Unified Review of Column Generation Methods

François Vanderbeck 1, 2
1 Realopt - Reformulations based algorithms for Combinatorial Optimization
LaBRI - Laboratoire Bordelais de Recherche en Informatique, IMB - Institut de Mathématiques de Bordeaux, Inria Bordeaux - Sud-Ouest
Abstract : Large scale Mixed Integer Programming (MIP) optimization models are intricate to solve. When the model decomposes into blocs, for instance when optimizing the use of multiple ressources, relaxing the linking constraints in a Lagrangian way can make the model tractable. Exploiting such decomposition to develop tight approximations has lead to tremendous progress in solving important applications. In this presentation, we review the alternative methods to solve the so-called Lagrangian dual model or its linear programming counterpart, the Dantzig-Wolfe master (associated with the column generation algorithm). We highlight their drawbacks, their common base, and their specific features, while discussing extentions of such methods.
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https://hal.inria.fr/hal-01108093
Contributor : François Vanderbeck <>
Submitted on : Thursday, January 22, 2015 - 10:55:11 AM
Last modification on : Thursday, January 11, 2018 - 6:22:12 AM

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  • HAL Id : hal-01108093, version 1

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François Vanderbeck. Unified Review of Column Generation Methods. OPTIMIZATION 2014, Jul 2014, Guimaraes, Portugal. ⟨hal-01108093⟩

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