Evolution of affine transformations and iterated function systems using hierarchical evolution strategy

Abstract

Often optimization problems involve the discovery of many scalar coefficients. Although genetic programming (GP) has been applied to the optimization and discovery of functions with an arbitrary number of scalar coefficients, recent results indicate that a method for fine-tuning GP scalar terminals can assist the discovery of solutions. In this paper we demonstrate an approach where genetic programming and evolution strategies (ES) are seamlessly combined. We apply our GP/ES hybrid, which we name Hierarchical Evolution Strategy, to the problem of evolving affine transformations and iterated function systems (IFS). We compare the results of our approach with GP and notice an improvement in performance in terms of discovering bsetter solutions and speed.