Boltzmann machines and their applications

  • Emile H. L. Aarts
  • Jan H. M. Korst
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 258)


In this paper we present a formal model of the Boltzmann machine and a discussion of two different applications of the model, viz. (i) solving combinatorial optimization problems and (ii) carrying out learning tasks. Numerical results of computer simulations are presented to demonstrate the characteristic features of the Boltzmann machine.


Boltzmann machines simulated annealing combinatorial optimization learning 


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  1. [1]
    Aarts, E.H.L. and P.J.M. van Laarhoven, Statistical Cooling: A General Approach to Combinatorial Optimization Problems, Philips Journ. Res., 40(1985)193.Google Scholar
  2. [2]
    Aarts, E.H.L. and J.H.M. Korst, Simulation of Learning in Parallel Networks Based on the Boltzmann Machine, Proc. 2nd Eur. Simul. Congr., Antwerp, September 1986, p. 391.Google Scholar
  3. [3]
    Aarts, E.H.L. and J.H.M. Korst, Solving Traveling Salesman Problems with a Boltzmann Machine, The European Journal of Operations Research, to be submitted.Google Scholar
  4. [4]
    Ackley, D.H., G.E. Hinton and T.J. Sejnowski, A Learning Algorithm for Boltzmann Machines, Cognitive Science, 9(1985)147.Google Scholar
  5. [5]
    Feldman, J.A. and D.H. Ballard, Connectionist Models and Their Properties, Cognitive Science, 6(1982)205.Google Scholar
  6. [6]
    Fahlman, S.E., G.E. Hinton and T.J. Sejnowski, Massively Parallel Architectures for AI: NETL, Thistle and Boltzmann Machines, Proc. Nat. Conf. on AI, AAAI-83, August 1983, p. 109.Google Scholar
  7. [7]
    Fahlman, S.E and G.E. Hinton, Connectionist Architectures for Artificial Intelligence, Computer, January, 1987, p. 100.Google Scholar
  8. [8]
    Garfinkel, R.S., Motivation and Modeling, in: E.L. Lawler, J.K. Lenstra, A.H.G. Rinnooy Kan and D.B. Shmoys (eds.), The Traveling Salesman Problem, Wiley, Chichester, 1985, p. 17.Google Scholar
  9. [9]
    Hillis, W.D., The Connection Machine, MIT-press, Cambridge (MA), 1985.Google Scholar
  10. [10]
    Hinton G.E. and T.J. Sejnowski, Optimal Perceptual Inference, Proc. IEEE Conf. on Computer Vision and Pattern Recognition, Washington DC, June 1983, p. 448.Google Scholar
  11. [11]
    Hinton, G.E., T.J. Sejnowski and D.H. Ackley, Boltzmann Machines: Constraint Satisfaction Machines that Learn, Tech. Rep. CMU-CS-84-119, Carnegie-Mellon University, 1984.Google Scholar
  12. [12]
    Hopfield, J.J., Neural Networks and Physical Systems with Emergent Collective Computational Abilities, Proc. Nat. Academy Sciences, USA, 79(1982)2554.Google Scholar
  13. [13]
    Hopfield, J.J. and D.W. Tank, Neural Computational of Decisions in Optimization Problems, Biological Cybernetics, 52(1985)141.Google Scholar
  14. [14]
    Kirkpatrick, S., C.D. Gelatt Jr. and M.P. Vecchi, Optimization by Simulated Annealing, Science, 220(1983)671.Google Scholar
  15. [15]
    Korst, J.H.M. and E.H.L. Aarts, Solving Combinatorial Optimization Problems with Massively Parallel Computer Architectures Based on the Boltzmann Machine, Operations Research, to be submitted.Google Scholar
  16. [16]
    Kullbach, S., Information Theory and Statistics, Wiley, New York, 1959.Google Scholar
  17. [17]
    Laarhoven, P.J.M. van and E.H.L. Aarts, Simulated Annealing: Theory and Applications, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1987, in press.Google Scholar
  18. [18]
    Prager R.G. et al., Boltzmann Machines for Speech Recognition, Computer Speech and Language, Vol. 1, 1986.Google Scholar
  19. [19]
    Proceedings NASI on Pattern Recognition: Theory and Applications, P.A. DeVijver and J. Kittler (eds.), Springer, 1987 (and references therein).Google Scholar
  20. [20]
    Sejnowski, T.J. and C.R. Rosenberg, NETtalk: A Parallel Network that Learns to Speak Aloud, John Hopkins University, Technical Report, JHU/EECS-86/01, 1986.Google Scholar
  21. [21]
    Stevens, J.K., Reverse Engineering the Brain, Byte, 10(4)(1985)287.Google Scholar
  22. [22]
    Traherne, J.F. et al., Speech Processing with a Boltzmann Machine, Proc. IEEE ICASSP-86, Tokyo, 1986, p. 725.Google Scholar
  23. [23]
    Treleaven, P.C., A.N. Refenes, K.J. Lees and S.C. McCabe, Computer Architectures for Artificial Intelligence, Lecture Notes, University of Reading, Reading, 1985.Google Scholar
  24. [24]
    Waldrop, M.M., Artificial Intelligence in Parallel, Science, 225(1985)608.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1987

Authors and Affiliations

  • Emile H. L. Aarts
    • 1
  • Jan H. M. Korst
    • 1
  1. 1.Philips Research LaboratoriesEindhoventhe Netherlands

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