Multiple cardinality constraints and automatic member grouping in the optimal design of steel framed structures

For structural optimization problems, such as the weight minimization of steel framed structures, the sizing design variables are often defined as the cross-sectional areas of the members, which are to be chosen from commercially available tables such as those provided by the American Institute of Steel Construction. Alternatively, the cross-section dimensions, b_f, t_f, d and t_w (which may be discrete or continuous) can be defined independently for each profile. This paper discusses the structural optimization problem of framed structures involving sizing design variables where a special genetic algorithm encoding is proposed in order to establish a strategy to discover ideal member grouping of members. Advantages in fabrication, checking, assembling, and welding, which are usually not explicitly included in the cost function, are thus expected. The adaptive penalty method (APM) previously developed by the authors is applied to enforce all other mechanical constraints considered in the structural optimization problems discussed in this paper.