Minimization of multivalued multithreshold perceptrons using genetic algorithms

We address the problem of computing and learning multivalued multithreshold perceptrons. Every n-input X-valued logic function can be implemented using a (k, s)-perceptron, for some number of thresholds s. We propose a genetic algorithm to search for an optimal (k, s)-perceptron that efficiently realizes a given multiple-valued logic function, that is to minimize the number of thresholds. Experimental results show that the genetic algorithm find optimal solutions in most cases.

[1]  Zoran Obradovic,et al.  Learning with Discrete Multi-valued Neurons , 1990, J. Comput. Syst. Sci..

[2]  Marvin Minsky,et al.  Perceptrons: An Introduction to Computational Geometry , 1969 .

[3]  Zoran Obradovic,et al.  Learning with Discrete Multi-Valued Neurons , 1990, ML.

[4]  Koichi Tanno,et al.  Learning multiple-valued logic networks based on backpropagation , 1995, Proceedings 25th International Symposium on Multiple-Valued Logic.

[5]  Ivan Stojmenovic,et al.  Learning with permutably homogeneous multiple-valued multiple-threshold perceptrons , 1998, Proceedings. 1998 28th IEEE International Symposium on Multiple- Valued Logic (Cat. No.98CB36138).

[6]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

[7]  Tsutomu Sasao.  On the Optimal Design of Multiple-Valued PLA's , 1989, IEEE Trans. Computers.

[8]  Zvonko G. Vranesic,et al.  Synthesis of Multivalued Multithreshold Functions for CCD Implementation , 1986, IEEE Transactions on Computers.

[9]  Masayuki Matsumoto,et al.  A design of multiple-valued logic neuron , 1990, Proceedings of the Twentieth International Symposium on Multiple-Valued Logic.

[10]  Okihiko Ishizuka.  Multi-valued multi-threshold networks , 1976 .

[11]  Zoran Obradovic,et al.  Computing with Discrete Multi-Valued Neurons , 1992, J. Comput. Syst. Sci..

[12]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[13]  OKIHIKO ISHIZUKA.  On Multivalued Multithreshold Networks Composed of Conventional Threshold Elements , 1977, IEEE Transactions on Computers.

[14]  Ivan Stojmenovic,et al.  Synthesis of multiple-valued logic functions by neural networks , 1998 .