Hybrid Benders Decomposition Algorithms in Constraint Logic Programming
Benders Decomposition is a form of hybridisation that allows linear programming to be combined with other kinds of algorithms. It extracts new constraints for one subproblem from the dual values of the other subproblem. This paper describes an implementation of Benders Decomposition, in the ECLiPSe language, that enables it to be used within a constraint programming framework. The programmer is spared from having to write down the dual form of any subproblem, because it is derived by the system. Examples are used to show how problem constraints can be modelled in an undecomposed form. The programmer need only specify which variables belong to which subproblems, and the Benders Decomposition is extracted automatically. A class of minimal perturbation problems is used to illustrate how different kinds of algorithms can be used for the different subproblems. The implementation is tested on a set of minimal perturbation benchmarks, and the results are analysed.
KeywordsColumn Generation Master Problem Global Constraint Hybridisation Form Bender Decomposition
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