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arXiv · 2609.13945

SAILOR: Solver-Assisted Interactive LLM-based Optimization Recovery

Shaghayegh Sadeghi·Stephen L. Smith·David C. Del Rey Fern'andez
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Abstract

Natural-language descriptions of optimization problems may be incomplete or vague about numerical information that a solver requires, including costs, capacities, demands, bounds, and penalties. A language model can translate the description into code, but when a required value is absent it must either stop or guess. We present SAILOR, a proof-of-concept system that detects such unsupported numerical choices, asks the user targeted follow-up questions, and updates the optimization model before returning a solution. Questions are prioritized using uncertainty and solver-derived estimates of how strongly each missing value affects the current model. We evaluate the pipeline on 1,723 instances from seven masked benchmarks using an idealized simulator that returns ground-truth values. Exact objective-value agreement ranges from 27.0% to 87.6% across datasets, with 1.4--5.7 questions per instance on average. These results establish feasibility under controlled branch-and-reveal feedback; they do not measure performance with human users or general structural model repair. Code is available at: https://github.com/sshaghayeghs/SAILOR.

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Shaghayegh Sadeghi, Stephen L. Smith, David C. Del Rey Fern'andez. 2026-09-12. SAILOR: Solver-Assisted Interactive LLM-based Optimization Recovery. https://arxiv.org/abs/2609.13945

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