Inhalt des Dokuments
Preprint 25-2003
Combinatorial Optimization & Graph Algorithms group (COGA-Preprints)- Title
- On Compact Formulations for Integer Programs Solved by Column Generation
- Authors
- Daniel Villeneuve, Jacques Desrosiers, Marco E. Lübbecke, and Francois Soumis
- Publication
- Submitted to: Annals of Operations Research
- Classification
-
MSC: primary: 90C10 Integer programming secondary: 49M27 Decomposition methods 65K05 Mathematical programming algorithms 90C06 Large-scale problems 90C57 Polyhedral combinatorics, branch-and-bound, branch-and-cut - Keywords
-
Integer programming, branch and bound, column generation
- Abstract
-
Column generation has become a powerful tool in solving large scale integer programs. It is well known that most of the often reported compatibility issues between pricing subproblem and branching rule disappear when branching decisions are based on imposing constraints on the subproblem's variables. This can be generalized to branching on variables of a so-called compact formulation. We constructively show that such a formulation always exists under mild assumptions. It has a block diagonal structure with identical subproblems, each of which contributes only one column in an integer solution. This construction has an interpretation as reversing a Dantzig-Wolfe decomposition. Our proposal opens the way for the development of branching rules adapted to the subproblem's structure and to the linking constraints.
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