A Sequential Optimization Algorithm Using Metamodel-Based Multilevel Analysis

An efficient sequential optimization approach for metamodel was presented by Choi et al. (13) This paper describes a new approach of the multilevel optimization method studied in Refs. (2) and (20,21). The basic idea is concerned with multilevel iterative methods which combine a descent scheme with a hierarchy of auxiliary problems in lower dimensional subspaces. After fitting a metamodel based on an initial space filling design, this model is sequentially refined by the expected improvement criterion. The advantages of the method are that it does not require optimum sensitivities, nonlinear equality constraints are not needed, and the method is relatively easy to understand and use. As a check on effectiveness, the proposed method is applied to an engineering example.