4 research outputs found
Markov Chain methods for the Bipartite Boolean Quadratic Programming Problem
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
Conditional Markov Chain Search for the Generalised Travelling Salesman Problem for Warehouse Order Picking
The Generalised Travelling Salesman Problem (GTSP) is a well-known problem
that, among other applications, arises in warehouse order picking, where each
stock is distributed between several locations -- a typical approach in large
modern warehouses. However, the instances commonly used in the literature have
a completely different structure, and the methods are designed with those
instances in mind. In this paper, we give a new pseudo-random instance
generator that reflects the warehouse order picking and publish new benchmark
testbeds. We also use the Conditional Markov Chain Search framework to
automatically generate new GTSP metaheuristics trained specifically for
warehouse order picking. Finally, we report the computational results of our
metaheuristics to enable further competition between solvers