# Polar IFS + Parisian GP = Efficient IFS inverse problem solving

Abstract : The inverse problem for Iterated Functions Systems (finding an IFS whose attractor is a target 2D shape) with non-affine IFS is a very complex task. Successful approaches have been made using Genetic Programming, but there is still room for improvement in both the IFS and the GP parts. This paper introduces Polar IFS: a specific representation of IFS functions which shrinks the search space to mostly contractive functions and gives direct access to the fixed points of the functions. On the evolutionary side, the Parisian'' approach is presented. It is similar 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. Both improvements show a drastic cut-down on CPU-time: good results are obtained with small populations in few generations.
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https://hal.inria.fr/inria-00000097
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Submitted on : Monday, October 31, 2005 - 7:22:27 AM
Last modification on : Wednesday, October 20, 2021 - 12:23:55 AM
Long-term archiving on: : Thursday, April 1, 2010 - 8:12:44 PM

### Identifiers

• HAL Id : inria-00000097, version 1

### Citation

Pierre Collet, Evelyne Lutton, Frédéric Raynal, Marc Schoenauer. Polar IFS + Parisian GP = Efficient IFS inverse problem solving. Genetic Programming and Evolvable Machines, Springer Verlag, 2000, 1 (4), pp.339-361. ⟨inria-00000097⟩

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