Scalability problems of digital circuit evolution evolvability and efficient designs

A major problem in the evolutionary design of combinational circuits is the problem of scale. This refers to the design of electronic circuits in which the number of gates required to implement the optimal circuit is too high to search the space of all designs in reasonable time, even by evolution. The reason is twofold: firstly, the size of the search space becomes enormous as the number of gates required to implement the circuit is increased, and secondly, the time required to calculate the fitness of a circuit grows as the size of the truth table of the circuit. This paper studies the evolutionary design of combinational circuits, particularly the three-bit multiplier circuit, in which the basic building blocks are small sub-circuits, modules inferred from other evolved designs. The structure of the resulting fitness landscapes is studied and it is shown that in general the principles of evolving digital circuits are scalable. Thus to evolve digital circuits using modules is faster, since the building blocks of the circuit are sub-circuits rather than two-input gates. This can also be a disadvantage, since the number of gates of the evolved designs grows as the size of the modules used.

[1]  Hans-Paul Schwefel,et al.  Numerical Optimization of Computer Models , 1982 .

[2]  Hiroshi Yokoi,et al.  A Gate-Level EHW Chip: Implementing GA Operations and Reconfigurable Hardware on a Single LSI , 1998, ICES.

[3]  Katsunori Shimohara,et al.  AdAM: a hardware evolutionary system , 1997, Proceedings of 1997 IEEE International Conference on Evolutionary Computation (ICEC '97).

[4]  Vesselin K. Vassilev,et al.  Digital circuit evolution: the ruggedness and neutrality of two-bit multiplier landscapes , 1999 .

[5]  S. L. Hurst,et al.  A Comparison of Universal-Logic-Module Realizations and Their Application in the Synthesis of Combinatorial and Sequential Logic Networks , 1982, IEEE Transactions on Computers.

[6]  Hitoshi Iba,et al.  Evolving hardware with genetic learning: a first step towards building a Darwin machine , 1993 .

[7]  Riccardo Poli,et al.  Evolution of Graph-Like Programs with Parallel Distributed Genetic Programming , 1997, ICGA.

[8]  Julian Francis Miller,et al.  Embedding Landscape Neutrality to Build a Bridge from the Conventional to a More Efficient Three-bit Multiplier Circuit , 2000, GECCO.

[9]  Wolfgang Banzhaf,et al.  Genetic Programming: An Introduction , 1997 .

[10]  Vesselin K. Vassilev,et al.  Digital circuit evolution and fitness landscapes , 1999, Proceedings of the 1999 Congress on Evolutionary Computation-CEC99 (Cat. No. 99TH8406).

[11]  Thomas Bäck,et al.  A Survey of Evolution Strategies , 1991, ICGA.

[12]  Julian Francis Miller,et al.  Cartesian genetic programming , 2000, GECCO '10.

[13]  Katsunori Shimohara,et al.  Development and Evolution of Hardware Behaviors , 1995, Towards Evolvable Hardware.

[14]  Julian Francis Miller,et al.  Aspects of Digital Evolution: Geometry and Learning , 1998, ICES.

[15]  Julian Francis Miller,et al.  Aspects of Digital Evolution: Evolvability and Architecture , 1998, PPSN.

[16]  Adrian Thompson,et al.  Hardware evolution - automatic design of electronic circuits in reconfigurable hardware by artificial evolution , 1999, CPHC/BCS distinguished dissertations.

[17]  Julian Francis Miller,et al.  On the nature of two-bit multiplier landscapes , 1999, Proceedings of the First NASA/DoD Workshop on Evolvable Hardware.

[18]  Sushil J. Louis,et al.  Genetic algorithms as a computational tool for design , 1993 .

[19]  Tim Jones.  Evolutionary Algorithms, Fitness Landscapes and Search , 1995 .

[20]  Julian Francis Miller,et al.  Information Characteristics and the Structure of Landscapes , 2000, Evolutionary Computation.

[21]  John R. Koza,et al.  Genetic programming - on the programming of computers by means of natural selection , 1993, Complex adaptive systems.

[22]  J. Miller.  An empirical study of the efficiency of learning boolean functions using a Cartesian Genetic Programming approach , 1999 .

[23]  Peter F. Stadler,et al.  Towards a theory of landscapes , 1995 .

[24]  Heinz Mühlenbein,et al.  The Science of Breeding and Its Application to the Breeder Genetic Algorithm (BGA) , 1993, Evolutionary Computation.

[25]  Jim Tørresen,et al.  A Divide-and-Conquer Approach to Evolvable Hardware , 1998, ICES.

[26]  P. Stadler,et al.  Anisotropy in fitness landscapes. , 1993, Journal of theoretical biology.

[27]  Isamu Kajitani,et al.  Hardware Evolution at Function Level , 1996, PPSN.

[28]  Hitoshi Iba,et al.  Machine Learning Approach to Gate-Level Evolvable Hardware , 1996, ICES.

[29]  John R. Koza,et al.  Genetic programming 2 - automatic discovery of reusable programs , 1994, Complex Adaptive Systems.