Abstract: In practical engineering applications, components of a steel frame are selected from a standard steel library according to the design code for steel structures. The cross-section sizes of components in a frame are non-continuous, thusly the optimized selection of standard cross-section types is a typical discrete optimization problem. When the number of cross-section types is large, using heuristic-based algorithms (such as genetic algorithm, etc) results in inefficiency of resolving this problem. In this paper, the high-dimensional Lagrange interpolation functions are introduced to make the discrete design problem be continuous. The model of cross-section selection optimization is formulated, and it can be solved by gradient-based method. In this model, design variables are reduced obviously, and only n variables are needed to describe 2n types of cross-sections. Compared with genetic algorithm, the numerical examples show that the calculation efficiency can be improved 1-2 orders of magnitude by the method proposed, and less cross-section types can be obtained under the condition of roughly equal performance with genetic algorithm, which satisfies the engineering applications well.