Models Can Model, But Can't Bind: Structured Grounding in Text-to-Optimization

Optimization modeling translates real decision-making problems into mathematical optimization models and solver-executable implementations. Although language models are increasingly used to generate optimization formulations and solver code, existing benchmarks are almost entirely text-only. This omits many optimization-modeling tasks that arise in operational practice, where requirements are described in text but instance information is conveyed through visual artifacts such as tables, graphs, maps, schedules, and dashboards. We introduce multimodal optimization modeling, a benchmark setting in which models must construct both a mathematical formulation and executable solver code from a text-and-visual problem specification. To evaluate this setting, we develop a solver-grounded framework that generates structured optimization instances, verifies each with an exact solver, and builds both the model-facing inputs and hidden reference files from the same verified source. We instantiate the framework as MM-OptBench, a benchmark of 780 solver-verified instances spanning 6 optimization families, 26 subcategories, and 3 structural difficulty levels. We evaluate 9 multimodal large language models (MLLMs), including 6 frontier general-purpose models and 3 math-specialized models, with aggregate, family-level, difficulty-level, and failure-mode analyses. The results show that the task remains far from solved: the best two models reach 52.1% and 51.3% pass@1, while on average across the six general-purpose MLLMs, pass@1 is 43.4% on easy instances and 15.9% on hard instances. All three math-specialized MLLMs solve 0/780 instances. Failure attribution shows that errors arise both when extracting instance data from text and visuals and when turning extracted data into solver-correct formulations and code. MM-OptBench provides a testbed for solver-grounded, decision-oriented multimodal intelligence.

Can a single LLM-based optimization system match specialized tools across fundamentally different domains? We show that when optimization problems are formulated as improving a text artifact evaluated by a scoring function, a single AI-based optimization system-supporting single-task search, multi-task search with cross-problem transfer, and generalization to unseen inputs-achieves state-of-the-art results across six diverse tasks. Our system discovers agent architectures that nearly triple Gemini Flash's ARC-AGI accuracy (32.5% to 89.5%), finds scheduling algorithms that cut cloud costs by 40%, generates CUDA kernels where 87% match or beat PyTorch, and outperforms AlphaEvolve's reported circle packing solution (n=26). Ablations across three domains reveal that actionable side information yields faster convergence and substantially higher final scores than score-only feedback, and that multi-task search outperforms independent optimization given equivalent per-problem budget through cross-task transfer, with benefits scaling with the number of related tasks. Together, we show for the first time that text optimization with LLM-based search is a general-purpose problem-solving paradigm, unifying tasks traditionally requiring domain-specific algorithms under a single framework. We open-source optimize_anything with support for multiple backends as part of the GEPA project at https://github.com/gepa-ai/gepa .

Optimization problems are pervasive in sectors from manufacturing and distribution to healthcare. However, most such problems are still solved heuristically by hand rather than optimally by state-of-the-art solvers because the expertise required to formulate and solve these problems limits the widespread adoption of optimization tools and techniques. We introduce a Large Language Model (LLM)-based system designed to formulate and solve (mixed integer) linear programming problems from their natural language descriptions. Our system can develop mathematical models, write and debug solver code, evaluate the generated solutions, and improve efficiency and correctness of its model and code based on these evaluations. OptiMUS is designed as a productivity tool for optimization practitioners who understand the problem domain and can describe it precisely, but seek to accelerate the modeling and implementation workflow. OptiMUS-0.3 utilizes a modular structure to process problems, allowing it to handle problems with long descriptions and complex data without long prompts. Experiments demonstrate that OptiMUS-0.3 outperforms direct-prompting baselines by over 43% on easy and 18% on hard instances. It remains competitive with fine-tuned specialist models on benchmark problems, and outperforms them on real-world case studies (28.6% vs. 0%) where fine-tuned models fail to generalize. Ablation studies show that modular architecture with error correction is central to these gains. A key finding is that system architecture is a stronger driver of performance than model capability. Structured decomposition with targeted error correction enables weaker models to match stronger models under naive prompting, and remains competitive with fine-tuned specialist models without retraining costs.