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

arXiv: https://arxiv.org/abs/2606.26578 · HTML: https://mlsanity.com/paper/2606.26578/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 29 of its 51 references that are in the map.
- First posted on arXiv 25 Jun 2026.

## Builds on (most cited first, 29 of 29)

- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [LlamaFactory: Unified Efficient Fine-Tuning of 100+ Language Models](https://mlsanity.com/paper/2403.13372/) (2024)
- [Tulu 3: Pushing Frontiers in Open Language Model Post-Training](https://mlsanity.com/paper/2411.15124/) (2024)
- [Exact Combinatorial Optimization with Graph Convolutional Neural Networks](https://mlsanity.com/paper/1906.01629/) (2019)
- [ReEvo: Large Language Models as Hyper-Heuristics with Reflective Evolution](https://mlsanity.com/paper/2402.01145/) (2024)
- [Evolution of Heuristics: Towards Efficient Automatic Algorithm Design Using Large Language Model](https://mlsanity.com/paper/2401.02051/) (2024)
- [NL4Opt Competition: Formulating Optimization Problems Based on Their Natural Language Descriptions](https://mlsanity.com/paper/2303.08233/) (2023)
- [ORLM: A Customizable Framework in Training Large Models for Automated Optimization Modeling](https://mlsanity.com/paper/2405.17743/) (2024)
- [OptiMUS: Scalable Optimization Modeling with (MI)LP Solvers and Large Language Models](https://mlsanity.com/paper/2402.10172/) (2024)
- [Monte Carlo Tree Search for Comprehensive Exploration in LLM-Based Automatic Heuristic Design](https://mlsanity.com/paper/2501.08603/) (2025)
- [LLMOPT: Learning to Define and Solve General Optimization Problems from Scratch](https://mlsanity.com/paper/2410.13213/) (2024)
- [OptMATH: A Scalable Bidirectional Data Synthesis Framework for Optimization Modeling](https://mlsanity.com/paper/2502.11102/) (2025)
- [Autoformulation of Mathematical Optimization Models Using LLMs](https://mlsanity.com/paper/2411.01679/) (2024)
- [Solver-Informed RL: Grounding Large Language Models for Authentic Optimization Modeling](https://mlsanity.com/paper/2505.11792/) (2025)
- [VLA-R1: Enhancing Reasoning in Vision-Language-Action Models](https://mlsanity.com/paper/2510.01623/) (2025)
- [Towards Foundation Models for Mixed Integer Linear Programming](https://mlsanity.com/paper/2410.08288/) (2024)
- [A Survey of Optimization Modeling Meets LLMs: Progress and Future Directions](https://mlsanity.com/paper/2508.10047/) (2025)
- [Process Supervision-Guided Policy Optimization for Code Generation](https://mlsanity.com/paper/2410.17621/) (2024)
- [Retrieval-Augmented Process Reward Model for Generalizable Mathematical Reasoning](https://mlsanity.com/paper/2502.14361/) (2025)
- [A Deep Instance Generative Framework for MILP Solvers Under Limited Data Availability](https://mlsanity.com/paper/2310.02807/) (2023)
- [MILP-StuDio: MILP Instance Generation via Block Structure Decomposition](https://mlsanity.com/paper/2410.22806/) (2024)
- [Constructing Industrial-Scale Optimization Modeling Benchmark](https://mlsanity.com/paper/2602.10450/) (2026)
- [SAC-Opt: Semantic Anchors for Iterative Correction in Optimization Modeling](https://mlsanity.com/paper/2510.05115/) (2025)
- [From Verifiable Dot to Reward Chain: Harnessing Verifiable Reference-based Rewards for Reinforcement Learning of Open-ended Generation](https://mlsanity.com/paper/2601.18533/) (2026)
- [Are Your Generated Instances Truly Useful? GenBench-MILP: A Benchmark Suite for MILP Instance Generation](https://mlsanity.com/paper/2505.24779/) (2025)

## Abstract (arXiv)

Automating optimization modeling from natural language with large language models (LLMs) faces two key challenges. First, training corpora lack structural diversity. Second, data generation pipelines remain static and decoupled from model learning. To address these challenges, we propose EvoOptiGraph, a novel framework where data and model co-evolve, driven by model weaknesses. EvoOptiGraph represents each mixed-integer linear program (MILP) as an attributed bipartite graph and applies validity-preserving evolutionary operators to generate structurally diverse instances. The evolved graphs are converted into solver code and natural language via deterministic compilation and verified back-translation. Training proceeds in two stages: supervised fine-tuning (SFT) on an initial dataset, followed by reinforcement learning with verifiable rewards (RLVR), where graph-derived weakness signals guide the generation of new instances targeting the model's failures. This forms a closed loop that continuously updates the training distribution. Empirical results on six public datasets show that EvoOptiGraph significantly outperforms larger generalist models, agentic methods, and specialized baselines in accuracy, executability, and generalization. These results demonstrate that targeted data-model coevolution is an effective strategy for improving LLMs on optimization modeling tasks.