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

Official implementation for:

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

Junbo Jacob Lian, Yujun Sun, Huiling Chen, Chaoyu Zhang, Chung-Piaw Teo

arXiv preprint, 2026

Resource	Link
Paper	arXiv:2602.15983
RetailOpt-190 Dataset	Hugging Face · GitHub
ReLoop Code	GitHub

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TL;DR

LLMs can generate optimization code that executes perfectly but solves the wrong problem—silent failures. On compositional problems, we observe up to 91.1% solver-feasibility but only 0.5% correctness (a 90-point gap). ReLoop addresses this from two directions:

• Structured generation: a 4-stage reasoning chain (understand → formalize → synthesize → verify) that mirrors expert modeling practice
• Behavioral verification: solver-based perturbation testing that detects missing constraints and objective terms without ground truth

These two mechanisms are complementary: structured generation dominates on complex compositional problems, while behavioral verification is the largest single contributor on problems with localized defects. Together, ReLoop raises correctness from 22.6% to 31.1% and execution from 72.1% to 100.0% on the strongest model, with gains across five models, three paradigms (foundation, SFT, RL), and three benchmarks.

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Framework

Structured Generation decomposes code production into four stages executed in a single LLM call: (1) understand the problem, (2) formalize the mathematical model with explicit variable-type reasoning, (3) synthesize Gurobi code with data extraction, and (4) self-verify completeness. Behavioral Verification operates in two layers: L1 checks execution correctness with IIS-enhanced diagnostics (Fatal → regeneration); L2 tests constraint presence (CPT) and objective completeness (OPT) via solver-based perturbation (Warning/Pass). Diagnosis-Guided Repair targets only high-confidence issues with regression rollback protection.

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Main Results

RetailOpt-190 (pass@1)

Type	Model	Exec%			Acc% (ε=10⁻⁴)			Acc% (ε=10⁻²)
		Base	CoT	ReLoop	Base	CoT	ReLoop	Base	CoT	ReLoop
Foundation	Claude Opus 4.6	72.1	93.7	100.0	22.6	31.1	31.1	26.8	34.7	35.3
Foundation	DeepSeek-V3.2	91.1	53.2	97.4	0.5	3.7	5.8	3.7	5.8	11.1
Foundation	Qwen3-32B	0.0	0.0	2.1	0.0	0.0	0.0	0.0	0.0	0.0
Offline SFT	OptMATH-Qwen2.5-32B	2.6	2.6	17.9	0.0	0.0	0.0	0.0	0.0	0.5
Online RL	SIRL-Qwen2.5-32B	0.0	0.0	1.6	0.0	0.0	0.0	0.0	0.0	0.0

Cross-Benchmark Generalization (Acc%, ε=10⁻⁶)

Type	Model	MAMO-ComplexLP			IndustryOR
		Base	CoT	+ReLoop	Base	CoT	+ReLoop
Foundation	Claude Opus 4.6	70.4	73.9	79.8	66.0	66.0	68.0
Foundation	DeepSeek-V3.2	60.1	59.6	62.6	50.0	54.0	62.0
Foundation	Qwen3-32B	40.4	37.4	46.3	43.0	43.0	46.0
Offline SFT	OptMATH-Qwen2.5-32B	56.2	30.0	31.0	34.0	31.0	34.0
Online RL	SIRL-Qwen2.5-32B	53.2	46.8	54.2	40.0	40.0	43.0

Ablation (pass@1)

Config	Claude (RetailOpt)			DeepSeek (RetailOpt)			Claude (MAMO)		DeepSeek (MAMO)
	Exec	ε=10⁻⁴	ε=10⁻²	Exec	ε=10⁻⁴	ε=10⁻²	Exec	Acc	Exec	Acc
Direct	72.1	22.6	26.8	91.1	0.5	3.7	94.1	70.4	93.6	60.1
+CoT	93.7	31.1	34.7	53.2	3.7	5.8	95.6	73.9	87.7	59.6
+CoT+L1	99.5	31.1	35.3	97.4	5.8	10.5	98.0	75.4	88.7	60.6
+CoT+L1+L2	100.0	31.1	35.3	97.4	5.8	11.1	98.0	79.8	88.7	62.6

CoT is the primary accuracy driver on RetailOpt (+8.5pp for Claude); L1 dominates execution recovery (+44.2pp for DeepSeek); L2 is the largest single accuracy contributor on MAMO (+4.4pp for Claude). See the paper for full analysis.

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Installation

git clone https://github.com/junbolian/ReLoop.git
cd ReLoop
pip install -r requirements.txt

Requirements: Python ≥ 3.8, Gurobi ≥ 11.0 (with valid license).

---

Quick Start

ReLoop uses the OpenAI-compatible API interface. Any provider works (OpenAI, Anthropic via proxy, vLLM, Ollama, etc.).

export OPENAI_API_KEY="your-api-key"
export OPENAI_BASE_URL="https://api.openai.com/v1"  # or your endpoint

# Full ReLoop pipeline (CoT + L1 + L2)
python run_ablation.py \
    -d data/RetailOpt-190.jsonl \
    -m gpt-4.1 \
    --enable-cpt \
    --workers 5 \
    -v

CLI Options

Flag	Default	Description
-d, --dataset	(required)	Path to dataset JSONL
-m, --model	gpt-4.1	Model name (OpenAI SDK format)
--enable-cpt	off	Enable L2 behavioral testing (CPT + OPT)
--no-cot	off	Direct generation baseline (skip CoT)
--no-verify	off	CoT-only baseline (skip verification)
--workers	20	Concurrent workers
--local	off	Local mode (default endpoint http://127.0.0.1:8000/v1)
--base-urls	—	Comma-separated endpoints for multi-GPU load balancing
-v	off	Verbose logging

Local Model Deployment

# Deploy a local model via vLLM
python scripts/deploy_local_llm.py \
    --model qwen3-32b \
    --backend vllm \
    --gpus 4,5,6,7 \
    --port 8000

# Run against local endpoint
python run_ablation.py \
    -d data/RetailOpt-190.jsonl \
    -m Qwen3-32B \
    --local --enable-cpt --workers 5 -v

Python API

from reloop import run_reloop

result = run_reloop(
    problem_description="...",
    data=data,
    llm_client=llm_client,
    verbose=True
)
print(f"Status: {result.final_report.status}")   # VERIFIED / WARNINGS / ERRORS / FAILED
print(f"Objective: {result.final_report.objective}")

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Datasets

Dataset	Instances	Avg Tokens	Tolerance	Source
RetailOpt-190	190	~2,900	10⁻⁴ / 10⁻²	Ours
MAMO-ComplexLP	203	~459	10⁻⁶	Huang et al., 2024
IndustryOR	100	~267	10⁻⁶	Huang et al., 2025

All datasets are included in data/ in JSONL format (one problem per line).

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Project Structure

ReLoop/
├── reloop/                        # Core package
│   ├── __init__.py                # Public API exports
│   ├── pipeline.py                # Full generate → verify → repair orchestration
│   ├── generation.py              # 4-stage structured code generation
│   ├── verification.py            # L1 execution + L2 behavioral testing (CPT/OPT)
│   ├── repair.py                  # Diagnosis-guided repair with regression guard
│   ├── repair_safety.py           # Safety guardrails for repair outputs
│   ├── executor.py                # Sandboxed execution with IIS/ray diagnostics
│   ├── experiment_runner.py       # Batch experiment runner
│   ├── param_utils.py             # Data-dict perturbation engine
│   ├── perturbation.py            # AST-based source-code perturbation (fallback)
│   ├── prompts.py                 # All LLM prompt templates
│   └── data_extraction.py         # NL → structured JSON extraction
├── data/                          # Benchmark datasets (JSONL)
├── fig/                           # Framework diagram
├── scripts/                       # Deployment & automation
│   ├── deploy_local_llm.py        # Launch vLLM / llama.cpp server
│   └── run_all_local_ablation.sh  # Batch ablation for local models
├── run_ablation.py                # Main experiment entry point
├── analyze_layers.py              # Per-layer contribution analysis
├── requirements.txt               # Core dependencies
├── requirements.local-inference.txt  # Optional: vLLM / llama.cpp
├── pyproject.toml                 # Project metadata
└── LICENSE                        # MIT

---

Citation

@misc{lian2026reloop,
      title={ReLoop: Structured Modeling and Behavioral Verification for Reliable LLM-Based Optimization},
      author={Junbo Jacob Lian and Yujun Sun and Huiling Chen and Chaoyu Zhang and Chung-Piaw Teo},
      year={2026},
      eprint={2602.15983},
      archivePrefix={arXiv},
      primaryClass={cs.SE},
      url={https://arxiv.org/abs/2602.15983},
}

License

MIT License. See LICENSE for details.

Acknowledgments

We thank the developers of Gurobi, MAMO, IndustryOR, OptMATH, and SIRL for making their code and data publicly available.