Shape Representations and Evolution Schemes

The choice of a representation i.e. the deeni-tion of the search space, is of vital importance in all Evolutionary Optimization processes. In the context of Topological Optimum Design in Structural Mechanics, this paper investigates possible representations for evolutionary shape design. The goal is the identiication of a shape in IR n (n = 2 or n = 3) having optimal mechanical properties. Evolutionary Computation has been demonstrated a valuable tool for TOD problems. However, all past results are based on the straightforward bitstring representation whose complexity increases with that of the underlying Mechanical model. To overcome this diiculty, diier-ent representations for shapes are introduced, and compared on the benchmark problem of TOD using various evolutionary schemes. The results are discussed with respect to the diierent degrees of epistasis of the representations.