Certifying MIP-based Presolve Reductions for 0-1 Integer Linear Programs

Alexander Hoen, Andy Oertel, Ambros Gleixner, Jakob Nordström
21st International Conference on the Integration of Constraint Programming, Artificial Intelligence, and Operations Research (CPAIOR 2024), 2024

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It is well known that reformulating the original problem can be crucial for the performance of mixed-integer programming (MIP) solvers. To ensure correctness, all transformations must preserve the feasibility status and optimal value of the problem, but there is currently no established methodology to express and verify the equivalence of two mixed-integer programs. In this work, we take a first step in this direction by showing how the correctness of MIP presolve reductions on 0-1 integer linear programs can be certified by using (and suitably extending) the VeriPB tool for pseudo-Boolean proof logging. Our experimental evaluation on both decision and optimization instances demonstrates the computational viability of the approach and leads to suggestions for future revisions of the proof format that will help to reduce the verbosity of the certificates and to accelerate the certification and verification process further.