Major 3 Satisfiability logic in Discrete Hopfield Neural Network integrated with multi-objective Election Algorithm

Muhammad Aqmar Fiqhi Roslan; Nur Ezlin Zamri; Mohd. Asyraf Mansor; Mohd Shareduwan Mohd Kasihmuddin; Muhammad Aqmar Fiqhi Roslan; Nur Ezlin Zamri; Mohd. Asyraf Mansor; Mohd Shareduwan Mohd Kasihmuddin

doi:10.3934/math.20231145

AIMS Mathematics

2023, Volume 8, Issue 9: 22447-22482. doi: 10.3934/math.20231145

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Major 3 Satisfiability logic in Discrete Hopfield Neural Network integrated with multi-objective Election Algorithm

1.
School of Mathematical Sciences, Universiti Sains Malaysia, 11800 USM, Penang, Malaysia
2.
School of Distance Education, Universiti Sains Malaysia, 11800 USM, Penang, Malaysia

Received: 20 October 2022 Revised: 24 March 2023 Accepted: 29 March 2023 Published: 14 July 2023

Discrete Hopfield Neural Network is widely used in solving various optimization problems and logic mining. Boolean algebras are used to govern the Discrete Hopfield Neural Network to produce final neuron states that possess a global minimum energy solution. Non-systematic satisfiability logic is popular due to the flexibility that it provides to the logical structure compared to systematic satisfiability. Hence, this study proposed a non-systematic majority logic named Major 3 Satisfiability logic that will be embedded in the Discrete Hopfield Neural Network. The model will be integrated with an evolutionary algorithm which is the multi-objective Election Algorithm in the training phase to increase the optimality of the learning process of the model. Higher content addressable memory is proposed rather than one to extend the measure of this work capability. The model will be compared with different order logical combinations $ k = \mathrm{3, 2} $, $ k = \mathrm{3, 2}, 1 $ and $ k = \mathrm{3, 1} $. The performance of those logical combinations will be measured by Mean Absolute Error, Global Minimum Energy, Total Neuron Variation, Jaccard Similarity Index and Gower and Legendre Similarity Index. The results show that $ k = \mathrm{3, 2} $ has the best overall performance due to its advantage of having the highest chances for the clauses to be satisfied and the absence of the first-order logic. Since it is also a non-systematic logical structure, it gains the highest diversity value during the learning phase.
- Discrete Hopfield Neural Network,
- non-systematic logic,
- flexible logical rule,
- Major 3 Satisfiability logic,
- Election Algorithm
Citation: Muhammad Aqmar Fiqhi Roslan, Nur Ezlin Zamri, Mohd. Asyraf Mansor, Mohd Shareduwan Mohd Kasihmuddin. Major 3 Satisfiability logic in Discrete Hopfield Neural Network integrated with multi-objective Election Algorithm[J]. AIMS Mathematics, 2023, 8(9): 22447-22482. doi: 10.3934/math.20231145

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Abstract

Discrete Hopfield Neural Network is widely used in solving various optimization problems and logic mining. Boolean algebras are used to govern the Discrete Hopfield Neural Network to produce final neuron states that possess a global minimum energy solution. Non-systematic satisfiability logic is popular due to the flexibility that it provides to the logical structure compared to systematic satisfiability. Hence, this study proposed a non-systematic majority logic named Major 3 Satisfiability logic that will be embedded in the Discrete Hopfield Neural Network. The model will be integrated with an evolutionary algorithm which is the multi-objective Election Algorithm in the training phase to increase the optimality of the learning process of the model. Higher content addressable memory is proposed rather than one to extend the measure of this work capability. The model will be compared with different order logical combinations $ k = \mathrm{3, 2} $, $ k = \mathrm{3, 2}, 1 $ and $ k = \mathrm{3, 1} $. The performance of those logical combinations will be measured by Mean Absolute Error, Global Minimum Energy, Total Neuron Variation, Jaccard Similarity Index and Gower and Legendre Similarity Index. The results show that $ k = \mathrm{3, 2} $ has the best overall performance due to its advantage of having the highest chances for the clauses to be satisfied and the absence of the first-order logic. Since it is also a non-systematic logical structure, it gains the highest diversity value during the learning phase.

References

[1]	M. Abdallah, M. A. Talib, S. Feroz, Q. Nasir, H. Abdalla, B. Mahfood, Artificial intelligence applications in solid waste management: A systematic research review, Waste Manage., 109 (2020), 231–246. https://doi.org/10.1016/j.wasman.2020.04.057 doi: 10.1016/j.wasman.2020.04.057
[2]	S. Agatonovic-Kustrin, R. Beresford, Basic concepts of artificial neural network (ANN) modeling and its application in pharmaceutical research, J Pharm. Biomed. Anal., 22 (2000), 717–727. https://doi.org/10.1016/s0731-7085(99)00272-1 doi: 10.1016/s0731-7085(99)00272-1
[3]	J. J. Hopfield, D. W. Tank, "Neural" computation of decisions in optimization problems, Biol. Cybern., 52 (1985), 141–152. https://doi.org/10.1007/bf00339943 doi: 10.1007/bf00339943
[4]	W. A. T. W. Abdullah, Logic programming on a neural network, Int. J. Intell. Syst., 7 (1992), 513–519. https://doi.org/10.1002/int.4550070604 doi: 10.1002/int.4550070604
[5]	A. Alway, N. E. Zamri, S. A. Karim, M. A. Mansor, M. S. M. Kasihmuddin, M. M, Bazuhair, Major 2 satisfiability logic in discrete Hopfield neural network, Int. J. Comput. Math. 99 (2022), 924–948. https://doi.org/10.1080/00207160.2021.1939870 doi: 10.1080/00207160.2021.1939870
[6]	S. A. Karim, M. S. M. Kasihmuddin, S. Sathasivam, M. A. Mansor, S. Z. M. Jamaludin, M. R. Amin, A Novel Multi-Objective Hybrid Election Algorithm for Higher-Order Random Satisfiability in Discrete Hopfield Neural Network, Mathematics, 10 (2022), 1963. https://doi.org/10.3390/math10121963 doi: 10.3390/math10121963
[7]	M. M. Bazuhair, S. Z. M. Jamaludin, N. E. Zamri, M. S. M. Kasihmuddin, M. A. Mansor, A. Alway, S. A. Karim, Novel Hopfield Neural Network Model with Election Algorithm for Random 3 Satisfiability, Processes, 9 (2021), 1292. https://doi.org/10.3390/pr9081292 doi: 10.3390/pr9081292
[8]	M. S. M. Kasihmuddin, M. A. Mansor, S. Sathasivam, Hybrid Genetic Algorithm in the Hopfield Network for Logic Satisfiability Problem, Pertanika J. Sci. Technol., 25 (2017), 139–152. https://doi.org/10.1063/1.4995911 doi: 10.1063/1.4995911
[9]	M. A. Mansor, M. S. M. Kasihmuddin, S. Sathasivam, Artificial Immune System Paradigm in the Hopfield Network for 3-Satisfiability Problem, Pertanika J. Sci. Technol., 25 (2017), 1173–1188.
[10]	N. E. Zamri, M. A. Mansor, M. S. M. Kasihmuddin, A. Alway, S. Z. M. Jamaludin, S. A. Alzaeemi, Amazon employees resources access data extraction via clonal selection algorithm and logic mining approach, Entropy, 22 (2020), 596. https://doi.org/10.3390/e22060596 doi: 10.3390/e22060596
[11]	S. A. Karim, N. E. Zamri, A. Alway, M. S. M. Kasihmuddin, A. I. M. Ismail, M. A. Mansor, et al., Random satisfiability: A higher-order logical approach in discrete Hopfield Neural Network, IEEE Access, 9 (2021), 50831–50845. https://doi.org/10.1109/access.2021.3068998 doi: 10.1109/access.2021.3068998
[12]	E. Pacuit, S. Salame, Majority Logic, KR, 4 (2004), 598–605.
[13]	Z. Zheng, S. Yang, Y. Guo, X. Jin, R. Wang, Meta-heuristic Techniques in Microgrid Management: A Survey, Swarm Evol. Comput., 78 (2023), 101256. https://doi.org/10.1016/j.swevo.2023.101256 doi: 10.1016/j.swevo.2023.101256
[14]	H. Emami, F. Derakhshan, Election algorithm: A new socio-politically inspired strategy, AI Commun., 28 (2015), 591–603. https://doi.org/10.3233/aic-140652 doi: 10.3233/aic-140652
[15]	H. Emami, Chaotic election algorithm, Comput. Inform. 38 (2019), 1444–1478. https://doi.org/10.31577/cai_2019_6_1444 doi: 10.31577/cai_2019_6_1444
[16]	S. Sathasivam, M. A. Mansor, M. S. M. Kasihmuddin, H. Abubakar, Election algorithm for random k satisfiability in the Hopfield neural network, Processes, 8 (2020), 568. https://doi.org/10.3390/pr8050568 doi: 10.3390/pr8050568
[17]	B. F. B. A. Boya, B. Ramakrishnan, J. Y. Effa, J. Kengne, K. Rajagopal, Effects of bias current and control of multistability in 3D hopfield neural network, Heliyon, 9 (2023), 13034. https://doi.org/10.1016/j.heliyon.2023.e13034. doi: 10.1016/j.heliyon.2023.e13034
[18]	S. Z. M. Jamaludin, N. A. Romli, M. S. M. Kasihmuddin, A. Baharum, M. A. Mansor, M.F. Marsani, Novel logic mining incorporating log linear approach, J. King Saud Univ. Comput. Inform. Sci., 34 (2022), 9011–9027.
[19]	M. S. M. Kasihmuddin, S. Z. M. Jamaludin, M. A. Mansor, H. A. Wahab, S. M. S. Ghadzi, Supervised learning perspective in logic mining, Mathematics, 10 (2022), 915.
[20]	Y. Guo, M. S. M. Kasihmuddin, Y. Gao, M. A. Mansor, H. A. Wahab, N. E. Zamri, et al., YRAN2SAT: A novel flexible random satisfiability logical rule in discrete hopfield neural network, Adv. Eng. Software, 171 (2022), 103169. https://doi.org/10.1016/j.advengsoft.2022.103169 doi: 10.1016/j.advengsoft.2022.103169
[21]	N. Bacanin, C. Stoean, M. Zivkovic, M. Rakic, R. Strulak-Wójcikiewicz, R. Stoean, On the Benefits of Using Metaheuristics in the Hyperparameter Tuning of Deep Learning Models for Energy Load Forecasting, Energies, 16 (2023), 1434. https://doi.org/10.3390/en16031434 doi: 10.3390/en16031434
[22]	S. Z. M. Jamaludin, M. S. M. Kasihmuddin, A. I. M. Ismail, M. A. Mansor, M.F.M. Basir, Energy based logic mining analysis with hopfield neural network for recruitment evaluation. Entropy, 23 (2020), 40. https://doi.org/10.3390/e23010040 doi: 10.3390/e23010040
[23]	J. Chen, M. S. M. Kasihmuddin, Y. Gao, Y. Guo, M. A. Mansor, N.A. Romli, et al., PRO2SAT: Systematic Probabilistic Satisfiability logic in Discrete Hopfield Neural Network, Adv. Eng. Software, 175 (2023), 103355. https://doi.org/10.1016/j.advengsoft.2022.103355 doi: 10.1016/j.advengsoft.2022.103355
[24]	L. C. Kho, M. S. M. Kasihmuddin, M. A. Mansor, S. Sathasivam, Logic Mining in League of Legends, Pertanika J. Sci. Technol., 28 (2020), 211–225.
[25]	N. Khentout, G. Magrotti, Fault supervision of nuclear research reactor systems using artificial neural networks: A review with results, Ann. Nucl. Energy, 185 (2023), 109684. https://doi.org/10.1016/j.anucene.2023.109684 doi: 10.1016/j.anucene.2023.109684
[26]	N. Kanwisher, M. Khosla, K. Dobs, Using artificial neural networks to ask 'why'questions of minds and brains, Trends Neurosci., 46 (2023), 240–254. https://doi.org/10.1016/j.tins.2022.12.008 doi: 10.1016/j.tins.2022.12.008
[27]	S. S. M. Sidik, N. E. Zamri, M. S. M. Kasihmuddin, H. A. Wahab, Y. Guo, M. A. Mansor, Non-Systematic Weighted Satisfiability in Discrete Hopfield Neural Network Using Binary Artificial Bee Colony Optimization, Mathematics, 10 (2022), 1129. https://doi.org/10.3390/math10071129 doi: 10.3390/math10071129
[28]	S. Subiyanto, A. Mohamed, M. A. Hannan, Intelligent maximum power point tracking for PV system using Hopfield neural network optimized fuzzy logic controller, Energ. Buildings, 51 (2012), 29–38.
[29]	L. Abualigah, A. Diabat, S. Mirjalili, M. Abd Elaziz, A. H. Gandomi, The arithmetic optimization algorithm, Comput. Method. Appl. M., 376 (2021), 113609. https://doi.org/10.1016/j.cma.2020.113609 doi: 10.1016/j.cma.2020.113609
[30]	Z. Wang, L. Shen, X. Li, L. Gao, An improved multi-objective firefly algorithm for energy-efficient hybrid flowshop rescheduling problem, J. Clean. Produc., 385 (2023), 135738. https://doi.org/10.1016/j.jclepro.2022.135738 doi: 10.1016/j.jclepro.2022.135738
[31]	W. H. Bangyal, A. Hameed, J. Ahmad, K. Nisar, M. R. Haque, A. A. A. Ibrahim, et al., New modified controlled bat algorithm for numerical optimization problem, Comput., Mater. Con., 70 (2022), 2241–2259.
[32]	M. Kobayashi, Quaternion projection rule for rotor hopfield neural networks, IEEE T. Neur. Net. Lear., 32 (2020), 900–908.
[33]	M. Safavi, A. K. Siuki, S. R. Hashemi, New optimization methods for designing rain stations network using new neural network, election, and whale optimization algorithms by combining the Kriging method, Environ. Monit. Assess., 193 (2021), 4. https://doi.org/10.1007/s10661-020-08726-z doi: 10.1007/s10661-020-08726-z
[34]	X. Dang, X. Tang, Z. Hao, J. Ren, Discrete Hopfield neural network based indoor Wi-Fi localization using CSI, EURASIP J. Wirel. Commun., 2020 (2020), 76.
[35]	G. J. Sawale, S. R. Gupta, Use of artificial neural network in data mining for weather forecasting, Int. J. Comput. Sci. Appl., 6 (2013), 383–387.
[36]	Z. Zhang, L. Zheng, Y. Zhou, Q. Guo, A Novel Finite-Time-Gain-Adjustment Controller Design Method for UAVs Tracking Time-Varying Targets, IEEE T. Intell. Transport. Syst., 23 (2021), 12531–12543.

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