AutoHOPT: From Natural Language to Model-Conditioned Metaheuristic Search

Existing language-to-optimization systems primarily treat mathematical models as inputs to solvers. Yet the same constraint structure that defines feasibility can also guide how solutions are constructed and improved. We introduce AutoHOpt, a framework that turns natural-language requirements into modelconditioned metaheuristic search. AutoHOpt first recovers a source-reviewed executable model, OPTSPEC, and then uses its decisions and constraints to generate SEARCHIR, a task-specific search program. The accepted model remains fixed while execution feedback refines initialization and neighborhood-repair operators, which run within adaptive large neighborhood search without per-iteration LLM calls. Across ten external benchmarks, AutoHOpt achieves the highest mean zerogap success on eight. On IndustryOR and MIPLIB-NL, it reaches 83.5% and 78.8%, exceeding the strongest baseline by 20.2 and 9.5 percentage points, respectively. Ablations and common-budget controls demonstrate the contributions of modeling feedback and model-conditioned search. These results establish executable models as an effective interface between natural-language problem understanding and automated search design.