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EvoOptiGraph: Weakness-Driven Coevolution via Graph-Based Structural Generation for Optimization Modeling

NeurIPS 2026 · Large language models › Agents, code and math · approach: LLMs for optimization and heuristics · 0 citations (OpenAlex)

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Proposes EvoOptiGraph, a closed-loop framework where graph-based evolution of MILP instances and weakness-driven RLVR (GRPO) co-evolve with an 8B model (Qwen3-8B) for NL-to-optimization modeling.

Problem

Natural-language-to-optimization-modeling with LLMs suffers from narrow, structurally homogeneous training data and static data pipelines decoupled from model failures.

Approach

Represent each MILP as an attributed variable-constraint bipartite graph, apply validity-preserving crossover/mutation to generate structurally diverse instances, and use SHAP attributions from an XGBoost failure predictor over graph features as a weakness vector that steers further evolution and RLVR data generation in an iterative loop.

Key results

• EvoOptiGraph (8B) reaches 78.1% macro-average Pass@1 across six benchmarks, above DeepSeek-V3 (73.3%) and OptiMUS-v0.3 (70.1%).
• On MAMO ComplexLP it scores 69.4% vs 59.5% for ORLM (8B fine-tuned baseline).
• Generated data has 66.93% structural similarity to the 53 seed types vs 93.04% for OptMATH, indicating greater diversity.

Surprising findings

• An 8B model surpasses larger generalist models such as DeepSeek-V3 (671B) on macro-average accuracy.
• RL-only without SFT warm-up gives limited gains (63.4% avg), and SFT-only saturates or degrades in later rounds.

Limitations

• Limited to MILPs and the coverage of available seed generators.
• Verification becomes expensive for larger instances.
• Weakness vector is a practical prioritization signal, not a causal explanation.

Experimental setup

Datasets: OptMATH seed generators (53 families) NL4Opt MAMO NLP4LP ComplexOR IndustryOR

Benchmarks: NL4Opt MAMO EasyLP MAMO ComplexLP NLP4LP ComplexOR IndustryOR

Metrics: Pass@1 accuracy structural similarity (GenBench-MILP)

Baselines: GPT-4o DeepSeek-V3 Qwen3-32B Qwen2.5-72B-Instruct OptiMUS-v0.3 Chain-of-Thought Chain-of-Experts ORLM LLMOPT OptMATH

Builds on: GRPO OptMATH MILP-Evolve GenBench-MILP

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• Evolution Fine-Tuning: Learning to Discover Across 371 Optimization Tasks (NeurIPS 2026 · similarity 0.89)
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• $\texttt{STRCMP}$: Integrating Graph Structural Priors with Language Models for Combinatorial Optimization (NeurIPS 2025 · similarity 0.87)
• Structure-Aware Cooperative Ensemble Evolutionary Optimization on Combinatorial Problems with Multimodal Large Language Models (NeurIPS 2025 · similarity 0.87)
• ThetaEvolve: Test-time Learning on Open Problems (ICML 2026 · similarity 0.87)
• ReEvo: Large Language Models as Hyper-Heuristics with Reflective Evolution (NeurIPS 2024 · similarity 0.87)