An Efficient Hybrid Multi-Objective Optimization Method Coupling Global Evolutionary and Local Gradient Searches for Solving Aerodynamic Optimization Problems - Cao, Fan; Tang, Zhili; Zhu, Caicheng; Zhao, Xin (Mathematics (Basel), 2023)
Aerodynamic shape optimization is frequently complicated and challenging due to the involvement of multiple objectives, large-scale decision variables, and expensive cost function evaluation. This paper presents a bilayer parallel hybrid algorithm framework coupling multi-objective local search and global evolution mechanism to improve the optimization efficiency and convergence accuracy in high-dimensional design space. Specifically, an efficient multi-objective hybrid algorithm (MOHA) and a gradient-based surrogate-assisted multi-objective hybrid algorithm (GS-MOHA) are developed under this framework. In MOHA, a novel multi-objective gradient operator is proposed to accelerate the exploration of the Pareto front, and it introduces new individuals to enhance the diversity of the population. Afterward, MOHA achieves a trade-off between exploitation and exploration by selecting elite individuals in the local search space during the evolutionary process. Furthermore, a surrogate-assisted hybrid algorithm based on the gradient-enhanced Kriging with the partial least squares(GEKPLS) approach is established to improve the engineering applicability of MOHA. The optimization results of benchmark functions demonstrate that MOHA is less constrained by dimensionality and can solve multi-objective optimization problems (MOPs) with up to 1000 decision variables. Compared to existing MOEAs, MOHA demonstrates notable enhancements in optimization efficiency and convergence accuracy, specifically achieving a remarkable 5–10 times increase in efficiency. In addition, the optimization efficiency of GS-MOHA is approximately five times that of MOEA/D-EGO and twice that of K-RVEA in the 30-dimensional test functions. Finally, the multi-objective optimization results of the airfoil shape design validate the effectiveness of the proposed algorithms and their potential for engineering applications.