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

Jakob Puchinger (1) , Peter J. Stuckey (2, 3) , Mark Wallace (4) , Sebastian Brand (2, 3)

1 AIT - Austrian Institute of Technology [Vienna]
2 NICTA - National ICT Australia [Sydney]
3 University of Melbourne
4 Monash University [Malaysia]

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 spe-cialised 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.

Mots clés: Modelling; Hybrid solving; Column generation; Branch and price

Domaines: Recherche opérationnelle [math.OC]

Jakob Puchinger, Peter J. Stuckey, Mark Wallace, Sebastian Brand. Dantzig-Wolfe decomposition and branch-and-price solving in G12. Constraints, 2011, 16 (1), pp.77-99. ⟨10.1007/s10601-009-9085-0⟩. ⟨hal-01224910⟩