Principles in the Evolutionary Design of Digital Circuits J. F. Miller, D. Job, and V. K. Vassilev Genetic Programming and Evolvable Machines

Abstract An evolutionary algorithms is used as an engine for discovering new designs of digital circuits. These designs are radically different from those produced by rule-based approaches.

Introduction Assemble-and-test: assembling a larger system from a number of component parts and then testing the organism in the environment in which it finds itself

Is it possible to extract the general principle and hence discover new principles by evolving a series of subsystems of increasing size? Identifying Principles in Evolving Circuits (Landscape Analysis) Identifying Principles in Evolved Circuits (Data mining) Evolutionary Algorithm Evolved Data

Exploring the space of all representations Assembling a function from a number of component parts begins in the space of all representations and maps it into the space of all the truth tables. The evolutionary algorithms then gradually pulls the specification of the circuit towards the target truth table.

Digital Circuit Evolution Input redundancy Cell redundancy (Functional redundancy) Fitness: the number of correct output bits : Encoding scheme

algorithms Randomly initialize a population of genotype Evaluate fitness Copy fittest genotype into new population Fill remaining places in population by mutated versions of fittest genotypes Replace old population by new and return to step 2

Evolved Circuits 30gates => 21gates

Analysis (1) Analysis of fitness graph  By increasing the scale, the corresponding landscape becomes continuous and perhaps easier for evolutionary search  By using more sets of logic functions, evolutionary search becomes more easier

Analysis (2) CBR as principle identification technology  It does not require a domain models or rules  It can provide an explanation of its own reasoning  It provides data mining, indexing, matching, retrieval, and adaptation  It relies upon cases that have known structure  Each principle contains knowledge pertaining to a particular sub-program, and collections of principles form the cases in the case-base.  Case-based retrieval is then used to retrieve appropriate principles based on specified requirements

CBR-continued 1. The removal of redundant information and duplication of programs  Compression and normalization of remaining programs 2. Splitting the normalized programs into sub-programs and calculation of their structure, behavior and functionality 3. Separation of the sub-programs 4. Indexing of the programs