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Markov Chain methods for the Bipartite Boolean Quadratic Programming Problem

Karapetyan, Daniel; Punnen, Abraham; Parkes, Andrew J.

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Abraham Punnen


We study the Bipartite Boolean Quadratic Programming Problem (BBQP) which is an extension of the well known Boolean Quadratic Programming Problem (BQP). Applications of the BBQP include mining discrete patterns from binary data, approximating matrices by rank-one binary matrices, computing the cut-norm of a matrix, and solving optimisation problems such as maximum weight biclique, bipartite maximum weight cut, maximum weight induced sub-graph of a bipartite graph, etc. For the BBQP, we first present several algorithmic components, specifically, hill climbers and mutations, and then show how to com- bine them in a high-performance metaheuristic. Instead of hand-tuning a standard metaheuristic to test the efficiency of the hybrid of the components, we chose to use an automated generation of a multi- component metaheuristic to save human time, and also improve objectivity in the analysis and compar- isons of components. For this we designed a new metaheuristic schema which we call Conditional Markov Chain Search (CMCS). We show that CMCS is flexible enough to model several standard metaheuristics; this flexibility is controlled by multiple numeric parameters, and so is convenient for automated genera- tion. We study the configurations revealed by our approach and show that the best of them outperforms the previous state-of-the-art BBQP algorithm by several orders of magnitude. In our experiments we use benchmark instances introduced in the preliminary version of this paper and described here, which have already become the de facto standard in the BBQP literature.


Karapetyan, D., Punnen, A., & Parkes, A. J. (2017). Markov Chain methods for the Bipartite Boolean Quadratic Programming Problem. European Journal of Operational Research, 260(2), 494-506.

Journal Article Type Article
Acceptance Date Jan 2, 2017
Online Publication Date Jan 6, 2017
Publication Date Jul 16, 2017
Deposit Date Mar 3, 2017
Publicly Available Date Mar 3, 2017
Journal European Journal of Operational Research
Print ISSN 0377-2217
Electronic ISSN 1872-6860
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 260
Issue 2
Pages 494-506
Keywords Artificial intelligence ; Bipartite Boolean quadratic programming ; Automated heuristic configuration ; Benchmark
Public URL
Publisher URL
Additional Information This article is maintained by: Elsevier; Article Title: Markov Chain methods for the Bipartite Boolean Quadratic Programming Problem; Journal Title: European Journal of Operational Research; CrossRef DOI link to publisher maintained version:; Content Type: article; Copyright: © 2017 The Authors. Published by Elsevier B.V.
Contract Date Mar 3, 2017


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