# LLM-Based Optimization Modeling

Translating natural-language optimization problems into solver code hinges on the quality of template retrieval. Structured retrieval methods had relied on traversal rules that were fixed or decided by a language model at inference time, so retrieval could not improve from past successes and failures. COMPASS organizes the template library as a directed acyclic graph and uses a deep Q-network to learn a reusable traversal policy from template-level judgments and solver execution feedback, scoring newly inserted templates in a shared semantic space; across several LLM backbones and optimization-modeling benchmarks it consistently beats heuristic structured retrieval, with the largest gains on complex and mixed-category problems.

Translating natural-language optimization problems into solver code hinges on the quality of template retrieval. Structured retrieval methods had relied on traversal rules that were fixed or decided by a language model at inference time, so retrieval could not improve from past successes and failures. COMPASS organizes the template library as a directed acyclic graph and uses a deep Q-network to learn a reusable traversal policy from template-level judgments and solver execution feedback, scoring newly inserted templates in a shared semantic space; across several LLM backbones and optimization-modeling benchmarks it consistently beats heuristic structured retrieval, with the largest gains on complex and mixed-category problems.