A New Local Search Algorithm for Binary Optimization

Authors:
Dimitris Bertsimas;Dan A. Iancu;Dmitriy Katz
Affiliations:
Operations Research Center and Sloan School of Management, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139;Graduate School of Business, Stanford University, Stanford, California 94305;IBM T. J. Watson Research Center, Yorktown Heights, New York 10598
Venue:
INFORMS Journal on Computing
Year:
2013

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Abstract

We develop a new local search algorithm for binary optimization problems, whose complexity and performance are explicitly controlled by a parameter Q, measuring the depth of the local search neighborhood. We show that the algorithm is pseudo-polynomial for general cost vector c, and achieves a w2/2w-1 approximation guarantee for set packing problems with exactly w ones in each column of the constraint matrix A, when using Q = w2. Most importantly, we find that the method has practical promise on large, randomly generated instances of both set covering and set packing problems, as it delivers performance that is competitive with leading general-purpose optimization software CPLEX 11.2.