A novel non-probabilistic reliability-based design optimization method using bilevel accelerated microbial genetic algorithm

In this study, an efficient algorithm for non-probabilistic reliability-based design optimization (NRBDO) is presented. To improve the convergence rate, the sequential Kriging model is applied to the inner-layer optimization of the double-nested optimization model, maximizing the utility of each sampling point. During the global exploration stage, the algorithm employs an expected improvement criterion and a parallel sampling strategy. In the local exploration stage, a minimum surrogate prediction criterion is utilized to identify new sampling points, resulting in enhanced efficiency and accuracy of Kriging surrogate model. The optimization of each sampling criterion is performed using the differential evolution algorithm. Adaptive switching between global and local exploration is achieved by considering the relationship between new and known sample points, ensuring the identification of the optimal solution. To further enhance optimization efficiency, an Aitken \(\Delta^{2}\) ${\mathrm{\Delta }}^2$ acceleration strategy is applied to improve the current population, while a heuristic pattern-based local search method is employed to enhance the subpopulation, developing of a bilevel accelerated microbial genetic algorithm to solve optimal solution. The efficiency of the proposed method is demonstrated through two numerical cases and an engineering application involving the ram of the TK6932 heavy-duty floor-type milling and boring machine.