Selection of appropriate approximation schemes in multi-disciplinary engineering optimization

Abstract

Convex approximation methods used in structural optimization are discussed in this paper. These methods ranging from CONvex LINearization method (CONLIN), the Method of Moving Asymptotes (MMA) to the Sequential Quadratic Programming method (SQP) can be basically classified as monotonic and non-monotonic approximations. It is shown that for the considered problems of different nature, the achievement of a successful and efficient design will essentially depend upon whether approximation schemes can be appropriately selected. To ensure the approximation quality, a Generalized Method of the Moving Asymptotes (GMMA) and a Diagonal Quadratic Approximation (DQA) based optimizers are developed, respectively, in this work. In addition, it can be seen that the mixed approximation DQA-GMMA can be also established. Numerical examples of truss design will be used to illustrate these methods.