2004 | OriginalPaper | Buchkapitel
Semi-continuous Cuts for Mixed-Integer Programming
verfasst von : I. R. de Farias Jr.
Erschienen in: Integer Programming and Combinatorial Optimization
Verlag: Springer Berlin Heidelberg
Enthalten in: Professional Book Archive
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We study the convex hull of the feasible set of the semi-continuous knapsack problem, in which the variables belong to the union of two intervals. Besides being important in its own right, the semi-continuous knapsack problem is a relaxation of general mixed-integer programming. We show how strong inequalities that are valid for the semi-continuous knapsack polyhedron can be derived and used as cuts in a branch-and-cut scheme for mixed-integer programming and problems with semi-continuous variables. We present computational results that demonstrate the effectiveness of these inequalities, which we call collectively semi-continuous cuts. Our computational experience also shows that dealing with semi-continuous constraints directly in the branch-and-cut algorithm through a specialized branching scheme and semi-continuous cuts is considerably more practical than the “textbook” approach of modeling semi-continuous constraints through the introduction of auxiliary binary variables in the model.