A family of MMA approximations for structural optimization

Abstract

This paper deals with the approximation concepts approach applied to structural optimization.In 1987, Svanberg proposed the method of moving asymptotes for solving structural optimization problems. This approximation is monotonous and can efficiently treat problems characterized by such a behavior. Svanberg (1995) proposed a modification of the MMA approximation by making it non monotonous. This property is based on an heuristically updated parameter. The resulting approximation is called GCMMA. In Bruyneel et al. (1999), it is shown that it is possible to generate non monotonous GCMMA based approximations, called GBMMA, by using the gradient and/or the function values from previous iteration. It was shown that such approximations improve the convergence speed of the optimization process.In many optimization problems (for example composite structures optimization or simultaneous sizing and optimal configuration of truss structures), the structural responses present both monotonous and non monotonous behaviors. A mixed monotonous/non monotonous approximation scheme has to be used for approximating in the best way the optimization problem (Zhang et al., 1998 andFleury, 2000).In this paper, we propose to show that it is possible to derive a very general approximation of the MMA family based on gradients and/or functions values at two successive design step,

Optimization of forging processes using Finite Element simulations

“…This makes them useful when a quick, but not too large improvement is required. For a more global convergence, other algorithms could be studied, such as GCMMA (Svanberg 1995;Bruyneel et al 2002). However, an important disadvantage of such algorithms is the necessity to calculate sensitivities.…”

First-order sequential convex programming using approximate diagonal QP subproblems

“…Several variants of, and extensions to, the original MMA algorithm have been developed during the last decades, e.g. see Borrval and Petersson (2001), Bruyneel et al (2002) and Zillober (2002). Various approaches for enforcing global convergence have also been proposed.…”

“…see Zhang and Fleury (1997) and Bruyneel et al (2002). In other words: using the approximate curvatures (15) in (12) implies that (12) becomes the quadratic approximation to the reciprocal approximation in the point x {k} (Haftka 2007, personal communication).…”

“…These algorithms-and some related variants, e.g. see Borrval and Petersson (2001), Bruyneel et al (2002) and Zillober et al (2004)-are also known as sequential convex programming (SCP) methods (Fleury 1993;Zillober et al 2004;Duysinx et al 2009). …”

Application of a bi-level scheme including topology optimization to the design of an aircraft pylon

“…Here the Conlin approximation (Fleury and Braibant, 1986) is used in conjunction with efficient dual solvers (Fleury, 1993) in a multi-objective formulation. The GCM approximation (Bruyneel et al, 2002) is also available in TOPOL for problems including body forces and presenting non-monotonous behaviors (Bruyneel and Duysinx, 2005;Bruyneel, 2006). …”