Evolving Multi-Output Digital Circuits Using Multi-Genome Grammatical Evolution

Abstract

Grammatical Evolution is a Genetic Programming variant which evolves problems in any arbitrary language that is BNF compliant. Since its inception, Grammatical Evolution has been used to solve real-world problems in different domains such as bio-informatics, architecture design, financial modelling, music, software testing, game artificial intelligence and parallel programming. Multi-output problems deal with predicting numerous output variables simultaneously, a notoriously difficult problem. We present a Multi-Genome Grammatical Evolution better suited for tackling multi-output problems, specifically digital circuits. The Multi-Genome consists of multiple genomes, each evolving a solution to a single unique output variable. Each genome is mapped to create its executable object. The mapping mechanism, genetic, selection, and replacement operators have been adapted to make them well-suited for the Multi-Genome representation and the implementation of a new wrapping operator. Additionally, custom grammar syntax rules and a cyclic dependency-checking algorithm have been presented to facilitate the evolution of inter-output dependencies which may exist in multi-output problems. Multi-Genome Grammatical Evolution is tested on combinational digital circuit benchmark problems. Results show Multi-Genome Grammatical Evolution performs significantly better than standard Grammatical Evolution on these benchmark problems.