Compact Unstructured Representations for Evolutionary Design

Abstract

This paper proposes a few steps to escape structured extensive representations for objects, in the context of evolutionary Topological Optimum Design (TOD) problems : early results have demonstrated the potential power of Evolutionary methods to find numerical solutions to yet unsolved TOD problems, but those approaches were limited because the complexity of the representation was that of a fixed underlying mesh. Different compact unstructured representations are introduced, the complexity of which is self-adaptive, i.e. is evolved by the algorithm itself. The Voronoi-based representations are variable length lists of alleles that are directly decoded into object shapes, while the IFS representation, based on fractal theory, involves a much more complex morphogenetic process. First results demonstrates that Voronoi-based representations allow one to push further the limits of Evolutionary Topological Optimum Design by actually removing the correlation between the complexity of the representations and that of the discretization. Further comparative results among all these representations on simple test problems seems to indicate that the complex causality in the IFS representation disfavor it compared to the Voronoi-based representations.