Automatic Decomposition and Branch-and-Price—A Status Report

  • Marco E. Lübbecke
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7276)

Abstract

We provide an overview of our recent efforts to automatize Dantzig-Wolfe reformulation and column generation/branch-and-price for structured, large-scale integer programs. We present the need for and the benefits from a generic implementation which does not need any user input or expert knowledge. A focus is on detecting structures in integer programs which are amenable to a Dantzig-Wolfe reformulation. We give computational results and discuss future research topics.

Keywords

Integer Program Column Generation Knapsack Constraint Primal Heuristic Column Generation Process 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Achterberg, T.: SCIP: Solving constraint integer programs. Math. Programming Computation 1(1), 1–41 (2009)MathSciNetMATHCrossRefGoogle Scholar
  2. 2.
    Bergner, M., Caprara, A., Furini, F., Lübbecke, M.E., Malaguti, E., Traversi, E.: Partial Convexification of General MIPs by Dantzig-Wolfe Reformulation. In: Günlük, O., Woeginger, G.J. (eds.) IPCO 2011. LNCS, vol. 6655, pp. 39–51. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  3. 3.
    Desrosiers, J., Lübbecke, M.: A primer in column generation. In: Desaulniers, G., Desrosiers, J., Solomon, M. (eds.) Column Generation, pp. 1–32. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  4. 4.
    Desrosiers, J., Lübbecke, M.: Branch-price-and-cut algorithms. In: Cochran, J. (ed.) Encyclopedia of Operations Research and Management Science. John Wiley & Sons, Chichester (2011)Google Scholar
  5. 5.
    Ferris, M., Horn, J.: Partitioning mathematical programs for parallel solution. Math. Programming 80, 35–61 (1998)MathSciNetMATHGoogle Scholar
  6. 6.
    Gamrath, G., Lübbecke, M.E.: Experiments with a Generic Dantzig-Wolfe Decomposition for Integer Programs. In: Festa, P. (ed.) SEA 2010. LNCS, vol. 6049, pp. 239–252. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  7. 7.
    Joncour, C., Michel, S., Sadykov, R., Sverdlov, D., Vanderbeck, F.: Column generation based primal heuristics. In: International Conference on Combinatorial Optimization (ISCO). Electronic Notes in Discrete Mathematics, vol. 36, pp. 695–702. Elsevier (2012)Google Scholar
  8. 8.
    Lübbecke, M., Puchert, C.: Primal heuristics for branch-and-price algorithms. In: Operations Research Proceedings 2011. Springer (to appear, 2012)Google Scholar
  9. 9.
    Puchinger, J., Stuckey, P., Wallace, M., Brand, S.: Dantzig-Wolfe decomposition and branch-and-price solving in G12. Constraints 16(1), 77–99 (2011)MathSciNetMATHCrossRefGoogle Scholar
  10. 10.
    Ralphs, T., Galati, M.: DIP – decomposition for integer programming (2009), https://projects.coin-or.org/Dip
  11. 11.
    Vanderbeck, F.: On Dantzig-Wolfe decomposition in integer programming and ways to perform branching in a branch-and-price algorithm. Oper. Res. 48(1), 111–128 (2000)MathSciNetMATHCrossRefGoogle Scholar
  12. 12.
    Vanderbeck, F.: BaPCod – a generic branch-and-price code (2005), https://wiki.bordeaux.inria.fr/realopt/pmwiki.php/Project/BaPCod
  13. 13.
    Vanderbeck, F.: Implementing mixed integer column generation. In: Desaulniers, G., Desrosiers, J., Solomon, M. (eds.) Column Generation, pp. 331–358. Springer (2005)Google Scholar
  14. 14.
    Vanderbeck, F.: A generic view of Dantzig-Wolfe decomposition in mixed integer programming. Oper. Res. Lett. 34(3), 296–306 (2006)MathSciNetMATHCrossRefGoogle Scholar
  15. 15.
    Vanderbeck, F.: Branching in branch-and-price: A generic scheme. Math. Programming 130(2), 249–294 (2011)MathSciNetMATHCrossRefGoogle Scholar
  16. 16.
    Vanderbeck, F., Wolsey, L.: Reformulation and decomposition of integer programs. In: Jünger, M., Liebling, T., Naddef, D., Nemhauser, G., Pulleyblank, W., Reinelt, G., Rinaldi, G., Wolsey, L. (eds.) 50 Years of Integer Programming 1958–2008. Springer, Berlin (2010)Google Scholar
  17. 17.
    Villeneuve, D., Desrosiers, J., Lübbecke, M., Soumis, F.: On compact formulations for integer programs solved by column generation. Ann. Oper. Res. 139(1), 375–388 (2005)MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Marco E. Lübbecke
    • 1
  1. 1.Operations ResearchRWTH Aachen UniversityAachenGermany

Personalised recommendations