Markov Chain methods for the Bipartite Boolean Quadratic Programming Problem

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

Abstract

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.

Citation

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. https://doi.org/10.1016/j.ejor.2017.01.001

• 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: 0377-2217
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 260
• Issue: 2
• Pages: 494-506
• DOI: https://doi.org/10.1016/j.ejor.2017.01.001
• Keywords: Artificial intelligence ; Bipartite Boolean quadratic programming ; Automated heuristic configuration ; Benchmark
• Public URL: https://nottingham-repository.worktribe.com/output/869661
• Publisher URL: http://www.sciencedirect.com/science/article/pii/S0377221717300061
• 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: https://doi.org/10.1016/j.ejor.2017.01.001; Content Type: article; Copyright: © 2017 The Authors. Published by Elsevier B.V.