Implicit cover inequalities
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In this paper we consider combinatorial optimization problems whose feasible sets are simultaneously restricted by a binary knapsack constraint and a cardinality constraint imposing the exact number of selected variables. In particular, such sets arise when the feasible set corresponds to the bases of a matroid with a side knapsack constraint, for instance the weighted spanning tree problem and the multiple choice knapsack problem. We introduce the family of implicit cover inequalities which generalize the well-known cover inequalities for such feasible sets and discuss the lifting of the implicit cover inequalities. A computational study for the weighted spanning tree problem is reported.
KeywordsCover inequalities Weighted minimal spanning tree problem Lifting Matroidal knapsack
Research partially funded by CIDMA (Centro de Investigação e Desenvolvimento em Matemática e Aplicações) through the FCT (Fundação para a Ciência e a Tecnologia) within project PEst-OE/MAT/UI4106/2014, and by FCT through program COMPETE: FCOMP-01-0124-FEDER-041898 within project EXPL/MAT-NAN/1761/2013.
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