Abstract
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.
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- 1.
Note that we do not consider vertices as being adjacent to themselves by their loops. In this work we rather use loops to represent the weight of vertices.
- 2.
The hamming distance of two vectors is defined as the number of positions in which these two disagree.
References
Aarts, E., Korst, J.: Simulated Annealing and Boltzmann Machines. Wiley, Hoboken (1988)
Bashiri, M., Geranmayeh, A.F.: Tuning the parameters of an artificial neural network using central composite design and genetic algorithm. Scientia Iranica 18(6), 1600–1608 (2011)
Hifi, M., Paschos, V.T., Zissimopoulos, V.: A neural network for the minimum set covering problem. Chaos, Solitons Fractals 11(13), 2079–2089 (2000)
Kampel, L., Garn, B., Simos, D.E.: Covering arrays via set covers. Electron. Notes Discrete Math. 65, 11–16 (2018)
Kampel, L., Simos, D.E.: A survey on the state of the art of complexity problems for covering arrays. Theoret. Comput. Sci. 800, 107–124 (2019)
Lundy, M., Mees, A.: Convergence of an annealing algorithm. Math. Program. 34(1), 111–124 (1986)
Ma, L., et al.: Combinatorial testing for deep learning systems. arXiv preprint arXiv:1806.07723 (2018)
Pérez-Espinosa, H., Avila-George, H., Rodriguez-Jacobo, J., Cruz-Mendoza, H.A., Martínez-Miranda, J., Espinosa-Curiel, I.: Tuning the parameters of a convolutional artificial neural network by using covering arrays. Res. Comput. Sci. 121, 69–81 (2016)
Silver, D., et al.: Mastering the game of Go without human knowledge. Nature 550(7676), 354 (2017)
Smith, K.A.: Neural networks for combinatorial optimization: a review of more than a decade of research. INFORMS J. Comput. 11(1), 15–34 (1999)
Torres-Jimenez, J., Izquierdo-Marquez, I.: Survey of covering arrays. In: 2013 15th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, pp. 20–27, September 2013
Vazirani, V.V.: Approximation Algorithms. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-662-04565-7
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This research was carried out as part of the Austrian COMET K1 program (FFG).
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Kampel, L., Wagner, M., Kotsireas, I.S., Simos, D.E. (2020). How to Use Boltzmann Machines and Neural Networks for Covering Array Generation. In: Matsatsinis, N., Marinakis, Y., Pardalos, P. (eds) Learning and Intelligent Optimization. LION 2019. Lecture Notes in Computer Science(), vol 11968. Springer, Cham. https://doi.org/10.1007/978-3-030-38629-0_5
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