MM-OptBench: A Solver-Grounded Benchmark for Multimodal Optimization Modeling

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 for this capability are almost entirely text-only. This omits many optimization-modeling tasks that arise in operational practice, where requirements are described in text but essential instance information is often conveyed through visual artifacts such as tables, graphs, maps, schedules, and planning dashboards. We introduce \emph{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 instance with an exact solver, and builds both the model-facing inputs and the 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 then 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 concrete testbed for solver-grounded, decision-oriented multimodal intelligence.