Filter-based adaptive Kriging method for black-box optimization problems with expensive objective and constraints

To reduce the computational cost of solving engineering design optimization problems with both expensive objective and constraints, a novel filter-based adaptive Kriging method notated as FLT-AKM is proposed in this paper. In FLT-AKM, a probability of constrained improvement (PCI) criterion is developed based on the notion of filter to sequentially generate new samples for updating Kriging metamodels of objective and constraints. At each iteration, an infill sample point is allocated at the position where the PCI is maximized to achieve potential improvement in optimality and feasibility. And the Kriging metamodels are consecutively updated by the newly-added infill sample points, which leads the FLT-AKM search to rapidly converge to the global optimum. The performance of the proposed FLT-AKM method is tested on a number of numerical benchmark problems via comparing with several widely-used metamodel-based constrained optimization methods. The comparison results indicate that FLT-AKM generally outperforms the competitors in terms of global convergence and efficiency performance. Finally, FLT-AKM is successfully applied to an all-electric GEO satellite MDO problem. The optimization results show that FLT-AKM is able to find a better feasible design with fewer computational budgets compared with our previous study, which demonstrates the effectiveness and practicality of the proposed FLT-AKM method for solving real-world expensive black-box engineering design optimization problems.