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Column Generation based Primal Heuristics

Cédric Joncour 1, 2 Sophie Michel 1, 3 Ruslan Sadykov 1, 2 Dmitry Sverdlov 1, 2 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 : In the past decade, significant progress has been achieved in developing generic primal heuristics that made their way into commercial mixed integer programming (MIP) solver. Extensions to the context of a column generation solution approach are not straightforward. The Dantzig-Wolfe decomposition principle can indeed be exploited in greedy, local search, rounding or truncated exact methods. The price coordination mechanism can bring a global view that may be lacking in some ''myopic'' approaches based on a compact formulation. However, the dynamic generation of variables requires specific adaptation of heuristic paradigms. The column generation literature reports many application specific studies where primal heuristics are a key to success. There remains to extract generic methods that could be seen as black-box primal heuristics for use across applications. In this paper we review generic classes of column generation based primal heuristics. We then focus on a so-called ''diving'' method in which we introduce diversification based on Limited Discrepancy Search. While being a general purpose approach, the implementation of our heuristic illustrates the technicalities specific to column generation. The method is numerically tested on variants of the cutting stock and vehicle routing problems.
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Submitted on : Wednesday, February 20, 2013 - 3:34:02 PM
Last modification on : Saturday, June 25, 2022 - 10:33:32 AM



Cédric Joncour, Sophie Michel, Ruslan Sadykov, Dmitry Sverdlov, François Vanderbeck. Column Generation based Primal Heuristics. International Symposium on Combinatorial Optimization (ISCO), Mar 2010, HaMMamet, Tunisia. pp.695-702, ⟨10.1016/j.endm.2010.05.088⟩. ⟨hal-00790610⟩



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