Optimal representation to High Order Random Boolean kSatisability via Election Algorithm as Heuristic Search Approach in Hopeld Neural Networks



  • Hamza Abubakar School of Mathematical Sciences, Universiti Sains Malaysia
  • Abdu Sagir Masanawa Department of Mathematical Sciences, Federal Uniersity Dutsin-Ma, Katsina, Nigeria
  • Surajo Yusuf Department of Mathematical Sciences, Federal Uniersity Dutsin-Ma, Katsina, Nigeria
  • G. I. Boaku Department of Mathematical Sciences, Federal Uniersity Dutsin-Ma, Katsina, Nigeria


Hopfield neural network, Election algorithm, Boolean satisfiability, Random kSatisfiability


This study proposed a hybridization of higher-order Random Boolean kSatisfiability (RANkSAT) with the Hopfield neural network (HNN) as a neuro-dynamical model designed to reflect knowledge efficiently. The learning process of the Hopfield neural network (HNN) has undergone significant changes and improvements according to various types of optimization problems. However, the HNN model is associated with some limitations which include storage capacity and being easily trapped to the local minimum solution. The Election algorithm (EA) is proposed to improve the learning phase of HNN for optimal Random Boolean kSatisfiability (RANkSAT) representation in higher order. The main source of inspiration for the Election Algorithm (EA) is its ability to extend the power and rule of political parties beyond their borders when seeking endorsement. The main purpose is to utilize the optimization capacity of EA to accelerate the learning phase of HNN for optimal random k Satisfiability representation. The global minima ratio (mR) and statistical error accumulations (SEA) during the training process were used to evaluate the proposed model performance. The result of this study revealed that our proposed EA-HNN-RANkSAT outperformed ABC-HNN-RANkSAT and ES-HNN-RANkSAT models in terms of mR and SEA.This study will further be extended to accommodate a novel field of Reverse analysis (RA) which involves data mining techniques to analyse real-life problems. 


W. A. T. W. Abdullah, “Logic programming on a neural network”, International journal of intelligent systems 7 (1992) 513. DOI: https://doi.org/10.1002/int.4550070604

H. Abubakar, S. A. Mmasanwa, S. Yusuf & Y. Abdurrahman, “Agent Based Computational Modelling For Mapping Of Exact Ksatisfiability Representation In Hopfield Neural Network Model”, International Journal of Scientific and Technology Research 9 (2020) 76.

H. Abubakar, S. R. M. Sabri, S. A. Masanawa & S. Yusuf, “Modified election algorithm in hopfield neural network for optimal random k satisf iability representation”, International Journal for Simulation and Multidisciplinary Design Optimization 11 (2020) 16. DOI: https://doi.org/10.1051/smdo/2020008

H. Abubakar & S. Sathasivam, “Developing random satisfiability logic programming in Hopfield neural network”, AIP Conference Proceedings, AIP Publishing LLC 2266 (2020). DOI: https://doi.org/10.1063/5.0018058

H. Abubakar, S. Sathasivam & S. A. Alzaeemi, “Effect of negative campaign strategy of election algorithm in solving optimization problem”, Journal of Quality Measurement and Analysis JQMA 16 (2020) 171.

H. Abubakar, S. Yusuf & S. A. Masanwa, “Exploring the Feasibility of Integrating Random k-Satisfiability in Hopfield Neural Network”, International Journal of Modern Mathematical Sciences 18 (2020) 92.

D. Achli optas, Random satisfiability, IOS press 185 (2009) 245.

B.U.Ayhan&O.B.Tokdemir,“Accidentanalysis for construction safety using latent class clustering and artificial neural networks”, Journal of Construction Engineering and Management 146 (2020) 1. DOI: https://doi.org/10.1061/(ASCE)CO.1943-7862.0001762

A. Biere, M. Heule & H. van Maaren, Handbook of satisfiability, IOS press 185 (2009).

H. Emami, “Chaotic election algorithm”, Computing and Informatics 38 (2019) 1444. DOI: https://doi.org/10.31577/cai_2019_6_1444

H.Emami&F.Derakhshan, “Election algorithm: A new socio-politically inspired strategy”, AI Communications 28 (2015) 591. DOI: https://doi.org/10.3233/AIC-140652

S. Emami, Y. Choopan & J. Parsa, “Modeling the Groundwater Level of the MiandoabPlain Using Artificial Neural Network Method and Election and Genetic Algorithms”, Iranian journal of Ecohydrology 5 (2018) 1175.

V.Feldman, W.Perkins &S.Vempala, “Onthecomplexityof randomsatisfiability problems with planted solutions”, SIAM Journal on Computing 47 (2018) 1294. DOI: https://doi.org/10.1137/16M1078471

J. Heo, J. G. Yoon, H. Park, Y. D. Kim, H. S. Nam & J. H. Heo, “Machine learning–based model for prediction of outcomes in acute stroke”, Stroke 50 (2019) 1263. DOI: https://doi.org/10.1161/STROKEAHA.118.024293

J. J. Hopfield, “Neural networks and physical systems with emergent collective computational abilities”, Proceedings of the national academy of sciences 79 (1982) 2554. DOI: https://doi.org/10.1073/pnas.79.8.2554

Z. Meng, X. Guo, Z. Pan, D. Sun & S. Liu, “Data segmentation and augmentation methods based on raw data using deep neural networks approach for rotating machinery fault diagnosis”, IEEE Access 7 (2019) 79510. DOI: https://doi.org/10.1109/ACCESS.2019.2923417

C. R. Rahman, P. S. Arko, M. E. Ali, M. A. I. Khan, S. H. Apon, F. Nowrin & A. Wasif, “Identification and recognition of rice diseases and pests using convolutional neural networks” Biosystems Engineering 194 (2020) 112. DOI: https://doi.org/10.1016/j.biosystemseng.2020.03.020

F. Sarafa, A. Souri & M. Serrizadeh, “Improved intrusion detection method for communication networks using association rule mining and artificial neural networks”, IET Communications 14 (2020) 1192. DOI: https://doi.org/10.1049/iet-com.2019.0502

S. Sathasivam, “Upgrading logic programming in Hopfield network”, Sains Malaysiana 39 (2010) 115. DOI: https://doi.org/10.1109/ICCTD.2009.52

S. Sathasivam, M. Mohd, M. S. M. Kasihmuddin & H. Abubakar, “Election algorithm for random k satisfiability in the Hopfield neural network”, Processes 8 (2020) 568. DOI: https://doi.org/10.3390/pr8050568

A. Wanto, A. P. Windarto, D. Hartama & I. Parlina, “Use of binary sigmoid function and linear identity in artificial neural networks for forecasting population density”,IJISTECH (International Journal of Information System & Technology) 1 (2017) 43. DOI: https://doi.org/10.30645/ijistech.v1i1.6



How to Cite

Abubakar, H., Masanawa, A. S., Yusuf, S., & Boaku, G. I. (2021). Optimal representation to High Order Random Boolean kSatisability via Election Algorithm as Heuristic Search Approach in Hopeld Neural Networks. Journal of the Nigerian Society of Physical Sciences, 3(3), 201–208. https://doi.org/10.46481/jnsps.2021.217



Original Research