Variable Length Shape Representations: Genotypic Distance and Fitness Landscape Analyses ------------------------------------------------- Authors: Leila Kallel and Marc Schoenauer ------- Centre de Mathematiques Appliquees, CNRS URA 756, Ecole Polytechnique, 91128 Palaiseau Cedex, France. Abstract: --------- A complete case study of problems raised by the use of variable-length representations is presented. In the context of Structural Mechanics, some variable length representations (unordered lists of alleles) have been empirically found to be a good choice. Their definitions are recalled, and their properties of redundancy and degenerascy outlined. No canonical distance exists on such space of unordered lists of real-valued alleles. A general approach to the design of genotypic distance is proposed, based on a similarity measure on the space of alleles values. Different choices for that similarity measure are possible resulting in different distances. The study of the connections between genotypic distances and the evolution operators (crossover and minimal mutation), together with their behavior with respect to degenercy, allows to choose between different distances for the same representation, in the perspective of analyzing the Fitness Landscape from an evolutionary point of view. The evidence of a link between the distance and the operators somehow justifies the study of the Fitness Landscape through that distance: the Fitness-Distance Correlation framework is extended, and applied to the different representations proposed for the mechanical identification problem. Strong results are obtained regarding the choice of an initialization procedure. Moreover, FDC results in conjunction with actual runs of an evolutionary algorithm allow to give a partial answers to the ultimate question of the a priori choice of a representation for a given problem. he whole paper is available as a compressed Postscript file by in procedure FTP anonymous on host barbes.polytechnique.fr ( 129.104.4.100 ) in the directory pub/RI/1997 under the name kallel_schoenauer_363.sept.ps.gz or by Netscape or any other www client via the CMAP www server "http://www.cmap.polytechnique.fr/"