Abstract Engineering structures typically use components selected from standard profile databases to ensure manufacturability, cost efficiency, and interchangeability. When combined with topology optimization, this requirement gives rise to challenging problems in which both the structural topology and the discrete cross-sectional sizes are determined simultaneously. This study proposes a two-level approximation method to efficiently address such problems, with particular consideration of the interdependence among discrete size variables inherent in standard profile selection. The first-level problem employs an extended approximation concept to evaluate structural responses and enables a binary-coded Genetic Algorithm to update topology with minimal structural analyses. The second-level problem relaxes the discrete constraints through a variable-continuation approach, derives a continuous optimum via the dual method, and then applies a sorting-and-filtering strategy to achieve discrete search space reduction, thereby enabling efficient determination of the discrete optimum within an integer-coded Genetic Algorithm. Numerical examples show that the proposed framework can achieve competitive designs with a limited number of full structural analyses, as analyses are invoked mainly for updating the first-level approximation problem, while candidate evaluations are carried out on inexpensive surrogate models.
Li et al. (Thu,) studied this question.