In this work, large-scale structural optimization problems involving non-ordinal categorical design variables and continuous variables are investigated. The aim is to minimize the weight of a structure with respect to cross-section areas, with materials and stiffening principles selection. First, the problem is formulated using a bi-level decomposition involving master and slave problems. The master problem is given by a first-order-like approximation that helps to drastically reduce the combinatorial explosion raised by the categorical variables. Continuous variables are handled in a slave problem solved using a gradient-based approach, where the categorical variables are driven by the master problem. The proposed algorithm is tested on three different structural optimization test cases. A comparison to state-of-the-art algorithms emphasize efficiency of the proposed algorithm in terms of the optimum quality, the computation cost, and the scaling with respect to the problem dimension.

在这项工作中，研究了涉及非常规分类设计变量和连续变量的大规模结构优化问题。目的是通过选择材料和加劲原理来使结构相对于横截面面积的重量最小。首先，使用涉及主问题和从问题的两级分解来表述问题。主要问题由一阶近似给出，该近似有助于极大地减少由类别变量引起的组合爆炸。连续变量在使用基于梯度的方法解决的从属问题中处理，其中分类变量由主问题驱动。该算法在三个不同的结构优化测试案例中进行了测试。