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We study the Bipartite Boolean Quadratic Programming Problem (BBQP) which isan 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 amatrix, and solving optimisation problems such as maximum weight biclique,bipartite maximum weight cut, maximum weight induced sub-graph of a bipartitegraph, etc. For the BBQP, we first present several algorithmic components,specifically, hill climbers and mutations, and then show how to combine them ina high-performance metaheuristic. Instead of hand-tuning a standardmetaheuristic to test the efficiency of the hybrid of the components, we choseto use an automated generation of a multi-component metaheuristic to save humantime, and also improve objectivity in the analysis and comparisons ofcomponents. For this we designed a new metaheuristic schema which we callConditional Markov Chain Search (CMCS). We show that CMCS is flexible enough tomodel several standard metaheuristics; this flexibility is controlled bymultiple numeric parameters, and so is convenient for automated generation. Westudy the configurations revealed by our approach and show that the best ofthem outperforms the previous state-of-the-art BBQP algorithm by several ordersof magnitude. In our experiments we use benchmark instances introduced in thepreliminary version of this paper and described here, which have already becomethe de facto standard in the BBQP literature.

Markov Chain methods for the bipartite Boolean quadratic programming problem