## 4 Optimization Methods
### Optimization Process  
In this paper, the light optimization design platform software is used to build a visual optimization platform under the supercomputing Linux system. Automated optimization is achieved through the C language batch code and Isight Simcode plugin. Due to the objective function of optimization problems encountered in engineering being generally non-linear, the design space has characteristics of being discontinuous and non-linear. The traditional solutions that can be adopted are: adjoint method and surrogate model. The adjoint algorithm is essentially a gradient algorithm, which is easy to fall into local optimal value and cannot find the global optimal value. Thus the reliability of solving the aerodynamic problem of the multi-stage axial compressors is low [24; 25; 26]. The essence of the surrogate model is to establish a functional relationship between input and output. The disadvantage is that as the variables increase, the number of training samples and the calculation costs increase, and the accuracy deteriorates [27; 28; 29]. In this paper, the multi-island genetic algorithm (MIGA) is used for optimization. MIGA is a kind of parallel genetic algorithm. It divides the population of individuals into several sub-populations called \"islands.\" In the MIGA. each population of individuals is altered via the genetic operations of \"selection,\" \"crossover,\" and \"mutation.\" Each design of a population is then evaluated, and its fitness value is determined. All traditional genetic operations are performed separately on each sub-population. Then some individuals are selected from each island and migrated to different islands periodically, which is called \"migration.\" The parameters of the MIGA are set as follows: the sub-population size and number of generations are set to 10. The mutation rate and the migration rate are set to 0.01. The crossover rate is set to 1 and the migration interval is set to 5. More detail on the MIGA can be found in the literature [30; 31; 32]. It overcomes the premature convergence problem of traditional genetic algorithms by increasing the diversity of samples, and has a stronger multi-peak searching ability and global optimization capabilities. According to the engineering experience, the peak efficiency point below the design point flow rate is used as an optimization condition to improve the adiabatic efficiency and the surge margin of the original compressor simultaneously. The constraint is that the change in mass flow and total pressure ratio does not exceed 0.5%. The objective function \(f\) in the optimization process was set as follows:  
\[\max f=\eta\ \mathrm{if}\left\{ \begin{array}{l}\left|\frac{\pi_{t}-\pi_{t} Ori}{\pi_{t} Ori}\right|\leq 0.5\%\\ |m-m_{ori}|\leq 0.5\%\end{array} \right. \tag{7}\]  
where \(\eta\), \(\pi_{t}\), and \(m\) correspond to the adiabatic efficiency, the total pressure ratio of the optimized compressor, the mass flow of the optimized compressor, and \(\pi_{t}\)\({}^{Orig}\), \(m_{ori}\) are the total pressure ratio of the original compressor and the mass flow of the original compressor, respectively. The whole optimization process of the highly loaded compressor is shown in Figure 8. First, the modeling program reads the geometric information of the original compressor and then generates the Bezier surface modeling of the compressor blade, automatically generating the mesh to perform the three-dimensional CFD flow field calculation. Then, multi-island genetic algorithm optimization is performed to calculate the fitness; that is, the value of the objective function. If the condition for exiting the loop is reached (that is, the global optimal solution is found or the upper limit of the number of iterations is reached), then the optimization is completed and the optimized compressor is the output. Otherwise, the multi-island genetic algorithm will continue to optimize the exploration until the maximum feasible solution of the objective function is searched, thereby obtaining the final optimized compressor blade.