Polar IFS+Parisian Genetic Programming=Efficient IFS Inverse Problem Solving

This paper proposes a new method for treating the inverse problem for Iterated Functions Systems (IFS) using Genetic Programming. This method is based on two original aspects. On the fractal side, a new representation of the IFS functions, termed Polar Iterated Functions Systems, is designed, shrinking the search space to mostly contractive functions. Moreover, the Polar representation gives direct access to the fixed points of the functions. On the evolutionary side, a new variant of GP, the “Parisian” approach is presented. The paper explains its similarity to the “Michigan” approach of Classifier Systems: each individual of the population only represents a part of the global solution. The solution to the inverse problem for IFS is then built from a set of individuals. A local contribution to the global fitness of an IFS is carefully defined for each one of its member functions and plays a major role in the fitness of each individual. It is argued here that both proposals result in a large improvement in the algorithms. We observe a drastic cut-down on CPU-time, obtaining good results with small populations in few generations.