An LLM Evolved Faster Math for Hard Planning Problems

Researchers used a large language model to evolve new mathematical formulations of mixed-integer programming problems, the optimization math behind routing, scheduling, and production planning. The resulting formulations solved the same problems up to 5.5x faster than expert-written versions on benchmark problems, according to a new arXiv preprint.

The system, called FormuEvo, treats the math model handed to a solver as something to be searched, not written in one shot. The LLM proposes variations; the solver, the software that actually crunches a formulation, times them; the fastest candidates are kept and refined, with fine-grained solver statistics acting as "verbal gradients" that point to the slowest parts of each model. A separate structured memory module abstracts successful patterns so they can be applied to new, unseen problems and used to bootstrap smaller LLMs.

The claim is not that the LLM replaces operations researchers. It is that the formulation itself can be improved iteratively, and that the lessons transfer. Across the paper's benchmark suite, FormuEvo outperformed both expert-designed formulations and earlier LLM-based approaches.

What remains open: the 5.5x speedup is the paper's best case on its own problem set, and the preprint is not yet peer-reviewed. Production deployment at logistics or planning companies is not shown.