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

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Experimental Algorithms (SEA 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7276))

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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.

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References

  1. Achterberg, T.: SCIP: Solving constraint integer programs. Math. Programming Computation 1(1), 1–41 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Chapter  Google Scholar 

  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)

    Chapter  Google Scholar 

  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. Ferris, M., Horn, J.: Partitioning mathematical programs for parallel solution. Math. Programming 80, 35–61 (1998)

    MathSciNet  MATH  Google Scholar 

  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)

    Chapter  Google Scholar 

  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. Lübbecke, M., Puchert, C.: Primal heuristics for branch-and-price algorithms. In: Operations Research Proceedings 2011. Springer (to appear, 2012)

    Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  10. Ralphs, T., Galati, M.: DIP – decomposition for integer programming (2009), https://projects.coin-or.org/Dip

  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)

    Article  MathSciNet  MATH  Google Scholar 

  12. Vanderbeck, F.: BaPCod – a generic branch-and-price code (2005), https://wiki.bordeaux.inria.fr/realopt/pmwiki.php/Project/BaPCod

  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. Vanderbeck, F.: A generic view of Dantzig-Wolfe decomposition in mixed integer programming. Oper. Res. Lett. 34(3), 296–306 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  15. Vanderbeck, F.: Branching in branch-and-price: A generic scheme. Math. Programming 130(2), 249–294 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  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. 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)

    Article  MathSciNet  MATH  Google Scholar 

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Lübbecke, M.E. (2012). Automatic Decomposition and Branch-and-Price—A Status Report. In: Klasing, R. (eds) Experimental Algorithms. SEA 2012. Lecture Notes in Computer Science, vol 7276. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30850-5_1

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  • DOI: https://doi.org/10.1007/978-3-642-30850-5_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-30849-9

  • Online ISBN: 978-3-642-30850-5

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