Abstract
In this paper, we propose the use of Information Theory as the basis for designing a fitness function for Boolean circuit design using Genetic Programming. Boolean functions are implemented by replicating binary multiplexers. Entropy-based measures, such as Mutual Information and Normalized Mutual Information are investigated as tools for similarity measures between the target and evolving circuit. Three fitness functions are built over a primitive one. We show that the landscape of Normalized Mutual Information is more amenable for being used as a fitness function than simple Mutual Information. The evolutionary synthesized circuits are compared to the known optimum size. A discussion of the potential of the Information-Theoretical approach is given.
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References
Cheushev, V., Moraga, C., Yanushkevich, S., Shmerko, V. & Kolodziejczyk, J. (2001). Information Theory Method for Flexible Network Synthesis. In Proceedings of the IEEE 31st. International Symposium on Multiple-Valued Logic, 201–206. IEEE Press.
Coello Coello, C. A., Christiansen, A. D. & Hernández Aguirre, A. (2000). Use of Evolutionary Techniques to Automate the Design of Combinational Logic Circuits. International Journal of Smart Engineering System Design 2: 299–314.
Coello Coello, C. A., Christiansen, A. D. & Hernández Aguirre, A. (2001). Towards Automated Evolutionary Design of Combinational Circuits. Computers and Electrical Engineering 27: 1–28.
Coello Coello, C. A., Christiansen, A. D. & Hernández Aguirre, A. (1996). Using Genetic Algorithms to Design Combinational Logic Circuits. In Dagli, C. H., Akay, M., Chen, C. L. P., Benito, R. Farnández & Ghosh, J. (eds.) Intelligent Engineering Systems Through Artificial Neural Networks. Volume 6. Fuzzy Logic and Evolutionary Programming, 391–396. St. Louis, Missouri, USA: ASME Press, Nov.
Coello Coello, C. A., Christiansen, A. D. and Hernández, Aguirre A. (1997). Automated Design of Combinational Logic Circuits Using Genetic Algorithms. In Smith, D. G., Steele, N. C. & Albrecht, R. E(eds.) Proceedings of the International Conference on Artificial Neural Nets and Genetic Algorithms, 335–338. University of East Anglia, England: Springer-Verlag, April.
Cover, T. M. & Thomas, J. A. (1991). Elements of Information Theory. New York: John Wiley & Sons.
Dill, K. M., Herzog, J. H. & Perkowski, M. A. (1997). Genetic Programming and Its Application to the Synthesis of Digital Logic. In Proceedings of the 1997 IEEE Pacific Rim Conference on Communications, Computers, and Signal Processing, Vol 2, 823–826. IEEE Computer Society.
Drechsler, R., Becker, B. & Göckel, N. (1995). A Genetic Algorithm for Minimization of Fixed Polarity Reed-Muller Expressions. In Proceedings of the International Conference on Artificial Neural Networks and Genetic Algorithms, 392–395. Ales, April.
Drechsler, R., Göckel, N. & Becker, B. (1996). Learning Heuristics for OBDD Minimization by Evolutionary Algorithms. In Voigt, H.-M., Ebeling, W., Rechenberg, I. & Schwefel, H. P. (eds.) Proceedings of the Conference Parallel Problem Solving from Nature PPSN-IV, 730–739. Berlin: Springer.
Drechsler, R. & Becker, B. (1998). Binary Decision Diagrams: Theory and Implementation. Boston, USA: Kluwer Academic Publishers.
Droste, S. (1997). Efficient Genetic Programming for Finding Good Generalizing Boolean Functions. In Koza, J. R., Deb, K., Dorigo, M., Fogel, D. B., Garzon, M., Iba, H. & Riolo, R. L. (eds.) Genetic Programming 1997: Proceedings of the Second Annual Conference, 82–87. San Francisco, CA, USA: Morgan Kaufmann
Hartmann, C. R. P., Varshney, P. K., Mehrotra, K. G. & Gerberich, C. L. (1982). Application of Information Theory to the Construction of Efficient Decision Trees. IEEE Transactions on Information Theory 28(5): 565–577.
Hernández Aguirre, A., Buckles, B. P. & Coello Coello, C. A. (2001). Ga-Based Learning of kdnfsz Boolean Formulas. In Evolvable Systems: From Biology to Hardware, 279–290. Tokyo, Japan: Springer Verlag, 3–5 October.
Hernández Aguirre, A., Buckles, B. P. & Coello Coello, C. A. (2000). Evolutionary Synthesis of Logic Functions Using Multiplexers. In Dagli, C., Buczak, A. L. et al. (eds.) Proceed ings of the 10th Conference Smart Engineering System Design, 311–315. New York: ASME Press.
Hernández Aguirre, A., Buckles, B. P. & Alcántara, A. M. (2000a). The PAC Population Size of a Genetic Algorithm. In Twelfth International Conference on Tools with Artificial Intelligence, 199–202. Vancouver British Columbia, Canada: IEEE Computer Society, 13–15 November.
Hernández Aguirre, A., Buckles, B. P. & Coello Coello, C. A. (2000b). Gate-Level Synthesis of Boolean Functions Using Binary Multiplexers and Genetic Programming. In Conference on Evolutionary Computation 2000, 675–682. IEEE Computer Society.
Hernández Aguirre, A., Coello Coello, C. A. & Buckles, B. P. (1999). A Genetic Programming Approach to Logic Function Synthesis by Means of Multiplexers. In Stoica, A., Keymeulen, D. & Lohn, J. (eds.) Proceedings of the First NASA/DoD Workshop on Evolvable Hardware, 46–53. Los Alamitos, California: IEEE Computer Society.
Iba, H., Iwata, M. & Higuchi, T. (1997). Gate-Level Evolvable Hardware: Empirical Study and Application. In Dasgupta, D. & Michalewicz, Z. (eds.) Evolutionary Algorithms in Engineering Applications, 259–276. Berlin: Springer-Verlag.
Islas Pérez, E., Coello Coello, C. A. & Hernández Aguirre, A. (2003). Extracting and Re-Using Design Patterns from Genetic Algorithms Using Case-Based Reasoning. Engineering Optimization (April) 35(2): 121–141.
Kabakcioglu, A. M., Varshney, P. K. & Hartmann, C. R. P. (1990). Application of Information Theory to Switching Function Minimization. IEE Proceedings, Part E 137: 387–393.
Kalganova, T. (2000). Bidirectional Incremental Evolution in Extrinsic Evolvable Hardware. In Lohn, J., Stoica, A., Keymeulen, D. & Colombano, S. (eds.) Proceedings of the Second NASA/DoD Workshop on Evolvable Hardware, 65–74. Los Alamitos, California: IEEE Computer Society.
Koza, J. R. (1992). Genetic Programming. On the Programming of Computers by Means of Natural Selection. Massachusetts, USA: MIT Press.
Lloris, A., Gomez-Lopera, J. F. & Roman-Roldan, R. (1993). Using Decision Trees for the Minimization of Multiple-Valued Functions. International Journal of Electronics 75(6): 1035–1041.
Louis, S. J. (1993). Genetic Algorithms as a Computational Tool for Design. PhD thesis, Indiana University, Indiana, USA.
Louis, S. J. & Johnson, J. (1997). Solving Similar Problems using Genetic Algorithms CaseBased Memory. In Bäck, T. (ed.) Proceedings of the Seventh International Conference on Genetic Algorithms, 283–290. San Francisco, California: Morgan Kaufmann Publishers.
Luba, T., Moraga, C., Yanushkevich, S., Shmerko, V. & Kolodziejczyk, J. (2000). Application of Design Style in Evolutionary Multi-Level Network Synthesis. In Proceedings of the 26th EUROMICRO Conference Informatics:Inventing the Future, 156–163. IEEE Press.
Luba, T., Moraga, C., Yanushkevich, S., Opoka, M. & Shmerko, V. Evolutionary Multi-Level Network Synthesis in Given Design Style. In Proceedings of the 30th IEEE International Symposium on Multiple valued Logic, 253–258. IEEE Press.
Maes, F., Collignon, A., Vandermeulen, D., Marchal, G. & Suetens, P. (1997). Multimodality Image Registration by Maximization of Mutual Information. IEEE Transactions on Medical Imaging (April) 16(2): 187–198.
Miller, J. F., Thomson, P. & Fogarty, T. (1998). Designing Electronic Circuits Using Evolutionary Algorithms. Arithmetic Circuits: A Case Study. In Quagliarella, D., Pénaux, J., Poloni, C. & Winter, G. (eds.) Genetic Algorithms and Evolution Strategy in Engineering and Computer Science, 105–131. Chichester, England: Morgan Kaufmann.
Miller, J. F., Job, D. & Vassilev, V. K. (2000). Principles in the Evolutionary Design of Digital Circuits — Part I. Genetic Programming and Evolvable Machines (April) 1(1/2): 7–35.
Miller, J. F., Job, D. & Vassilev, V. K. (2000a). Principles in the Evolutionary Design of Digital Circuits — Part II. Genetic Programming and Evolvable Machines (July) 1(3): 259–288
Quinlan, J. R. Learning Efficient Classification Procedures and Their Application to Chess Games. (1983). In Michalski, R. S., Carbonell, J. G. & Mitchell, T. M. (eds.) Machine Learning: An Artificial Intelligence Approach, 463–482. Berlin, Heidelberg: Springer.
Shannon, C. E. (1948). A Mathematical Theory of Information. Bell System Technical Journal (July) 27: 379–423.
Scholl, C. & Becker, B. (2000). On the Generation of Multiplexer Circuits for Pass Transistor Logic. In Proceedings of Design, Automation, and Test in Europe.
Studholme, C., Hill, D. L. G. & Hawkes, D. J. (1999). An Overlap Invariant Entropy Measure of 3D Medical Image Alignment. Pattern Recognition 32: 71–86.
Torresen, J. (2002). A Scalable Approach to Evolvable Hardware. Genetic Programming and Evolvable Machines 3(3): 259–282.
Thompson, A., Layzell, P. & Zebulum R. S. (1999). Explorations in Design Space: Unconventional Design Through Artificial Evolution. IEEE Transactions on Evolutionary Computation (September) 3(3): 167–196.
Vassilev, V. K. & Miller, J. F. (2000). Scalability Problems of Digital Circuit Evolution In Lohn, J., Stoica, A., Keymeulen, D. & Colombano, S. (eds.) Proceedings of the Second NASA/DoD Workshop on Evolvable Hardware, 55–64. Los Alamitos, California: IEEE Computer Society.
Weaver, W. & Shannon, C. E. (1949). The Mathematical Theory of Communication. Urbana, Illinois: University of Illinois Press.
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Aguirre, A.H., Coello, C.A.C. (2004). Evolutionary Synthesis of Logic Circuits Using Information Theory. In: Artificial Intelligence in Logic Design. Artificial Intelligence in Logic Design, vol 766. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-2075-9_9
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DOI: https://doi.org/10.1007/978-1-4020-2075-9_9
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