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
Full Text (PDF, 304KB), PP.27-33
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
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.
J. J. Hopfield, D. W. Tank, Neural computation of decisions in optimization problem, Biological Cybernatics, 52, 141-152, 1985.
S. Haykin, Neural Networks: A Comprehensive Foundation, New York: Macmillan College Publishing, 1999.
W.A.T. Wan Abdullah, Logic Programming on a Neural Network. Malaysian Journal of computer Science, 9 (1), 1-5, 1993.
T. Larabee, Test pattern generation using Boolean satisfiability, IEEE Transaction on Computer Aided Design, 11(1), 4-15, 1992.
S. Sathasivam, Energy Relaxation for Hopfield Network with the New Learning Rule, International Conference on Power Control and Optimization, 1-5, 2009.
C. Rene & L. Daniel, Mathematical Logic: Propositional Calculus, Boolean Algebras, Predicate Calculus, United Kingdom: Oxford University Press, 2000.
V. Sivaramakhrisnan, C. S. Sharath, & P. Agrawal, Parallel test pattern generation using Boolean satisfiability, IEEE Int. Symposium on VLSI design, 69-74, 1991.
G. Pinkas, R. Dechter, Improving energy connectionist energy minimization, Journal of Artificial Intelligence Research, 3, 223-15, 1995.
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.
M. Velavan, Boltzman Machine and Hyperbolic Activation Function in Higher Order Network, 9 (2), 140-146, 2014.
R.A. Kowalski, Logic for Problem Solving. New York: Elsevier Science Publishing, 1979.
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.
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.
S. Sathasivam, P.F. Ng, N. Hamadneh, Developing agent based modelling for reverse analysis method, 6 (22), 4281-4288, 2013.
R. Rojas, Neural Networks: A Systematic Introduction. Berlin: Springer, 1996.
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.
F. A. Aloul, A. Sagahyroon, Using SAT-Based Techniques in Test Vectors Generation, Journal of Advance in Information Technology, 1 (4), 153-162, 2010.
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.
A. Cimatti, M. Roveri, Bertoli. P, Conformant planning via symbolic model checking and heuristic search, Artificial Intelligence, 159 (1), 127-206, 2004..
U. Aiman and N. Asrar, Genetic algorithm based solution to SAT-3 problem, Journal of Computer Sciences and Applications, 3, 33-39, 2015.
B. Tobias and K. Walter, An improved deterministic local search algorithm for 3-SAT, Theoretical Computer Science 329, 303-313, 2004.
D. Vilhelm, J. Peter, & W. Magnus, Counting models for 2SAT and 3SAT formulae. Theoretical Computer Science, 332 (1), 265-291, 2005.
J. Gu, Local Search for Satisfiability (SAT) Problem, IEEE Transactions on Systems, Man and Cybernetics, vol. 23 pp. 1108-1129, 1993.
N. Siddique, H. Adeli, Computational Intelligence Synergies of Fuzzy Logic, Neural Network and Evolutionary Computing. United Kingdom: John Wiley and Sons, 2013.
B. Sebastian, H. Pascal and H. Steffen, Connectionist model generation: A first-order approach, Neurocomputing, 71(13), 2420-2432, 2008.
S. Sathasivam, Upgrading Logic Programming in Hopfield Network, Sains Malaysiana, 39, 115-118, 2010.