Automatic DantzigWolfe reformulation of mixed integer programs
DantzigWolfe decomposition (or reformulation) is well-known to provide strong dual bounds for specially structured mixed integer programs (MIPs). However, the method is not implemented in any state-of-the-art MIP solver as it is considered to require structural problem knowledge and tailoring to this structure. We provide a computational proof-of-concept that the reformulation can be automated. That is, we perform a rigorous experimental study, which results in identifying a score to estimate the quality of a decomposition: after building a set of potentially good candidates, we exploit such a score to detect which decomposition might be useful for DantzigWolfe reformulation of a MIP. We experiment with general instances from MIPLIB2003 and MIPLIB2010 for which a decomposition method would not be the first choice, and demonstrate that strong dual bounds can be obtained from the automatically reformulated model using column generation. Our findings support the idea that DantzigWolfe reformulation may hold more promise as a general-purpose tool than previously acknowledged by the research community.
dantzigwolfe decomposition automatic reformulation column generation block-diagonal matrix matrix re-ordering hypergraph partitioning 90c11 49m27 65k05