Polar IFS + Parisian Genetic Programming = E cient IFS Inverse Problem

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 xed 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 Classiier 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 tness of an IFS is carefully deened for each one of its member functions and plays a major role in the tness 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.