A primer on the application of neural networks to covering array generation

Abstract

In the past, combinatorial structures have been used only to tune parameters of neural networks. In this work, we employ neural networks in the form of Boltzmann machines and Hopfield networks for the construction of a specific class of combinatorial designs, namely covering arrays (CAs). In past works, these neural networks were successfully used to solve set cover instances. For the construction of CAs, we consider the corresponding set cover instances and use neural networks to solve such instances. We adapt existing algorithms for solving general set cover instances, which are based on Boltzmann machines and Hopfield networks and apply them for CA construction. Furthermore, for the algorithm based on Boltzmann machines, we consider newly designed versions, where we deploy structural changes of the underlying Boltzmann machine, adding a feedback loop. Additionally, one variant of this algorithm employs learning techniques based on neural networks to adjust the various connections encountered in the graph representing the considered set cover instances. Culminating in a comprehensive experimental evaluation, our work presents the first study of applications of neural networks in the field of covering array generation and related discrete structures and may act as a guideline for future investigations.