ReLoop: Structured Modeling and Behavioral Verification for Reliable LLM-Based Optimization

Abstract:Large language models (LLMs) can translate natural language into optimization code, but silent failures pose a critical risk: code that executes and returns solver-feasible solutions may encode semantically incorrect formulations---a feasibility--correctness gap reaching 90 percentage points on compositional problems. We introduce ReLoop, which addresses this gap through two complementary mechanisms. Structured generation decomposes code production into a four-stage reasoning chain (understand, formalize, synthesize, verify), preventing formulation errors at their source. Behavioral verification detects errors that survive generation by testing whether the formulation responds correctly to solver-based parameter perturbation---an external semantic signal that bypasses LLM self-review and requires no ground truth. The two mechanisms are complementary by error structure: structured generation drives the largest gains on compositional problems (+8.5pp accuracy on RetailOpt-190 with Claude Opus 4.6), while behavioral verification dominates on localized defects +4.4pp on MAMO-ComplexLP, its largest contribution across benchmarks). Combined with diagnostic execution recovery, ReLoop reaches 100% executable code on Claude Opus 4.6 and consistently improves accuracy on chat-tuned foundation models across three benchmarks; we further identify a known limitation of narrowly-tuned SFT models, whose learned output formats are brittle to chain-of-thought prompts---an interaction we document and analyze. We release RetailOpt-190, 190 compositional retail optimization scenarios targeting the multi-constraint interactions where LLMs most frequently fail.

Software Engineering (cs.SE); Artificial Intelligence (cs.AI); Machine Learning (cs.LG); Optimization and Control (math.OC)

arXiv:2602.15983 [cs.SE]

(or arXiv:2602.15983v3 [cs.SE] for this version)

https://doi.org/10.48550/arXiv.2602.15983 Focus to learn more arXiv-issued DOI via DataCite

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