Abstract
In this paper a genetic model is presented and the dynamics in the thermodynamic limit is derived. Analogies and differences with neural networks are discussed and attractors of the genetic model are characterized as equilibria points of Hopfield's networks. The neural network and the genetic system are experimentally compared as approximate algorithms for the MAX-CUT problem.
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References
M. A. Alberti, A. Bertoni, P. Campadelli, G. Grossi, R. Posenato, A Neural Algorithm for MAX-2SAT: Performance Analysis and Circuit Implementation, to be published on Neural Networks.
G. Ausiello, P. Crescenzi, M. Protasi, Approximate Solution of NP Optimization Problems, Theoretical Computer Science, Vol. 150, 1995.
A. E. Eiben, E. H. L. Aarts, K. M. van Hee, Global Convergence of Genetic Algorithms: a Markov Chain Analysis, Parallel Problem Solving from Nature, 1st Workshop PPSN I, Berlin, 1991.
M. R. Garey, D. S. Johnson, Computers and Intractability. A Guide to the Theory of NP-Completeness, W. H. Freeman & Co., San Francisco, 1979.
D. E. Goldberg, Genetic Algorithms in Search, Optimization and Machine Learning, Addison-Wesley, Reading, MA, 1989.
D. E. Goldberg, P. Segrest, Finite Markov Chain Analysis of Genetic Algorithms, Genetic Algorithms and their Aplication: Proceedings of the Second International Conference on Genetic Algorithms, pp. 1–8, 1987.
M. Goemans, D. Williamson, 878 approximation algorithms for the max cut and max 2sat, Proceedings of the twenty-sixth annual symposium on the theory of computing, pag. 422, 1994.
J. Hertz, A. Krogh, R. J. Palmer, Introduction to the Theory of Neural Computation, Addison-Wesley, 1991.
J. J. Hopfield, Neural networks and physical systems with emergent collective computational abilities, Proceedings of the National Academy of Sciences 79, pp. 2554–2558, 1982.
J. H. Holland, Induction, Processes of Inference, Learning and Discovery, MIT Press, Cambridge, 1989.
J. H. Holland, Adaptation in Natural and Artificial Systems, MIT Press, Cambridge, 1992.
J. R. Koza, Genetic Programming, MIT Press, Cambridge, 1992.
A. E. Nix, M. D. Vose, Modelling Genetic Algorithms with Markov Chains, Annals of Mathematics and Artificial Intelligence, Vol. 5, pp. 79–88, 1992.
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© 1996 Springer-Verlag Berlin Heidelberg
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Bertoni, A., Campadelli, P., Carpentieri, M., Grossi, G. (1996). A genetic model and the Hopfield networks. In: von der Malsburg, C., von Seelen, W., Vorbrüggen, J.C., Sendhoff, B. (eds) Artificial Neural Networks — ICANN 96. ICANN 1996. Lecture Notes in Computer Science, vol 1112. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61510-5_80
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DOI: https://doi.org/10.1007/3-540-61510-5_80
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