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

Authors:
Jakob Puchinger;Peter J. Stuckey;Mark G. Wallace;Sebastian Brand
Affiliations:
Mobility Department, Austrian Institute of Technology, Vienna, Austria;NICTA Victoria Research Laboratory, Department of Computer Science & Software Engineering, University of Melbourne, Melbourne, Australia;Faculty of Information Technology, Monash University, Melbourne, Australia;NICTA Victoria Research Laboratory, Department of Computer Science & Software Engineering, University of Melbourne, Melbourne, Australia
Venue:
Constraints
Year:
2011

Citing 12
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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.