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Dantzig-Wolfe decomposition and branch-and-price solving in G12

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Abstract

The G12 project is developing a software environment for stating and solving combinatorial problems by mapping a high-level model of the problem to an efficient combination of solving methods. Model annotations are used to control this process. In this paper we explain the mapping to branch-and-price solving. Dantzig-Wolfe decomposition is automatically performed using the additional information given by the model annotations. The models obtained can then be solved using column generation and branch-and-price. G12 supports the selection of specialised subproblem solvers, the aggregation of identical subproblems to reduce symmetries, automatic disaggregation when required by branch-and-bound, the use of specialised subproblem constraint-branching rules, and different master problem solvers including a hybrid solver based on the volume algorithm. We demonstrate the benefits of the G12 framework on three examples: a trucking problem, cutting stock, and two-dimensional bin packing.

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Authors and Affiliations

  1. Mobility Department, Austrian Institute of Technology, Vienna, Austria

    Jakob Puchinger

  2. NICTA Victoria Research Laboratory, Department of Computer Science & Software Engineering, University of Melbourne, Melbourne, Australia

    Peter J. Stuckey & Sebastian Brand

  3. Faculty of Information Technology, Monash University, Melbourne, Australia

    Mark G. Wallace

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  1. Jakob Puchinger
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  2. Peter J. Stuckey
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  3. Mark G. Wallace
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  4. Sebastian Brand
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Correspondence to Jakob Puchinger.

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Puchinger, J., Stuckey, P.J., Wallace, M.G. et al. Dantzig-Wolfe decomposition and branch-and-price solving in G12. Constraints 16, 77–99 (2011). https://doi.org/10.1007/s10601-009-9085-0

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