## 1 Introduction
[PERSON] et al. [13] used the B-spline curve interpolation to change the three-dimensional stacking law of the compressor rotor rotor37. After optimization, the adiabatic efficiency was improved by 1.28%. [PERSON] et al. [14] found an optimized sweep stator which is beneficial for decreasing the total pressure loss at the hub region and improving the performance of a multistage axial-flow compressor. [PERSON] et al. [15] systematically expounded the influence mechanism of three-dimensional stacking on axial compressors. It is proposed that the forward-sweep in the tip region of a transonic rotor can significantly improve the stall margin. Besides, designers can reduce losses by changing the distribution of reaction in the span height to avoid applying too much or too little reaction to the hub region. In 2003, [PERSON] et al. [16] proposed a novel geometric modeling method. This method uses the Bezier surface method to modify the suction surface of an axial compressor rotor and uses a Navier-Stokes code coupled to the gradient method to improve efficiency by moreover 1% with little change in operating range. Later, [PERSON] et al. [17] proposed a quasi-3D aerodynamic design concept for blade modeling. In this study, the Bezier surface was chosen to parameterize the camber line angle distribution in the radial direction of the blade along the chord length from the leading edge to the trailing edge. The geometric blades are formed by superimposing the camber line with a given thickness distribution, thereby ensuring a smooth blade shape with few design parameters. In the field of optimization algorithms, [PERSON] et al. [18] in 1983 first integrated numerical optimization technology with the aerodynamic design of a compressor blade, and successfully used the local optimization algorithm of Control Program for Engineering Synthesis (COPES) to improve the aerodynamic performance of a controlled diffusion airfoil. Subsequently, [PERSON] et al. [19] optimized and tested several compressor cascades by using an inviscid/viscous two-dimensional flow solver with the normal distribution random search and the gradient method. It reduces the losses of airfoils and widens the range of available incidences. [PERSON] et al. [20] used a multi-objective evolutionary algorithm and the Pareto optimal concept to optimize the compressor rotor with a higher pressure ratio and higher efficiency than those of the original rotor. [PERSON] et al. [21] used the genetic algorithm and response surface model for global optimization to obtain an optimized design of the NASA rotor37, where the adiabatic efficiency was increased by 1.58%. However, the aerodynamic design and optimization of a high loaded axial compressor with high aerodynamic performance still have three problems, which are rich engineering design experience, high dimensions, and time-consuming calculations. To overcome these three problems, this paper takes an engineering-designed 2.5-stage highly loaded axial flow compressor as an example to introduce the design process and the adopted design philosophies. Then, this paper verifies the numerical method of computational fluid dynamics. A new Bezier surface modeling method for the entire suction surface and pressure surface of blades is developed, and the multi-island genetic algorithm is directly used for further optimization. The new Bezier surface modeling method and the multi-island genetic algorithm greatly overcome the problem of high dimensions and time-consuming calculations. Finally, this paper reveals the internal complex flow mechanism of the peak efficiency and stall margin of the axial compressor before and after optimization.