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.

过去，组合结构仅用于调整神经网络的参数。在这项工作中，我们采用玻尔兹曼机和 Hopfield 网络形式的神经网络来构建特定类别的组合设计，即覆盖阵列 (CA)。在过去的工作中，这些神经网络成功地用于解决集合覆盖实例。对于 CA 的构建，我们考虑相应的集合覆盖实例并使用神经网络来解决这些实例。我们采用现有算法来解决一般集覆盖实例，这些算法基于玻尔兹曼机和 Hopfield 网络，并将它们应用于 CA 构造。此外，对于基于玻尔兹曼机的算法，我们考虑了新设计的版本，其中我们部署了底层玻尔兹曼机的结构变化，添加反馈循环。此外，该算法的一个变体采用基于神经网络的学习技术来调整在表示所考虑的集合覆盖实例的图中遇到的各种连接。在全面的实验评估中达到高潮，我们的工作首次研究了神经网络在覆盖阵列生成和相关离散结构领域的应用，并可作为未来研究的指南。