Retrieval-Assisted Instantiation of Natural-Language Optimization Problems

Abstract Many engineering optimization problems are first described in natural language and only later translated into formal mathematical models, but this translation remains difficult to automate reliably. Rather than targeting full solver-ready generation, this paper studies a narrower intermediate task: retrieval-assisted optimization problem instantiation, viewed as a knowledge-processing problem of grounding natural-language numeric evidence into a structured, typed optimization schema. The contribution is a transparent and reproducible framework that first retrieves the most compatible optimization schema from a fixed catalog and then deterministically instantiates that schema's scalar parameters from numeric evidence in the text, combining lexical schema retrieval, rule-based numeric extraction, coarse type inference, and deterministic compatibility-based slot assignment. We evaluate the framework on the NLP4LP benchmark of natural-language optimization problems, together with complementary structural and solver-backed validation subsets. Schema retrieval is already strong across query variants, with term frequency--inverse document frequency (TF--IDF) retrieval achieving the best average top-1 schema accuracy (Schema R@1 \((=0.9094)\) on original-text queries). The strongest non-oracle method reaches an InstantiationReady score of \((0.5287)\), while an oracle control with perfect schema retrieval reaches only \((0.5680)\): this modest oracle gain shows that the main remaining bottleneck is downstream number-to-slot grounding rather than schema retrieval itself. A numeric-type compatibility ablation supports this conclusion: correcting how float-valued slots are matched to extracted numeric mentions yields large improvements in type consistency and query-level readiness. Restricted structural and solver-backed subset studies further suggest downstream optimization-oriented usefulness on compatible cases, without claiming benchmark-wide solver readiness.