Retrieval-Assisted Instantiation of Natural-Language Optimization Problems

Optimization problems are often described first in natural language and only later translated into formal mathematical models, yet 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. Given a natural-language problem description, the proposed framework first retrieves the most compatible optimization schema from a fixed catalog and then deterministically instantiates the scalar parameters of that schema from textual numeric evidence. The pipeline is transparent and reproducible, combining lexical schema retrieval with rule-based numeric mention extraction, coarse type inference, and deterministic compatibility-based slot assignment.We evaluate the approach on the NLP4LP benchmark using three deterministic lexical retrievers: BM25, TF–IDF, and latent semantic analysis. Schema retrieval is already strong across query variants, with TF–IDF achieving the best average top-1 schema accuracy. The measured downstream benchmark shows that deterministic retrieval-assisted grounding recovers a substantial fraction of usable scalar structure on the original queries, and that the strongest non-oracle methods achieve InstantiationReady on more than half of the test instances. At the same time, the oracle condition yields only moderate gains over the best retrieval-based setting, indicating that the main remaining bottleneck is not schema retrieval itself, but downstream number-to-slot grounding. A measured pre-fix versus post-fix ablation confirms this interpretation: correcting the numeric type-handling logic, especially for float-valued slots, produces large improvements in TypeMatch and InstantiationReady.These findings position retrieval-assisted schema grounding and scalar parameter instantiation as useful intermediate expert-support capabilities between natural-language problem descriptions and fully automated optimization modeling.