In this paper, mixed categorical structural optimization problems are investigated. The aim is to minimize the weight of a truss structure with respect to cross-section areas, materials and cross-section type. The proposed methodology consists of using a bi-level decomposition involving two problems: master and slave. The master problem is formulated as a mixed integer linear problem where the linear constraints are incrementally augmented using outer approximations of the slave problem solution. The slave problem addresses the continuous variables of the optimization problem. The proposed methodology is tested on three different structural optimization test cases with increasing complexity. The comparison to state-of-the-art algorithms emphasizes the efficiency of the proposed methodology in terms of the optimum quality, computation cost, as well as its scalability with respect to the problem dimension. A challenging 120-bar dome truss optimization problem with 90 categorical choices per bar is also tested. The obtained results showed that our method is able to solve efficiently large scale mixed categorical structural optimization problems.

翻译：在本文中,对结构优化的混合绝对问题进行了调查,目的是在跨部门领域、材料和跨部门类型方面最大限度地减少Trus结构的重量。拟议方法包括使用涉及两个问题的双层分解:主子和奴隶。主子问题是一个混合的整线问题,使用奴隶问题解决办法的外部近似值逐步增加线性限制。奴隶问题涉及优化问题的连续变数。拟议方法在三个不同的结构优化测试案例中进行测试,其复杂性越来越大。与最新算法的比较强调拟议方法在最佳质量、计算成本和在问题层面的可调整性方面的效率。一个具有挑战性的120巴圆顶峰优化问题,每条有90个绝对选择。获得的结果表明,我们的方法能够有效地解决大规模混合结构优化问题。