Journal of Convex Analysis 09 (2002), No. 2, 503--517
Copyright Heldermann Verlag 2002
Topological Optimum Design with Evolutionary Algorithms
Hatem Hamda
CMAP - UMR CNRS 7641, Ecole Polytechnique, 91128 Palaiseau, France
hatem@cmapx.polytechnique.fr
Marc Schoenauer
CMAP - UMR CNRS 7641, Ecole Polytechnique, 91128 Palaiseau, France
This paper addresses a constrained optimization problem in the context of Topological Optimum Design (TOD) : the aim is to find the optimal shape of a structure (i.e a repartition of material in a given design domain) such that the mechanical behavior of that structure meets some requirement (e.g. a bound on the maximal displacement under a prescribed loading). We restrict to stochastic optimization methods such as Evolutionary Algorithms (EAs): they do not require any a priori assumption about the function to optimize (or about the constraints) and they are able to tackle optimization problems on different kinds of search spaces. The most crucial step when constructing an EA is the choice of representation, which determines the search space. In order to overcome limitation of previous works, a new representation is presented, termed Voronoi representation, which is independent of any priori discretization. Moreover, constraints are accounted for through penalty function, and a new adaptive penalty method is proposed to explore the neighborhood of the boundary of the feasible region. The results of TOD of standard benchmark 2-D cantilever problems are improved. Further, this approach allows to address 3-D problems, on which it demonstrates its ability to find multiple quasi-optimal solutions.
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