Dynamic Co-Kriging Method Using Probability of Multi-Objective Constrained Improvement for Aerospace System Optimization

To effectively solve the aerospace system multi-objective optimization problems with expensive black-box constraints, a novel dynamic Co-Kriging method (DCK) is proposed in this paper. Via taking full advantages of multi-fidelity simulation models, Co-Kriging metamodels are constructed for multi-objective optimization to efficiently obtain the pseudo Pareto frontier. And a probability of multi-objective constrained improvement (PMCI) function is developed to measure the potential improvements of optimality, feasibility, and uniformity for the Pareto frontier. During the optimization process, the pseudo Pareto frontier points with maximum PMCI are identified as the infill multi-fidelity samples to dynamically refine the Co-Kriging metamodels, which leads the search to the true Pareto frontier rapidly. A two-dimensional numerical example is employed to demonstrate the optimization capacity of DCK. Finally, a low-thrust GEO transfer trajectory optimization problem and a satellite structure optimization problem are investigated. The optimization results indicate that DCK performs better than the competitive algorithms in both computational cost and Pareto frontier exploration performance, which illustrates the effectiveness and practicality of the proposed method for solving real-world aerospace system multi-objective optimization problems.