###### 1 Introduction  
Aircraft shape optimization is one of the key problems in aerodynamic configuration design. The traditional aerodynamic optimization design methods mainly rely on experience and trial-and-error methods, which require a lot of human, material and financial resources, and not only take a long time but also require a lot of computational resources [1]. In recent years, with the rapid development of computational fluid dynamics (CFD) technology, the combination of numerical methods and optimization algorithms for the aerodynamic shape optimization of aircraft can significantly shorten the development cycle and reduce the design cost [2]. Therefore, it is important to carry out research on efficient aerodynamic optimization design methods based on the combination of CFD technology and optimization algorithms for the development of aerodynamic optimization design. Among numerous aerodynamic optimization studies, gradient-based methods and heuristic algorithms are two of the most widely used methods. Gradient-based methods are particularly attractive due to their ability to significantly improve the efficiency of high-dimensional optimization problems. The adjoint method proposed by [PERSON] [3] is an effective sensitivity analysis method that evaluates sensitivity information by solving the adjoint problem regardless of the number of design variables. Therefore, the computational time of sensitivity analysis can be significantly reduced. By combining the adjoint method with the gradient method, the optimization efficiency can be greatly improved. In recent years, this technique has been widely used in aerodynamic optimization [4,5]. However, two reasons make this technique less attractive: one is its difficulty in dealing with constrained/multi-objective problems, and the other is that it is easy for it to fall into local optima. Heuristic algorithms do not need to rely on information about a specific problem and have good global performance in finding the optima; they are thus particularly suitable for solving problems with complex multiple local optima. Among them, genetic algorithms (GAs), differential evolution (DE) algorithm and particle swarm optimization (PSO) algorithm are the most popular methods in the field of aerodynamic optimization, and they have all been successfully applied in aerodynamic optimization [6, 7, 8, 9]. However, their evolutionary procedures require multiple calls to the CFD analysers, which significantly increases the computational cost. Therefore, it is necessary to improve the optimal efficiency and therefore to develop optimization algorithms in particular allowing for balanced exploitation and exploration capabilities [10]. Many engineering problems are complex high-dimensional multimodal problems, so that most algorithms converge slowly, easily fall into local optima and are inefficient in dealing with such problems. Aerodynamic optimization is a highly complex nonlinear problem with multi-parameter, high-dimensional and multimodal characteristics. In order to solve aerodynamic optimization problems effectively, it is undoubtedly necessary to develop new intelligent and knowledge-based algorithms with satisfactory performance. The genetic algorithm has good robustness and global search capability [11, 12, 13, 14, 15], and can be well adapted to solve various types of problems. The cultural algorithm is a knowledge-based super-heuristic algorithm, and its unique two-layer evolutionary mechanism can improve the evolutionary efficiency very well. The hybrid of genetic algorithms and cultural algorithm can combine the advantages of both, and then solve aerodynamic optimization problems efficiently. Cultural algorithm (CA) [16] is an evolutionary algorithm based on the simulation of a two-layer evolutionary mechanism of human society, proposed by [PERSON] in 1994. It was inspired by and developed from human sociology and aimed to model the evolution of the cultural component of evolutionary systems over time [17].