*Article* **An Efficient Hybrid Evolutionary Optimization Method Coupling Cultural Algorithm with Genetic Algorithms and Its Application to Aerodynamic Shape Design**

**Xin Zhao <sup>1</sup> , Zhili Tang 1,\*, Fan Cao <sup>1</sup> , Caicheng Zhu <sup>1</sup> and Jacques Periaux <sup>2</sup>**


**Abstract:** Evolutionary algorithms have been widely used to solve complex engineering optimization problems with large search spaces and nonlinearity. Both cultural algorithm (CA) and genetic algorithms (GAs) have a broad prospect in the optimization field. The traditional CA has poor precision in solving complex engineering optimization problems and easily falls into local optima. An efficient hybrid evolutionary optimization method coupling CA with GAs (HCGA) is proposed in this paper. HCGA reconstructs the cultural framework, which uses three kinds of knowledge to build the belief space, and the GAs are used as an evolutionary model for the population space. In addition, a knowledge-guided *t*-mutation operator is developed to dynamically adjust the mutation step and introduced into the influence function. HCGA achieves a balance between exploitation and exploration through the above strategies, and thus effectively avoids falling into local optima and improves the optimization efficiency. Numerical experiments and comparisons with several benchmark functions show that the proposed HCGA significantly outperforms the other compared algorithms in terms of comprehensive performance, especially for high-dimensional problems. HCGA is further applied to aerodynamic optimization design, with the wing cruise factor being improved by 23.21%, demonstrating that HCGA is an efficient optimization algorithm with potential applications in aerodynamic optimization design.

**Keywords:** evolutionary algorithms; cultural algorithm; genetic algorithms; aerodynamic optimization design
