Partial Convexification of General MIPs

DIKU-talk by Professor Marco Lübbecke, RWTH Aachen

Abstract:

Dantzig-Wolfe decomposition 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: it needs tailoring to the particular problem; the decomposition must be determined from the typical bordered block-diagonal matrix structure; the resulting column generation subproblems must be solved efficiently; etc.

We provide a computational proof-of-concept that the process can be automated in principle, and that strong dual bounds can be obtained on general MIPs for which a solution by a decomposition has not been the first choice.

We perform an extensive computational study on the 0-1 dynamic knapsack problem (without block-diagonal structure) and on general MIPLIB2003 instances.

Our results support that Dantzig-Wolfe reformulation may hold more promise as a general-purpose tool than previously acknowledged by the research community.

Bio

Marco Lübbecke is Professor and Chair of Operations Research, at the RWTH Aachen University. His primary research interests comprise:

  • Computational mixed integer programming
  • Column generation and branch-and-price
  • Combinatorial optimization
  • Operations research
  • Industrial applications (logistics, production)
  • Geometrically motivated optimization problems