Automatic Dantzig–Wolfe reformulation of mixed integer programs

Abstract

International audienceDantzig–Wolfe 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 Dantzig–Wolfe 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 Dantzig–Wolfe reformulation may hold more promise as a general-purpose tool than previously acknowledged by the research community

Local Cuts and Two-Period Convex Hull Closures for Big-Bucket Lot-Sizing Problems

“…In this section, we demonstrate computationally that the gap closed by the twoperiod closure algorithm in multiperiod problems can be substantial, and competitive or superior to the gap closed by other state-of-the-art approaches. Similar to other approaches that investigate the lower bound improvement by optimizing over a closure (Balas and Saxena 2008) or, more generally, by employing a computationally heavy algorithm (Bergner et al 2015), our framework needs to reach further computational maturity until it can be time efficient enough to be embedded in modern solvers. We therefore focus on obtaining the best lower bounds possible, possibly at the expense of CPU times, to gain a thorough understanding of multiperiod, multi-item, single-level, big-bucket relaxations.…”

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