Structural Engineering and Mechanics

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Hopfield neuron based nonlinear constrained programming to fuzzy structural engineering optimization

  • Shih, C.J. (Department of Mechanical Engineering, Tamkang University) ;
  • Chang, C.C. (Department of Mechanical Engineering, Tamkang University)
  • Published : 1999.05.25
⟨ Previous Next ⟩

Abstract

Using the continuous Hopfield network model as the basis to solve the general crisp and fuzzy constrained optimization problem is presented and examined. The model lies in its transformation to a parallel algorithm which distributes the work of numerical optimization to several simultaneously computing processors. The method is applied to different structural engineering design problems that demonstrate this usefulness, satisfaction or potential. The computing algorithm has been given and discussed for a designer who can program it without difficulty.

Keywords

References

  1. Carpenter, W.C. and Smith, E.A. (1977), "Computational efficiency of nonlinear programming methods on a class of structural problems", Int . J. Num. Meth. Eng., 1, 1203-1223.
  2. Cohen, M.A. and Grossberg, S. (1983), "Absolute stability of global formation and parallel memory storage by competitive neural networks", IEEE Transactions on Systems, Man, and Cybernetics, 13(5), 815-826.
  3. Dhingra, A.K. and Rao, S.S. (1992), "A neural network based approach to mechanical design optimization", Engineering Optimization, 20, 187-203. https://doi.org/10.1080/03052159208941280
  4. Fleury, C (1989), "First and second order convex approximation strategies in structural optimization", Strm:tural Optimization, 1, 3-10. https://doi.org/10.1007/BF01743804
  5. Grossberg, S. (1980), "How does a brain build a cognitive code?", Psychological Review, 87, 1-51. https://doi.org/10.1037/0033-295X.87.1.1
  6. Grossberg, S. (1987), The Adaptive Brains, II: Vision, Speech, Language, and Motor Control, NorthHolland, Amsterdam.
  7. Grossberg, S. (1988), Eds., "How does a brain build a cognitive code?", Psychological Review, 87, 1-51.
  8. Hajela, P. and Shih, C.J. (1990), "Muitiobjective optimum design in mixed integer and discrete design variable problems", AIAA Journal, 25(4), 670-675.
  9. Hebb, D.O. (1949), "The first stage of perception: growth of the assembly", The Organization of Behavior, Wiley, New York, 60-78.
  10. Hopfield , J.J. (1982), "Neural networks and physical systems with emergent collective computational abilities", Proceedings of the National Academy of Sciences USA, 79, 2554-2558. https://doi.org/10.1073/pnas.79.8.2554
  11. Hopfield, J.J. (1984), "Neurons with graded response have collective computational properties like those of two-state neurons", Proceedings of the National Academy of Sciences USA, 81, 3088-3092. https://doi.org/10.1073/pnas.81.10.3088
  12. Hopfield, J.J. and Tank, D.W. (1985), "Neural' computation of decision in optimization problems", Biological Cybernetics, 52, 141-152.
  13. Kohonen, T. (1982), "Self-organized formation of topologically correct feature maps", Biological Cybernetics, 43, 59-62. https://doi.org/10.1007/BF00337288
  14. Kohonen, T. (1988), Self-Organization and Associative Memory, Series in Information Sciences, 8, Spring-Verlag, 2nd ed.
  15. Mcclelland, J.L. and Rumelhart, D.E. (1981), "An interative activation model of context effects in letter perception: Part 1. An account of basic findings", Psychological Review, 88, 375-407. https://doi.org/10.1037/0033-295X.88.5.375
  16. Mcclelland, J.L. and Rumelhart, D.E. (1982), "An interative activation model of context effects in letter perception: Part 2. The contextual enhancement effects and some tests and extensions of the model", Psychological Review, 89, 60-94. https://doi.org/10.1037/0033-295X.89.1.60
  17. Mcclelland, J.L. and Rumelhart, D.E., Eds. (1986), Parallel Distributed Processing: Explorations in the Microstructures of Cognitions, 1, MIT Press, MA.
  18. Mcclelland, J.L. and Rumelhart, D.E., Eds. (1986), Parallel Distributed Processing: Explorations in the Microstructures of Cognitions, 2, MIT Press, MA.
  19. Rao, S.S. (1987), "Multi-objective optimization of fuzzy structural systems", Int. J. for Numerical Methods in Eng., 24, 1157-1171. https://doi.org/10.1002/nme.1620240608
  20. Rosenblatt, F. (1958), "The ferceptron : A prohahilistic model for information storage and organization in the brain", Psychological Review, 65, 386. https://doi.org/10.1037/h0042519
  21. Rumelhart, D.E., Hinton, G.E. and Williams, R.J. (1986), "Learning representations by backpropagating errors", Nature, 323, 533-536. https://doi.org/10.1038/323533a0
  22. Shih, C.J. and Lai, T.K. (1994), "Fuzzy weighting optimization with several objective functions in structural design", Computers and Structures, 52(5), 917-924. https://doi.org/10.1016/0045-7949(94)90076-0
  23. Tank, D.W. and Hopfield, J.J. (1986), "Simple neural optimization networks: An A/D converter, signal decision network, and a linear programming circuit", IEEE Transaction on Circuits and Systems, CAS-33(5), 533-541.
  24. Vanderplaats, G.N. (1984), Numerical Optimization Techniques for Engineering Design, McGraw-Hill, New York.
  25. Widrow, B. and Hof, M.E. (1960), "An adaptive switching circuits", IRE WESCON Convention Record, IRE, New York, 96-104.
  26. Zhang, C.-X. and Mylinski, D.A. (1990), "VLSI placement with a neural network model", IEEE International Symposium on Circuits and Systems, New Orleans, May.

Cited by

  1. Generalized Hopfield network based structural optimization using sequential unconstrained minimization technique with additional penalty strategy vol.33, pp.7-10, 2002, https://doi.org/10.1016/S0965-9978(02)00060-1