FROM-ROUTE: From Operations Research Problems To MIP Formulations For Better Solver Performance

Formulating real-world operations research problems as mixed-integer programs (MIPs) requires choices of variables, constraints, and representations that shape solver performance. We present FROM-ROUTE, a framework for enhancing LLM routing among MIP formulations to improve solution performance within a fixed program budget. Deterministic analysis connects the original problem's structure and numerical data to three natural-language mechanism cards, supporting an ordered selection from an existing formulation-expert library. Multicommodity network design is the primary study of routing mechanisms; vertex coloring and resource-constrained project scheduling explore cross-domain applicability through domain-specific adapters. On 2,335 instances evaluated through independently validated trajectories, mean normalized primal integral is 57.0%, 14.6%, and 3.6% lower than that of the best fixed expert in each respective domain, alongside more validated model completions. Knowledge comparisons favor instance-conditioned cards over absent or generic mechanism context; restricted-completion relay is explored only for network design. On network design and coloring, FROM-ROUTE also improves solution metrics over direct and expert-guided modeling-kernel generation systems, using fewer provider-reported tokens in the calls producing retained decisions or code. These are descriptive comparisons: the evaluation corpora informed method development, and generation systems use different model and inference configurations.