Title: A class of multi-level balanced Foundation-Penalty cuts for mixed-integer programs

Authors: Fred Glover, Hanif D. Sherali

Addresses: University of Colorado, Boulder, CO 80309-0419, USA. ' Grado Department of Industrial and Systems Engineering, (0118) Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, USA

Abstract: Glover and Sherali (2003) introduced a wide class of Foundation-Penalty (FP) cuts for GUB and ordinary mixed-integer programs. The FP cuts are easy to generate by exploiting routine branch-and-bound penalty calculations, and encompass other classical cuts such as disjunctive cuts, lift-and-project cuts, convexity cuts, Gomory cuts, and mixed-integer rounding cuts. Here we focus on two special classes of FP cuts, called balanced FP cuts and multi-level balanced FP cuts, and exhibit their relationship to special forms of disjunctive cuts. A numerical example illustrates the rich variety of cuts that can be generated.

Keywords: mixed-integer programming; foundation-penalty cuts; optimisation; branch-and-bound penalty calculations; disjunctive cuts; lift-and-project cuts; convexity cuts; Gomory cuts; mixed-integer rounding cuts.

DOI: 10.1504/IJCSE.2007.017826

International Journal of Computational Science and Engineering, 2007 Vol.3 No.3, pp.203 - 210

Published online: 18 Apr 2008 *

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