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Constraints

, Volume 16, Issue 1, pp 77–99 | Cite as

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

  • Jakob Puchinger
  • Peter J. Stuckey
  • Mark G. Wallace
  • Sebastian Brand
Article

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.

Keywords

Modelling Hybrid solving Column generation Branch and price 

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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  • Jakob Puchinger
    • 1
  • Peter J. Stuckey
    • 2
  • Mark G. Wallace
    • 3
  • Sebastian Brand
    • 2
  1. 1.Mobility DepartmentAustrian Institute of TechnologyViennaAustria
  2. 2.NICTA Victoria Research Laboratory, Department of Computer Science & Software EngineeringUniversity of MelbourneMelbourneAustralia
  3. 3.Faculty of Information TechnologyMonash UniversityMelbourneAustralia

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