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Multi-discrete genetic algorithm in hopfield neural network with weighted random k satisfiability

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Abstract

The existing Discrete Hopfield Neural Network with systematic Satisfiability models produced repetition of final neuron states which promotes to overfitting global minima solutions. Consequently, this has a negative impact to the neural network models, especially when handling real-life optimization problems. Thus, a non-systematic Satisfiability was formulated to counter this problem, which believed to have introduce more diversification of solutions in the network. However, minimal improvement was obtained due to lack of investigation on the impact of different distribution of negative literals in Satisfiability provides. Most existing works focused on different composition of literals per clause. To fill this gap, the study of Weighted Random k Satisfiability is formulated with randomized literals and desired ratio of negative literals in the logic. Before the logic is being trained in Discrete Hopfield Neural Network, a logic phase is introduced to optimally generate the right structure of Weighted Random k Satisfiability by using Genetic Algorithm with respect to the desired ratio of negative literals. Additionally, the training phase of the Discrete Hopfield Neural Network embedded Genetic Algorithm to find satisfied assignments of the proposed logic that corresponds to optimal synaptic weight management. From the conducted experiments of different optimization algorithms, the findings show that the Genetic Algorithm outperforms other algorithms in both the logic and training phases. The quality of the retrieved final neuron states achieved acceptable results.

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References

  1. Kaveh A, Bakhshpoori T (2019) Metaheuristics: outlines, MATLAB codes and examples. Springer, Cham

    Book  Google Scholar 

  2. Chen Y, Yan J, Feng J, Sareh P (2021) Particle swarm optimization-based metaheuristic design generation of non-trivial flat-foldable origami tessellations with degree-4 vertices. J Mech Design 143(1):011703. https://doi.org/10.1115/1.4047437

    Article  Google Scholar 

  3. Mousavi SK, Ghaffari A (2021) Data cryptography in the Internet of Things using the artificial bee colony algorithm in a smart irrigation system. J Inf Secur Appl 61:102945. https://doi.org/10.1016/j.jisa.2021.102945

    Article  Google Scholar 

  4. Mallika C, Selvamuthukumaran S (2021) A hybrid crow search and grey wolf optimization technique for enhanced medical data classification in diabetes diagnosis system. Int J Comput Int Syst 14(1):1–18. https://doi.org/10.1007/s44196-021-00013-0

    Article  Google Scholar 

  5. Angulo A, Rodríguez D, Garzón W, Gómez DF, Sumaiti AA, Rivera S (2021) Algorithms for Bidding strategies in local energy markets: exhaustive search through parallel computing and metaheuristic optimization. Algorithms 14(9):269. https://doi.org/10.3390/a14090269

    Article  Google Scholar 

  6. Huang C, Li Y, Yao X (2019) A survey of automatic parameter tuning methods for metaheuristics. IEEE Trans Evolut Comput 24(2):201–216. https://doi.org/10.1109/TEVC.2019.2921598

    Article  Google Scholar 

  7. Dokeroglu T, Sevinc E, Kucukyilmaz T, Cosar A (2019) A survey on new generation metaheuristic algorithms. Comput Ind Eng 137:106040. https://doi.org/10.1016/j.cie.2019.106040

    Article  Google Scholar 

  8. Wolpert DH, Macready WG (1997) No free lunch theorems for optimization. IEEE Trans Evolut Comput 1(1):67–82. https://doi.org/10.1109/4235.585893

    Article  Google Scholar 

  9. Morales-Castañeda B, Zaldivar D, Cuevas E, Fausto F, Rodríguez A (2020) A better balance in metaheuristic algorithms: Does it exist? Swarm Evol Comput 54:100671. https://doi.org/10.1016/j.swevo.2020.100671

    Article  Google Scholar 

  10. Holland JH (1992) Adaptation in natural and artificial systems: an introductory analysis with applications to biology, control, and artificial intelligence. MIT Press, Cambridge

    Book  Google Scholar 

  11. Zhang W, He H, Zhang S (2019) A novel multi-stage hybrid model with enhanced multi-population niche genetic algorithm: an application in credit scoring. Expert Syst Appl 121:221–232. https://doi.org/10.1016/j.eswa.2018.12.020

    Article  Google Scholar 

  12. Zhi H, Liu S (2019) Face recognition based on genetic algorithm. J Vis Commun Image R 58:495–502. https://doi.org/10.1016/j.jvcir.2018.12.012

    Article  Google Scholar 

  13. Hamamoto AH, Carvalho LF, Sampaio LDH, Abrão T, Proença ML Jr (2018) Network anomaly detection system using genetic algorithm and fuzzy logic. Expert Syst Appl 92:390–402. https://doi.org/10.1016/j.eswa.2017.09.013

    Article  Google Scholar 

  14. Lamini C, Benhlima S, Elbekri A (2018) Genetic algorithm based approach for autonomous mobile robot path planning. Procedia Comput Sci 127:180–189. https://doi.org/10.1016/j.procs.2018.01.113

    Article  Google Scholar 

  15. Hosseinabadi AAR, Vahidi J, Saemi B, Sangaiah AK, Elhoseny M (2019) Extended genetic algorithm for solving open-shop scheduling problem. Soft Comput 2313:5099–5116. https://doi.org/10.1007/s00500-018-3177-y

    Article  Google Scholar 

  16. Kasihmuddin MSM, Mansor MA, Sathasivam S (2017) Hybrid genetic algorithm in the hopfield network for logic satisfiability problem. Pertanika J Sci Technol 25(1):139–152

    Google Scholar 

  17. Cook SA (1971) The complexity of theorem-proving procedure. In: Proceedings of the third annual ACM symposium on Theory of computing, pp 151–158. https://doi.org/10.1145/800157.805047.

  18. Abdullah WATW (1992) Logic programming on a neural network. Int J of Intell Syst 7(6):513–519. https://doi.org/10.1002/int.4550070604

    Article  Google Scholar 

  19. Sathasivam S (2010) Upgrading logic programming in Hopfield network. Sains Malays 39(1):115–118

    MATH  Google Scholar 

  20. Mansor MA, Kasihmuddin MSM, Sathasivam S (2017) Artificial immune system paradigm in the hopfield network for 3-satisfiability problem. Pertanika J Sci Technol 25(4):1173–1188

    Google Scholar 

  21. Sathasivam S, Mansor MA, Ismail AIM, Jamaludin SZM, Kasihmuddin MSM, Mamat M (2020) Novel random k satisfiability for k≤ 2 in hopfield neural network. Sains Malays 4(11):2847–2857

    Article  Google Scholar 

  22. Karim SA, Zamri NE, Alway A, Kasihmuddin MSM, Ismail AIM, Mansor MA, Hassan NFA (2021) Random satisfiability: a higher-order logical approach in discrete hopfield neural network. IEEE Access 9:50831–50845. https://doi.org/10.1109/ACCESS.2021.3068998

    Article  Google Scholar 

  23. Alway A, Zamri NE, Karim SA, Mansor MA, Kasihmuddin MSM, Bazuhair MM (2021) Major 2 satisfiability logic in discrete hopfield neural network international. J Comput Math 1:45. https://doi.org/10.1080/00207160.2021.1939870

    Article  MATH  Google Scholar 

  24. Fan W, Chen Y, Li J, Sun Y, Feng J, Hassanin H, Sareh P (2021) Machine learning applied to the design and inspection of reinforced concrete bridges: Resilient methods and emerging applications. In Structures 33:3954–3963. https://doi.org/10.1016/j.istruc.2021.06.110

    Article  Google Scholar 

  25. Sherstinsky A (2020) Fundamentals of recurrent neural network (RNN) and long short-term memory (LSTM) network. Physica D 404:132306. https://doi.org/10.1016/j.physd.2019.132306

    Article  MathSciNet  MATH  Google Scholar 

  26. Kasihmuddin MSM, Mansor MA, Basir MFM, Sathasivam S (2019) Discrete mutation Hopfield neural network in propositional satisfiability. Math 7(11):1133. https://doi.org/10.3390/math7111133

    Article  Google Scholar 

  27. Zamri NE, Mansor MA, Kasihmuddin MSM, Alway A, Jamaludin SZM, Alzaeemi SA (2020) Amazon employees resources access data extraction via clonal selection algorithm and logic mining approach. Entropy 22(6):596. https://doi.org/10.3390/e22060596

    Article  Google Scholar 

  28. Mansor MA, Kasihmuddin MSM, Sathasivam S (2019) Modified artificial immune system algorithm with Elliot Hopfield neural network for 3-satisfiability programming. J Inform Math Sci 11(1):81–98

    Google Scholar 

  29. Mansor MA, Sathasivam S (2021) Optimal performance evaluation metrics for satisfiability logic representation in discrete hopfield neural network. Comput Sci 16(3):963–976

    MathSciNet  MATH  Google Scholar 

  30. Dubois D, Godo L, Prade H (2014) Weighted logics for Artifi Int—an introductory discussion. Int J Approx Reason 55(9):1819–1829. https://doi.org/10.1016/j.ijar.2014.08.002

    Article  MATH  Google Scholar 

  31. Hopfield JJ, Tank DW (1985) “Neural” computation of decisions in optimization problems. Biol Cybern 52:141–152. https://doi.org/10.1007/BF00339943

    Article  MATH  Google Scholar 

  32. Sathasivam S, Hamadneh N, Choon OH (2011) Comparing neural networks: Hopfield network and RBF network. Appl Math Sci 5(69):3439–3452

    Google Scholar 

  33. Aly M, Ahmed EM, Shoyama M (2018) A new single-phase five-level inverter topology for single and multiple switches fault tolerance. IEEE Trans Power Electr 33(11):9198–9208. https://doi.org/10.1109/TPEL.2018.2792146

    Article  Google Scholar 

  34. Sahoo RC, Pradhan SK (2021) Pattern storage and recalling analysis of hopfield network for handwritten odia characters using HOG. In: Advances in machine learning and computational intelligence. Springer, Singapore, pp 467–476. https://doi.org/10.1007/978-981-15-5243-4_43

  35. Gosti G, Folli V, Leonetti M, Ruocco G (2019) Beyond the maximum storage capacity limit in Hopfield recurrent neural networks. Entropy 21(8):726. https://doi.org/10.3390/e21080726

    Article  MathSciNet  Google Scholar 

  36. Mansor MA, Sathasivam S (2016) Accelerating activation function for 3-satisfiability logic programming. Int J Intel Syst Appl 8:44–50. https://doi.org/10.5815/ijisa.2016.10.05

    Article  Google Scholar 

  37. Bruck J, Goodman JW (1988) A generalized convergence theorem for neural networks. IEEE Trans Inform Theory 34(5):1089–1092. https://doi.org/10.1109/18.21239

    Article  MathSciNet  MATH  Google Scholar 

  38. Mirjalili S (2019) Evolutionary algorithms and neural networks. In: Studies in computational intelligence. Springer, vol 780.

  39. Katoch S, Chauhan SS, Kumar V (2021) A review on genetic algorithm: past present and future. Multimed Tools Appl 80(5):8091–8126. https://doi.org/10.1007/s11042-020-10139-6

    Article  Google Scholar 

  40. Hussain K, Salleh MNM, Cheng S, Shi Y (2019) Metaheuristic research: a comprehensive survey. Artifi Int Rev 52(4):2191–2233. https://doi.org/10.1007/s10462-017-9605-z

    Article  Google Scholar 

  41. Hiassat A, Diabat A, Rahwan I (2017) A genetic algorithm approach for location-inventory-routing problem with perishable products. J Manuf Syst 42:93–103. https://doi.org/10.1016/j.jmsy.2016.10.004

    Article  Google Scholar 

  42. Bouhmala N, Øvergård KI (2018) Combining genetic algorithm with variable neighborhood search for MAX-SAT. In: Innovative computing optimization and its applications. Springer, Cham, pp 73–92. https://doi.org/10.1007/978-3-319-66984-7_5

  43. Črepinšek M, Liu SH, Mernik M (2013) Exploration and exploitation in evolutionary algorithms: a survey. ACM Comput Surv (CSUR) 45(3):1–33. https://doi.org/10.1145/2480741.2480752

    Article  MATH  Google Scholar 

  44. Lin WY, Lee WY, Hong TP (2003) Adapting crossover and mutation rates in genetic algorithms. J Inf Sci Eng 19(5):889–903

    Google Scholar 

  45. Kaveh M, Kaveh M, Mesgari MS, Paland RS (2020) Multiple criteria decision-making for hospital location-allocation based on improved genetic algorithm. Appl Geomat 12(3):291–306. https://doi.org/10.1007/s40747-019-0102-7

    Article  Google Scholar 

  46. Karaboga D, Basturk B (2007) A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithm. J Global Optim 39(3):459–471

    Article  MathSciNet  Google Scholar 

  47. Kasihmuddin MSM, Mansor MA, Sathasivam S (2017) Robust artificial bee colony in the hopfield network for 2-satisfiability problem. Pertanika J Sci Technol 25(2):453–468

    Google Scholar 

  48. Kennedy J, Eberhart R (1995) Particle swarm optimization. In: Proceedings of ICNN'95-international conference on neural networks. IEEE, vol 4, pp 1942–1948. https://doi.org/10.1109/ICNN.1995.488968.

  49. Li G, Wang W, Zhang W, Wang Z, Tu H, You W (2021) Grid search based multi-population particle swarm optimization algorithm for multimodal multi-objective optimization. Swarm Evol Comput 62:100843. https://doi.org/10.1016/j.swevo.2021.100843

    Article  Google Scholar 

  50. Mirjalili S, Mirjalili SM (2014) A Lewis Grey wolf optimizer. Adv Eng Softw 69:46–61. https://doi.org/10.1016/j.advengsoft.2013.12.007

    Article  Google Scholar 

  51. Mansor MA, Kasihmuddin MSM, Sathasivam S (2021) Grey wolf optimization algorithm with discrete hopfield neural network for 3 Satisfiability analysis. J Phys Conf Ser IOP Publ 1821(1):012038. https://doi.org/10.1088/1742-6596/1821/1/012038

    Article  Google Scholar 

  52. Srinivas M, Patnaik LM (1994) Genetic algorithms: a survey. Computer 27(6):17–26. https://doi.org/10.1109/2.294849

    Article  Google Scholar 

  53. Karaboga D (2005) An idea based on honey bee swarm for numerical optimization. Technical report-tr06, Erciyes university, engineering faculty, computer engineering department, vol 200 pp 1-10

  54. Piotrowski AP, Napiorkowski JJ, Piotrowska AE (2020) Population size in particle swarm optimization. Swarm Evol Comput 58:100718. https://doi.org/10.1016/j.swevo.2020.100718

    Article  Google Scholar 

  55. Moldovan D, Slowik A (2021) Energy consumption prediction of appliances using machine learning and multi-objective binary grey wolf optimization for feature selection. Appl Soft Comput 111:107745. https://doi.org/10.1016/j.asoc.2021.107745

    Article  Google Scholar 

  56. Sathasivam S, Mansor MA, Kasihmuddin MSM, Abubakar H (2020) Election algorithm for random k satisfiability in the hopfield neural network. Processes 8(5):568. https://doi.org/10.3390/pr8050568

    Article  Google Scholar 

  57. Kho LC, Kasihmuddin MSM, Mansor MA, Sathasivam S (2020) Logic mining in league of legends. Pertanika J Sci Technol 28(1):211–225

    Google Scholar 

  58. Gower JC, Legendre P (1986) Metric and Euclidean properties of dissimilarity coefficients. J Classif 3(1):5–48. https://doi.org/10.1007/BF01896809

    Article  MathSciNet  MATH  Google Scholar 

  59. Bazuhair MM, Jamaludin SZM, Zamri NE, Kasihmuddin MSM, Mansor MA, Alway A, Karim SA (2021) Novel hopfield neural network model with election algorithm for random 3 satisfiability. Processes 9(8):1292. https://doi.org/10.3390/pr9081292

    Article  Google Scholar 

  60. Zhang C, Wang X, Chen S, Li H, Wu X, Zhang X (2021) A modified random forest based on kappa measure and binary artificial bee colony algorithm. IEEE Access 9:117679–117690. https://doi.org/10.1109/ACCESS.2021.3105796

    Article  Google Scholar 

  61. Kumari K, Singh JP, Dwivedi YK, Rana NP (2021) Multi-modal aggression identification using convolutional neural network and binary particle swarm optimization. Fut Gener Comp Syst 118:187–197. https://doi.org/10.1016/j.future.2021.01.014

    Article  Google Scholar 

  62. Kumar N, Kumar D (2021) An improved grey wolf optimization-based learning of artificial neural network for medical data classification. J Inf Commun Technol 20(2):213–248. https://doi.org/10.32890/jict2021.20.2.4

    Article  Google Scholar 

  63. Pattanayak P, Sarmah D, Paritosh P (2020) Low complexity based scheduling methods for multi-user MIMO systems. Phys Commun 43:101192. https://doi.org/10.1016/j.phycom.2020.101192

    Article  Google Scholar 

  64. Singh N (2020) A modified variant of grey wolf optimizer. Sci Iran 27(3):1450–1466. https://doi.org/10.24200/SCI.2018.50122.1523

    Article  Google Scholar 

  65. Teng ZJ, Lv JL, Guo LW (2019) An improved hybrid grey wolf optimization algorithm. Soft Comput 23(15):6617–6631. https://doi.org/10.1007/s00500-018-3310-y

    Article  Google Scholar 

  66. Gao Y (2009) Data reductions fixed parameter tractability and random weighted d-CNF satisfiability. Artif Int 173(14):1343–1366. https://doi.org/10.1016/j.artint.2009.06.005

    Article  MathSciNet  MATH  Google Scholar 

  67. Kiran MS (2021) A binary artificial bee colony algorithm and its performance assessment. Expert Syst Appl 175:114817. https://doi.org/10.1016/j.eswa.2021.114817

    Article  Google Scholar 

  68. Joya G, Atencia MA, Sandoval FF (2002) Hopfield neural networks for optimization: study of the different dynamics. Neurocomputing 43(1–4):219–237. https://doi.org/10.1016/S0925-2312(01)00337-X

    Article  MATH  Google Scholar 

  69. Chen HW, Liang CK (2022) Genetic algorithm versus discrete particle swarm optimization algorithm for energy-efficient moving object coverage using mobile sensors. Appl Sci 12(7):3340. https://doi.org/10.3390/app12073340

    Article  Google Scholar 

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Acknowledgements

All the authors gratefully acknowledge the financial support from the Ministry of Education Malaysia for the Transdisciplinary Research Grant Scheme (TRGS) and Universiti Sains Malaysia.

Funding

This research was supported by Ministry of Higher Education Malaysia for Transdisciplinary Research Grant Scheme (TRGS) with Project Code: TRGS/1/2020/USM/02/3/2.

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Authors and Affiliations

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

    Nur Ezlin Zamri & Mohd Asyraf Mansor

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

    Siti Aishah Azhar, Siti Syatirah Muhammad Sidik, Mohd Shareduwan Mohd Kasihmuddin, Siti Pateema Azeyan Pakruddin, Nurul Atirah Pauzi & Siti Nurhidayah Mat Nawi

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  1. Nur Ezlin Zamri
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Contributions

Nur Ezlin Zamri: Conceptualization, Software, Project Administration. Siti Aishah Azhar: Formal Analysis, Writing—Original Draft. Siti Syatirah Muhammad Sidik: Writing—Review and Editing. Siti Pateema Azeyan Pakruddin: Methodology. Nurul Atirah Pauzi: Investigation. Siti Nurhidayah Mat Nawi: Visualization. Mohd Shareduwan Mohd Kasihmuddin: Supervision. Mohd. Asyraf Mansor: Validation, Funding Acquisition. All authors have read and agreed to the published version of the manuscript.

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Zamri, N.E., Azhar, S.A., Sidik, S.S.M. et al. Multi-discrete genetic algorithm in hopfield neural network with weighted random k satisfiability. Neural Comput & Applic 34, 19283–19311 (2022). https://doi.org/10.1007/s00521-022-07541-6

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