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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.<\/jats:p>","DOI":"10.1093\/jcde\/qwag046","type":"journal-article","created":{"date-parts":[[2026,5,7]],"date-time":"2026-05-07T11:43:35Z","timestamp":1778154215000},"page":"203-214","source":"Crossref","is-referenced-by-count":0,"title":["Two-level approximation method for standard profile selection and topology optimization"],"prefix":"10.1093","volume":"13","author":[{"given":"Jia","family":"Li","sequence":"first","affiliation":[{"name":"School of Astronautics, Beihang University , 37 Xueyuan Rd, Beijing 100191 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