Synthesis of Digital Circuits with Genetic Algorithms: A Fractional-Order Approach

This paper analyses the performance of a genetic algorithm using a new concept, namely a fractional-order dynamic fitness function, for the synthesis of combinational logic circuits. The experiments reveal superior results in terms of speed and convergence to achieve a solution.

• Cecília Reis
• J. A. Tenreiro Machado
• J. Boaventura Cunha

• Circuit design
• fractional-order systems
• genetic algorithms
• logic circuits.

[1] Zebulum, R. S., Pacheco, M. A. and Vellasco, M. M., Evolutionary
Electronics: Automatic Design of Electronic Circuits and Systems by
Genetic Algorithms, CRC Press, 2001.
[2] Louis, S.J. and Rawlins, G. J., "Designer Genetic Algorithms: Genetic
Algorithms in Structure Design," in Proc. of the Fourth Int. Conference
on Genetic Algorithms, 1991.
[3] Coello, C. A., Christiansen, A. D. and Aguirre, A. H., "Using Genetic
Algorithms to Design Combinational Logic Circuits", Intelligent
Engineering through Artificial Neural Networks. Vol. 6, 1996, pp. 391-
396.
[4] Miller, J. F., Thompson, P. and Fogarty, T, Algorithms and Evolution
Strategies in Engineering and Computer Science: Recent Advancements
and Industrial Applications. Chapter 6, 1997, Wiley.
[5] Kalganova, T., Miller, J. F. and Lipnitskaya, N., "Multiple_Valued
Combinational Circuits Synthesised using Evolvable Hardware," in
Proceedings of the 7th Workshop on Post-Binary Ultra Large Scale
Integration Systems, 1998.
[6] Torresen, J., "A Divide-and-Conquer Approach to Evolvable
Hardware," in Proceedings of the Second International Conference on
Evolvable Hardware. Vol. 1478, 1998, pp. 57-65.
[7] Vassilev, V. K. and Miller, J. F., "Scalability Problems of Digital Circuit
Evolution," in Proc. of the Second NASA/DOD Workshop on Evolvable
Hardware, 2000, pp. 55-64.
[8] Y. Sano and H. Kita, Optimization of Noisy Fitness Functions by means
of Genetic Algorithms using History of Search with test of Estimation,
Proceedings of CEC, 2002.
[9] Cecília Reis, J. A. Tenreiro Machado, and J. Boaventura Cunha,
"Evolutionary Design of Combinational Logic Circuits", Journal of
Advanced Computational Intelligence and Intelligent Informatics, Fuji
Technology Press, Vol. 8, No. 5, pp. 507-513, Sep. 2004.
[10] Cecília Reis, J. A. Tenreiro Machado, and J. Boaventura Cunha,
"Synthesis of Logic Circuits Using Fractional-Order Dynamic Fitness
Functions", Proceedings of the ICCI-2004 - International Conference on
Computational Intelligence, 2004, pp. 77-79.
[11] K. B. Oldham and J. Spanier. The Fractional Calculus: Theory and
Application of Differentiation and Integration to Arbitrary Order.
Academic Press, New York, 1974.
[12] K. S. Miller and B. Ross. An Introduction to the Fractional Calculus and
Fractional Differential Equations. John Wiley & Sons, New York, 1993.
[13] J. A. Tenreiro Machado. Analysis and Design of Fractional-Order
Digital Control Systems. SAMS Journal Systems Analysis, Modelling,
Simulation, vol. 27: 107-122, 1997.