Knowledge-based global optimization of cold-formed steel columns

Abstract

Cold-formed steel member cross-section shapes are difficult to optimize because of the nonlinear behavior of such members under buckling loads. Traditional gradient-based optimization schemes, employing deterministic design specifications for the objective function, are inefficient and severely limited in their ability to search the full solution space of member cross-sections. Herein, a new global optimization approach that is well suited for optimization of such cross-sections is introduced. There are two distinguishing characteristics of this approach: (1) it operates within a low-dimensional expert-based feature space rather than the high-dimensional design space of cross-section parameters; and (2) it uses a numerical implementation of the direct strength method (DSM) for the objective function. Through the use of Bayesian classification trees, the most significant coordinates of the expert-based feature space are defined; these coordinates are of low dimension and are in terms of features which provide insight into structural behavior. The classification trees are then used to efficiently generate candidate member cross-section prototypes for subsequent refined local optimization. Optimization results are presented for three structurally distinguishable length regimes to provide proof-of-concept of the proposed scheme. It is demonstrated that an expert-based feature space and its associated classification tree can effectively encapsulate the knowledge gained in the design optimization process and can be subsequently used as a starting framework for related design optimization problems. This is, in essence, a highly efficient knowledge transfer mechanism that is absent in most optimization schemes. Optimization of thin-walled members stands to benefit greatly from the combination of more flexible and general design methodologies (e.g., the DSM) and novel, emerging, optimization schemes such as the one presented herein.