Automated shape optimization using a multigrid method and estimation of distribution algorithms
Document typeConference lecture
Rights accessOpen Access
Topological shape optimization refers to the problem of finding the optimal shape of a mechanical structure by using a process for removing or inserting new holes or parts, it is to say, using a process which produces topological changes.This article introduces a method for automated topological optimization via an Estimation of Distribution Algorithm (EDA) with a suitable representation of the optimization variables. The optimum structure is such with the minimum weight which does not exceed a maximum von Mises stress and displacement. The contributions of this proposal resides in the definition of a candidate solution and the optimization method. The candidate solution representation is independent of the finer discretization used for analyzing candidate structures using the finite element method. Given a domain, which corresponds to the physical space where candidate structures reside, a vector φ=[φ1,φ2,...,φm] is used to define a smooth function φ(x,y) on Ω. If φ(x,y) is less than 0.5, such region does not have material, otherwise, it has.The smooth function φ(x,y) provides the advantage of having continuous regions with or without material while it depends on few optimization parameters φ, in addition, we can define an arbitrary number of parts or gaps as thinner or larger as needed. The EDA benefits from this representation, sampling random arbitrary structures and using probabilistic learning to determine whether a region must have material. The EDA is a global optimizer which can propose different topologies without the need of a priori knowledge neither initial solutions. In addition it uses a probabilistic model which smoothly evolve through generations. In consequence, at the beginning of the optimization process it arbitrarily proposes topologically different structures, while at the convergence phase it performs similar to a local search algorithm. The EDA uses few parameters which can be set in a straight forward manner. We report several study cases from the specialized literature, showing that our proposal outperforms reported results from up-to-date well performed algorithms.
CitationValdez, S. I. [et al.]. Automated shape optimization using a multigrid method and estimation of distribution algorithms. A: COMPLAS XIII. "COMPLAS XIII : proceedings of the XIII International Conference on Computational Plasticity : fundamentals and applications". CIMNE ed. Barcelona: CIMNE, 2015, p. 818-833.
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