Lagrangian Heuristics for the Linear Ordering Problem
Two heuristics for the Linear Ordering Problem are investigated in this paper. These heuristics are embedded within a Lagrangian Relaxation framework and are started with a construction phase. In this process, some Lagrangian (dual) information is used as an input to guide the construction of initial Linear Orderings. Solutions thus obtained are then submitted to local improvement in an overall procedure that is repeated throughout Subgradient Optimization. Since a very large number of inequalities must be dualized in this application, Relax and Cut is used instead of a straightforward implementation of the Subgradient Method. Heuristics are tested for instances from the literature and also for some new hard to solve exactly ones. From the results obtained, one of the proposed heuristics has shown to be competitive with the best in the literature. In particular, it generates optimal solutions for all 79 instances taken from the literature. As a by-product, it also proves optimality for 72 of them.
KeywordsLinear ordering problem Lagrangian relaxation Relax and cut.
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