Polynomials, Basis Sets, and Deceptiveness in Genetic Algorithms

Abst ract . The degree to which the genetic opt imizat ion process is transparent is in part determined by the form of th e object ive funct ion. We develop two forms from first principles: polynomial forms and basis sets. We characterize three function classes that are fully easy for the genetic algorithm in terms of the polynomial representation. We generate functions of varying degrees of decepti veness in terms of the representation provided by basis sets. We furth er show the relationship between these representations and the more standard Walsh polynomia ls.