How to Use Boltzmann Machines and Neural Networks for Covering Array Generation

In the past, combinatorial structures have been used only to tune parameters of neural networks. In this paper, we employ for the first time, neural networks and Boltzmann machines for the construction of covering arrays (CAs). In past works, Boltzmann machines were successfully used to solve set cover instances. For the construction of CAs, we consider the equivalent set cover instances and use Boltzmann machines to solve these instances. We adapt an existing algorithm for solving general set cover instances, which is based on Boltzmann machines and apply it for CA construction. Furthermore, we consider newly designed versions of this algorithm, where we consider structural changes of the underlying Boltzmann machine, as well as a version with an additional feedback loop, modifying the Boltzmann machine. Last, one variant of this algorithm employs learning techniques based on neural networks to adjust the various connections encountered in the graph representation of the considered set cover instances. Supported by an experimental evaluation our findings can act as a beacon for future applications of neural networks in the field of covering array generation and related discrete structures.