A random search for discrete robust design optimization of linear-elastic steel frames under interval parametric uncertainty

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