Experiments with a Generic Dantzig-Wolfe Decomposition for Integer Programs

Abstract We report on experiments with turning the branch-price-andcut framework SCIP into a generic branch-price-and-cut solver. That is, given a mixed integer program (MIP), our code performs a DantzigWolfe decomposition according to the user’s specification, and solves the resulting re-formulation via branch-and-price. We take care of the column generation subproblems which are solved as MIPs themselves, branch and cut on the original variables (when this is appropriate), aggregate identical subproblems, etc. The charm of building on a well-maintained framework lies in avoiding to re-implement state-of-the-art MIP solving features like pseudo-cost branching, preprocessing, domain propagation, primal heuristics, cutting plane separation etc. 1 Situation Over the last 25 years, branch-and-price algorithms developed into a very powerful tool to optimally solve huge and extremely difficult combinatorial optimization problems. Their success relies on exploiting problem structures in a...

• Type: Conference
• Year: 2010
• Where: WEA
• Authors: Gerald Gamrath, Marco E. Lübbecke
• Keywords: Algorithms, Generic Branch-price-and-cut Solver, Generic Implementation, Integer Program, WEA 2010