Generic Dantzig-Wolfe Reformulation of Mixed Integer Programs

Dantzig-Wolfe decomposition (or reformulation) is well-known to provide strong dual bounds for specially structured mixed integer programs (MIPs) in practice. 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 process can be automated. In particular the detection (better: the construction) of a matrix structure that is useful for Dantzig-Wolfe reformulation of a MIP can be accomplished by suitably permuting rows and columns. 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 reformulated problem exploiting column generation. Our results support that Dantzig-Wolfe reformulation may hold more promise as a generalpurpose tool than previously acknowledged by the research community.