In this section, we will discuss how to represent a possible solution from its circuit elements. String representation1 and circuit constructing trees2 are two frequently used representations in evolvable hardware designs.

First, string representation can be a string of integers, characters or binary numbers, but in order to be easily recognised and analysed by processor, it is normally in binary form in digital circuit design. Therefore, a chromosome can be represented in a bit-stream where each bit in the string is one connecting point of a component or a description of the function of that component. One can imagine that the component's connecting points and function can be described by a genotype, and a chromosome is simply a collection of these genotypes.

Second, the circuit constructing trees representation could be used to convert cyclic graphs, which are normally used to represent circuits, into parse trees, each tree describes a function. The chromosome will now be represented as one of this type of tree.3 Using this representation, passive filters2, high gain amplifiers4 and more complex circuits can be transformed into computer recognisable and manipulatable parse trees.

References

1 Grimbleby, J. B.: Automatic Analogue Network Synthesis Using Genetic Algorithms, Proceedings of the First IEE/IEEE International Conference on Genetic Algorithms in Engineering Systems (GALESIAS - 95), pp. 53-58 (1995)

2 Koza J. R., Bennett III F. H., Andre, D., Keane, M. A.: Four Problems for which a Computer Program Evolved By Genetic Programming is Competitive with Human Performance, Proc. of 1996 IEEE International Conference on Evolutionary Computation, IEEE Press. pp. 1-10 (1996)

3 Zebulum, R. S., Pacheco, M.A., Vellasco, M.: Analog circuits evolution in extrinsic and intrinsic modes. Proceedings. Evolvable Systems: from biology to hardware 1478, pp.154-165 (1998)

4 Koza, John R., Andre, David, Bennett III, Forrest H, and Keane, Martin A.: Design of a high-gain operational amplifier and other circuits by means of genetic programming. In Angeline, Peter J., Reynolds, Robert G., McDonnell, John R., and Eberhart, Russ (editors). Evolutionary Programming VI. 6th International Conference, EP97, Indianapolis, Indiana, USA, April 1997 Proceedings. Lecture Notes in Computer Science, Volume 1213. Berlin: Springer-Verlag. pp. 125-136. (1997)