Lower Bound Improvement and Forcing Rule for Quadratic Binary Programming

Authors:
Hong-Xuan Huang;Panos M. Pardalos;Oleg A. Prokopyev
Affiliations:
Department of Industrial Engineering, Tsinghua University, Beijing, P.R. China 100084;Department of Industrial and Systems Engineering, University of Florida, Gainesville, USA 32611;Department of Industrial and Systems Engineering, University of Florida, Gainesville, USA 32611
Venue:
Computational Optimization and Applications
Year:
2006

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Abstract

In this paper several equivalent formulations for the quadratic binary programming problem are presented. Based on these formulations we describe four different kinds of strategies for estimating lower bounds of the objective function, which can be integrated into a branch and bound algorithm for solving the quadratic binary programming problem. We also give a theoretical explanation for forcing rules used to branch the variables efficiently, and explore several properties related to obtained subproblems. From the viewpoint of the number of subproblems solved, new strategies for estimating lower bounds are better than those used before. A variant of a depth-first branch and bound algorithm is described and its numerical performance is presented.