ABSTRACT
The Discrete Hopfield Neural Network introduces a G-Type Random 3 Satisfiability logic structure, which can improve the flexibility of the logic structure and meet the requirements of all combinatorial problems. Usually, Exhaustive Search (ES) is regarded as the basic learning algorithm to search the fitness of neurons. To improve the efficiency of the learning algorithm. In this paper, we introduce the Estimation of Distribution Algorithm (EDA) as a learning algorithm for the model. To study the learning mechanism of EDA to improve search efficiency, this study focuses on the impact of EDA on the model under different proportions of literals and evaluates the performance of the model at different phases through evaluation indicators. Analyze the effect of EDA on the synaptic weights and the global solution. From the discussion, it can be found that compared with ES, EDA has a larger search space at the same efficiency, which makes the probability of obtaining satisfactory weights higher, and the proportion of global solutions obtained is higher. Higher proportions of positive literals help to improve the model performance.
- Atul Adya,Hopfield, J. J. 1982. Neural networks and physical systems with emergent collective computational abilities. Proceedings of the national academy of sciences, 79(8), 2554-2558. https://doi.org/10.1073/pnas.79.8.2554Google ScholarCross Ref
- McCulloch W S, Pitts W. 1990. A logical calculus of the ideas immanent in nervous activity. Bulletin of mathematical biology, 52(1), 99-115.W. A. T. W. Abdullah, International journal of intelligent systems. 7, 513-519 (1992). https://doi.org/10.1007/BF02459570Google ScholarCross Ref
- Abdullah, W. A. T. W. 1992. Logic programming on a neural network. International journal of intelligent systems, 7(6), 513-519. https://doi.org/10.1002/int.4550070604Google ScholarCross Ref
- Mansor M A, Sathasivam S. 2016. Accelerating activation function for 3-satisfiability logic programming. International Journal of Intelligent Systems and Applications, 8(10), 44. https://doi.org/10.5815/ijisa.2016.10.05Google ScholarCross Ref
- Kasihmuddin M S M, Mansor M A, Sathasivam S. 2018. Discrete Hopfield neural network in restricted maximum k-satisfiability logic programming[J]. Sains Malaysiana, 47(6): 1327-1335. htpe://dx. doi. org/10.17576/jsm-2018-4706-30Google ScholarCross Ref
- Karim, S. A., Zamri, N. E., Alway, A., Kasihmuddin, M. S. M., Ismail, A. I. M., Mansor, M. A., Hassan, N. F. A. 2021. Random satisfiability: A higher-order logical approach in discrete Hopfield Neural Network. IEEE Access, 9, 50831-50845. https://doi.org/10.1109/ACCESS.2021.3068998Google ScholarCross Ref
- Guo, Y., Kasihmuddin, M. S. M., Gao, Y., Mansor, M. A., Wahab, H. A., Zamri, N. E., & Chen, J. 2022. YRAN2SAT: A novel flexible random satisfiability logical rule in discrete hopfield neural network. Advances in Engineering Software, 171, 103169. https://doi.org/10.1016/j.advengsoft.2022.103169Google ScholarDigital Library
- Zamri, N. E., Azhar, S. A., Mansor, M. A., Alway, A., & Kasihmuddin, M. S. M. (2022). Weighted Random k Satisfiability for k= 1, 2 (r2SAT) in Discrete Hopfield Neural Network. Applied Soft Computing, 109312. https://doi.org/10.1016/j.asoc.2022.109312Google ScholarDigital Library
- Gao, Y., Guo, Y., Romli, N. A., Kasihmuddin, M. S. M., Chen, W., Mansor, M. A., Chen, J. 2022. GRAN3SAT: Creating Flexible Higher-Order Logic Satisfiability in the Discrete Hopfield Neural Network. Mathematics, 10(11), 1899. https://doi.org/10.3390/math10111899Google ScholarCross Ref
- Mühlenbein, H., Paass, G. 1996. From recombination of genes to the estimation of distributions I. Binary parameters. In International conference on parallel problem solving from nature. 178-187. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61723-X_982Google ScholarCross Ref
- Peralta, J., Gutierrez, G., Sanchis, A. 2010. Time series forecasting by evolving artificial neural networks using genetic algorithms and estimation of distribution algorithms. In The 2010 international joint conference on neural networks (IJCNN) (pp. 1-8). IEEE. https://doi.org/10.1109/IJCNN.2010.5596892Google ScholarCross Ref
- Donate, J. P., Li, X., Sánchez, G. G., de Miguel, A. S. 2013. Time series forecasting by evolving artificial neural networks with genetic algorithms, differential evolution and estimation of distribution algorithm. Neural Computing and Applications, 22(1), 11-20. https://doi.org/10.1007/s00521-011-0741-0Google ScholarCross Ref
- Mühlenbein, H. 1997. The equation for response to selection and its use for prediction. Evolutionary computation, 5(3), 303-346. https://doi.org/10.1162/evco.1997.5.3.303Google ScholarDigital Library
Index Terms
- Estimation of Distribution Algorithm with Discrete Hopfield Neural Network for GRAN3SAT Analysis
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