中文摘要：

实际的工程应用中，钢框架的基本构件大多是根据钢结构设计规范要求，从标准型钢库中选取，所组成的框架结构的截面尺寸非连续变化。因此，钢结构截面优化设计是典型的离散设计变量优化问题。若采用基于启发式的算法（如遗传算法等）进行求解，当可选截面类型较多时，其计算量巨大，求解效率低下。该文通过引入高维拉格朗日插值函数对该离散设计问题进行连续化，建立了可采用梯度优化方法进行求解的钢结构标准截面选型设计模型，并且使得连续化以后的设计变量个数大幅度减少。对给定截面类型种数为2^n个的可选截面集合，其设计变量只需n个即可。具体算例表明：与基于遗传算法的优化方法相比，该方法的计算效率提高1～2个数量级，并且在结构性能基本相当的情况下，得到的型钢种类更少，便于工程应用。

英文摘要：

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 2^n 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.