International Journal of Intelligent Systems and Applications(IJISA)

ISSN: 2074-904X (Print), ISSN: 2074-9058 (Online)

Published By: MECS Press

IJISA Vol.8, No.11, Nov. 2016

Enhanced Hopfield Network for Pattern Satisfiability Optimization

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Mohd. Asyraf Mansor, Mohd Shareduwan M. Kasihmuddin, Saratha Sathasivam

Index Terms

Pattern-SAT;Hopfield Network;3-Satisfiability;Hyperbolic Tangent Activation Function;McCulloch-Pitts Function


Highly-interconnected Hopfield network with Content Addressable Memory (CAM) are shown to be extremely effective in constraint optimization problem. The emergent of the Hopfield network has producing a prolific amount of research. Recently, 3 Satisfiability (3-SAT) has becoming a tool to represent a variety combinatorial problems. Incorporated with 3-SAT, Hopfield neural network (HNN-3SAT) can be used to optimize pattern satisfiability (Pattern-SAT) problem. Hence, we proposed the HNN-3SAT with Hyperbolic Tangent activation function and the conventional McCulloch-Pitts function. The aim of this study is to investigate the accuracy of the pattern generated by our proposed algorithms. Microsoft Visual C++ 2013 is used as a platform for training, testing and validating our Pattern-SAT design. The detailed performance of HNN-3SAT of our proposed algorithms in doing Pattern-SAT will be discussed based on global pattern-SAT and running time. The result obtained from the simulation demonstrate the effectiveness of HNN-3SAT in doing Pattern-SAT.

Cite This Paper

Mohd. Asyraf Mansor, Mohd Shareduwan M. Kasihmuddin, Saratha Sathasivam,"Enhanced Hopfield Network for Pattern Satisfiability Optimization", International Journal of Intelligent Systems and Applications(IJISA), Vol.8, No.11, pp.27-33, 2016. DOI: 10.5815/ijisa.2016.11.04


[1]S. Kumar & M. P. Singh, Pattern recall analysis of the Hopfield network with a genetic algorithm, Computer and Mathematic with Applications, 60, 1049-1057, 2010.

[2]J. J. Hopfield, D. W. Tank, Neural computation of decisions in optimization problem, Biological Cybernatics, 52, 141-152, 1985.

[3]S. Haykin, Neural Networks: A Comprehensive Foundation, New York: Macmillan College Publishing, 1999.

[4]W.A.T. Wan Abdullah, Logic Programming on a Neural Network. Malaysian Journal of computer Science, 9 (1), 1-5, 1993.

[5]T. Larabee, Test pattern generation using Boolean satisfiability, IEEE Transaction on Computer Aided Design, 11(1), 4-15, 1992.

[6]S. Sathasivam, Energy Relaxation for Hopfield Network with the New Learning Rule, International Conference on Power Control and Optimization, 1-5, 2009.

[7]C. Rene & L. Daniel, Mathematical Logic: Propositional Calculus, Boolean Algebras, Predicate Calculus, United Kingdom: Oxford University Press, 2000.

[8]V. Sivaramakhrisnan, C. S. Sharath, & P. Agrawal, Parallel test pattern generation using Boolean satisfiability, IEEE Int. Symposium on VLSI design, 69-74, 1991.

[9]G. Pinkas, R. Dechter, Improving energy connectionist energy minimization, Journal of Artificial Intelligence Research, 3, 223-15, 1995.

[10]K. Bekir and A. O. Vehbi, Performance analysis of various activation functions in generalized MLP architectures of neural network. International Journal of Artificial Intelligence and Expert Systems 1(4), 111-122, 2010.

[11]M. Velavan, Boltzman Machine and Hyperbolic Activation Function in Higher Order Network, 9 (2), 140-146, 2014.

[12]R.A. Kowalski, Logic for Problem Solving. New York: Elsevier Science Publishing, 1979.

[13]A. Nag, S. Biswas, D. Sarkar, P. P. Sarkar & B. Gupta, A simple feature extraction technique of a pattern by Hopfield network, International Journal of Advancements in Technology, 45-49, 2000.

[14]C. Ramya, G. Kavitha, & K. S. Shreedhara, Recalling of images using Hopfield network model, Proceeding for National Conference on Computers, Communication and Control 11, 2011.

[15]S. Sathasivam, P.F. Ng, N. Hamadneh, Developing agent based modelling for reverse analysis method, 6 (22), 4281-4288, 2013.

[16]R. Rojas, Neural Networks: A Systematic Introduction. Berlin: Springer, 1996.

[17]R. Puff, J. Gu, A BDD SAT solver for satisfiability testing: An industrial case study, Annals of Mathematics and Artificial Intelligence, 17 (2), 315-337, 1996.

[18]F. A. Aloul, A. Sagahyroon, Using SAT-Based Techniques in Test Vectors Generation, Journal of Advance in Information Technology, 1 (4), 153-162, 2010.

[19]T. A. Junttila, I. Niemela, Towards an efficient tableau method for Boolean circuit satisfiability checking, in Computational Logic-CL 2000, Berlin, Heidelberg: Springer, 553-567, 2000.

[20]A. Cimatti, M. Roveri, Bertoli. P, Conformant planning via symbolic model checking and heuristic search, Artificial Intelligence, 159 (1), 127-206, 2004..

[21]U. Aiman and N. Asrar, Genetic algorithm based solution to SAT-3 problem, Journal of Computer Sciences and Applications, 3, 33-39, 2015.

[22]B. Tobias and K. Walter, An improved deterministic local search algorithm for 3-SAT, Theoretical Computer Science 329, 303-313, 2004.

[23]D. Vilhelm, J. Peter, & W. Magnus, Counting models for 2SAT and 3SAT formulae. Theoretical Computer Science, 332 (1), 265-291, 2005.

[24]J. Gu, Local Search for Satisfiability (SAT) Problem, IEEE Transactions on Systems, Man and Cybernetics, vol. 23 pp. 1108-1129, 1993.

[25]N. Siddique, H. Adeli, Computational Intelligence Synergies of Fuzzy Logic, Neural Network and Evolutionary Computing. United Kingdom: John Wiley and Sons, 2013.

[26]B. Sebastian, H. Pascal and H. Steffen, Connectionist model generation: A first-order approach, Neurocomputing, 71(13), 2420-2432, 2008.

[27]S. Sathasivam, Upgrading Logic Programming in Hopfield Network, Sains Malaysiana, 39, 115-118, 2010.