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

作者：Puchinger Jakob^*; Stuckey Peter J; Wallace Mark G; Brand Sebastian

来源：Constraints, 2011, 16(1): 77-99.

DOI：10.1007/s10601-009-9085-0

• Modelling
• Hybrid solving
• Column generation
• Branch and price

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.

• 出版日期2011-1