What Is MIPLIB, and Why Do Solvers Compete on It?

A mixed-integer program (MIP) is an optimization problem where you’re minimizing or maximizing something subject to constraints, and at least some of the variables have to be whole numbers — you can’t assign 2.3 trucks to a delivery route or open 1.7 of a factory. That integer requirement is what makes MIPs hard: relaxing it away turns a problem into ordinary linear programming, solvable efficiently, but putting it back makes the problem NP-hard in general, with no known algorithm that solves every instance quickly.

Why a shared benchmark matters

Every commercial and open-source MIP solver — Gurobi, CPLEX, SCIP, HiGHS, and others — claims to be fast. Without a shared, fixed set of test problems, that claim is unfalsifiable: a vendor could always benchmark on instances chosen to flatter their own solver. MIPLIB exists to close that gap. Maintained by a research collaboration centered at Zuse Institute Berlin, it’s a curated, versioned library of real-world and synthetic MIP instances — production scheduling, network design, vehicle routing, and more — with a published, independently checkable optimal (or best known) objective value for each one.

What “optimal” actually means here

MIPLIB’s official solution catalog marks each instance with a status: =opt= means a matching lower bound and feasible solution have been found, so the objective is proven optimal with no gap remaining; =best= means only the best feasible solution found so far is known, with no proof that a better one doesn’t exist. The Registry only publishes =opt= instances as PROVEN records — each one carries a matching LOWER_BOUND and UPPER_BOUND Claim that meet at the same value, the same closed-frontier pattern used everywhere else on the site.

What’s in the Registry today

382 MIPLIB v36 instances are published as individual Limits, each citing the official MIPLIB solution catalog as evidence. A sample: 30n20b8, a real scheduling-style instance, and wachplan, whose proven optimal objective happens to be negative. Browse the full set under Computing, subcategory “Mixed-integer optimization / MIPLIB 2017.”

Why it’s here

A MIPLIB optimal objective is exactly the kind of fact this Registry exists to track: a precise, independently verifiable number with a real proof behind it, not a vendor’s marketing claim about how fast their solver runs.