This study presents a new random search method for solving discrete robust design optimization (RDO) problem of planar linear-elastic steel frames. The optimization problem is formulated with an explicit objective function of discrete design variables, unknown-but-bounded uncertainty in material properties and external loads, and black-box constraint functions of the structural responses. Radial basis function (RBF) models serve as approximations of structural responses. The anti-optimization problem is approximated by an RBF-based optimization problem that is solved using an adaptive strategy coupled with a difference-of-convex functions algorithm. The adaptive strategy is embedded in an iterative process for solving the upper-level optimization problem. This process starts with a set of candidate solutions and iterates through selecting the best candidate among the available candidates and generating new promising candidates by performing a small random perturbation around the best solution found so far to refine the RBF approximations. It terminates when the number of iterations reaches an upper bound, and outputs the optimal solution that is the best solution obtained through the optimization process. Two test problems and two design examples demonstrate that the exact optimal or a good approximate solution can be found by the proposed method with a few trials of the algorithm.

这项研究提出了一种新的随机搜索方法，用于解决平面线弹性钢框架的离散鲁棒设计优化（RDO）问题。优化问题由离散设计变量的显式目标函数，材料特性和外部载荷的未知但有界的不确定性以及结构响应的黑匣子约束函数来表述。径向基函数（RBF）模型用作结构响应的近似值。反优化问题可以通过基于RBF的优化问题来近似，该问题使用自适应策略与凸函数函数算法相结合来解决。自适应策略嵌入在迭代过程中，用于解决上级优化问题。此过程从一组候选解决方案开始，并通过在可用候选中选择最佳候选并通过对迄今找到的最佳解决方案进行小的随机扰动来生成新的有希望的候选方案来进行迭代，以细化RBF近似值。当迭代次数达到上限时，它终止，并输出作为通过优化过程获得的最佳解决方案的最佳解决方案。两个测试问题和两个设计实例证明，通过该算法的几次试验，可以找到所提出的方法的精确最佳值或良好的近似解。当迭代次数达到上限时，它将终止，并输出作为通过优化过程获得的最佳解决方案的最佳解决方案。两个测试问题和两个设计实例证明，通过该算法的几次试验，可以找到所提出的方法的精确最佳值或良好的近似解。当迭代次数达到上限时，它终止，并输出作为通过优化过程获得的最佳解决方案的最佳解决方案。两个测试问题和两个设计实例证明，通过该算法的几次试验，可以找到所提出的方法的精确最佳值或良好的近似解。