Improving Convergence in Cartesian Genetic Programming Using Adaptive Crossover, Mutation and Selection

Genetic programming (GP) can be described as a paradigm which opens the automatic derivation of programs for problem solving. GP as popularized by Koza uses tree representation. The application of GP takes place on several types of complex problems and became very important for Symbolic Regression. Miller and Thomson introduced a new directed graph representation called Cartesian Genetic Programming (CGP). We use this representation for very complex problems. CGP enables a new application on classification and image processing problems. Previous research showed that CGP has a low convergence rate on complex problems. Like in other approaches of evolutionary computation, premature convergence is also a common issue. Modern GP systems produce population statistics in every iteration. In this paper we introduce a new adaptive strategy which uses population statistics to improve the convergence of CGP. A new metric for CGP is introduced to classify the healthy population diversity. Our strategy maintains population diversity by adapting the probabilities of the genetic operators and selection pressure. We demonstrate our strategy on several regression problems and compare it to the traditional algorithm of CGP. We conclude this paper by giving advices about parameterization of the adaptive strategy.