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

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. Code and benchmark will be released upon acceptance.