## 1 Introduction  
Military and civil gas turbine engines can be used for turboshaft engines, drones, missiles, auxiliary power units for large engines, and many more industrial applications. To decrease the energy consumption of gas turbine engines and meet the environmental constraints, higher requirements are put forward for the efficiency of the engine components [1]. The axial compressor is the main consumer of the energy produced by the gas turbine engines and an important component to provide the necessary pressure ratio to the combustion chamber. Therefore, the design requirements of axial compressors are moving towards highly loaded, highly efficient, and large stall margins. For decades, scholars from various countries and institutions have devoted themselves to engineering design to make compressor operation more efficient and have formed an engineering design process that combines one-dimensional analysis, two-dimensional calculation, and three-dimensional computational fluid dynamics (CFD) analysis. However, due to the complexity of the flow field of axial compressors, designing a compressor with highly loaded, highly efficient, and large stall margins is very challenging. Many engineering-design philosophies have emerged over the years. [PERSON] et al. [2] proposed that the simplified radial balance equation in the design process of compressors is inaccurate. The radial entropy gradient of the compressor should be considered to obtain a correct velocity distribution. [PERSON] et al. [3] designed and tested a three-stage axial compressor with various aerodynamic design philosophy concepts: for example, customizable rotor airfoils to reduce shock wave losses, an efficient variable inlet guide vane geometry, a variable stator hub profile to minimize gap losses, and so on. To predict the span-wise parameter and speed line more accurately, [PERSON] et al. [4] proposed a new streamline curvature method to improve the incidence models and loss characteristics, which is mainly used in modern axial transonic compressors. [PERSON] et al. [5,6] developed a new vortex solution for the preliminary design of the axial compressor. This takes into account the distribution of axial and circumferential velocities near the end wall, thereby achieving the purpose of improving the performance in the preliminary design period. Subsequently, in order to further improve the performance of axial compressors, many scholars introduced optimization technology into the aerodynamic design of axial compressors. Among them, geometric modeling and optimization algorithms are important topics of research. In the field of geometric modeling, the traditional modeling methods are to change the element blade profile of different span-wise sections and change the three-dimensional stacking characteristic. [PERSON] et al. [7] used two third-order spline functions to construct the pressure and suction surfaces, with the leading edge geometry consisting of an ellipse and the trailing edge being described by a circular arc. [PERSON] et al. [8] used the third-order B-spine curves to change the thickness distribution in different span sections and the mean camber line, thereby improving the efficiency of NASA rotor 67. [PERSON] et al. [9] adopted another element blade modeling method, which used nondimensional parameterization for the suction and pressure surface, which makes the designer able to change the overall suction or pressure surface with little geometric freedom. The three-dimensional stacking characteristic of the axial compressor mainly includes the sweep and dihedral technology. [PERSON] et al. [10] applied sweep and lean comprehensively to the booster stator of the BR710 engine, which improved the aerodynamic performance of stators and delayed the occurrence of corner stall. [PERSON] et al. [11,12] first successfully reported that the modifications of sweep and lean of the rotor blades in a multistage compressor in the open literature. It achieves the design goal of improving efficiency without significant loss in surge margin.