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

2026-06-24

AI Summary

This work addresses the limitations of current approaches to automatic translation from natural language to optimization models, which suffer from structurally homogeneous training data and a disconnect between data generation and model learning. The authors propose EvoOptiGraph, a novel framework that introduces, for the first time, a graph-based, weakness-driven co-evolutionary mechanism. It represents mixed-integer linear programming problems as attributed bipartite graphs and employs validity-preserving evolutionary operators to generate structurally diverse instances. By integrating supervised fine-tuning with reinforcement learning via verifiable rewards (RLVR), the framework establishes a closed-loop feedback system between data generation and model training. Evaluated on six public datasets, EvoOptiGraph significantly outperforms larger general-purpose models, agent-based methods, and specialized baselines in terms of accuracy, executability, and generalization capability.

Abstract

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.

Problem

• optimization modeling
• structural diversity
• data generation
• model learning
• large language models

Innovation

• coevolution
• graph-based generation
• weakness-driven learning
• MILP modeling
• reinforcement learning with verifiable rewards