitates low-cost solver adaptation.
Ditch the costly process supervision: EVOM trains LLMs to generate optimization code by treating solvers as deterministic reward functions, enabling zero-shot solver transfer and efficient adaptation.
Automating optimization modeling with LLMs is a promising path toward scalable decision intelligence, but existing approaches either rely on agentic pipelines built on closed-source LLMs with high inference latency, or fine-tune smaller LLMs using costly process supervision that often overfits to a single solver API. Inspired by reinforcement learning with verifiable rewards, we propose Execution-Verified Optimization Modeling (EVOM), an execution-verified learning framework that treats a mathematical programming solver as a deterministic, interactive verifier. Given a natural-language problem and a target solver, EVOM generates solver-specific code, executes it in a sandboxed harness, and converts execution outcomes into scalar rewards, optimized with GRPO and DAPO in a closed-loop generate-execute-feedback-update process. This outcome-only formulation removes the need for process-level supervision, and enables cross-solver generalization by switching the verification environment rather than reconstructing solver-specific datasets. Experiments on NL4OPT, MAMO, IndustryOR, and OptiBench across Gurobi, OR-Tools, and COPT show that EVOM matches or outperforms process-supervised SFT, supports zero-shot solver transfer, and achieves effective low-cost solver adaptation by continuing training under the target solver backend.
