# Modification of Genetic Algorithm Based on Extinction Events and Migration
## 4 Compressor Disc Optimization  
Using the previously presented algorithm, an optimization process was carried out (the part of the shield marked in orange in Figure 9). The optimization of such a design layout made it possible to analyze the validity and correctness of the modified genetic algorithm.  
Figure 8: Convergence for the WOA (**a**), SSA, (**b**) and SMA (**c**) algorithms.  
Model and analysis were based on a previous paper [25], where FEM was used to calculate stress (von Mises) distribution in the nodes of the disc. The disc was divided into eighteen finite elements. The elements were 1D with linearly variable thickness. The FEM algorithm was created by the authors and validated in paper [25]. In Figure 10, a simplified model of the disc was presented.  
The classic GA and GEGA were comprised. For both algorithms were added boundary conditions to prevent increasing the thickness of the disk for the i + 1 node relative to the i-th node. The GA was default by MATLAB. Aim function was mass minimization, assuming that the allowable stresses (von Mises) are not exceeded. This condition was taken into  
Figure 10: Model of profiled disc with computational mesh density shown, where \(\omega\)—angular velocity, \(R_{0}\)—radius of the central hole, \(R\)—outer radius of the disc, \(\sigma_{w}\)—rim drawing, \(r_{i}\)—radial coordinate of the i-th design node, \(h_{i}\)—thickness of the i-th node.  
Figure 9: The disk of the axial compressor stage of a turbine jet engine: the real object (**a**) and the reference model of the disc with the optimized area marked (**b**).  
account by means of a penalty function, the value of which depended on the difference between von Mises and allowable stresses.  
For GE and GEGA, starting from the same starting point, 10 optimization processes were carried out. On this basis, the mean running time of the algorithms, as well as the mean and minimum weight after optimization, were estimated.  
In Table 2 and Figure 11, time of optimization and mass were compared.  
In Figures 12-16, for ten cycles of optimization by GA and GEGA, thickness (\(h\)) and von Mises stresses distribution (\(\sigma\)) for mesh nodes was presented.  
In Figure 15, for GA and GEGA optimization, mean value thickness (\(h\)) and von Mises stresses (\(\sigma\)) distribution was presented.  
The results presented in Figure 15 are consistent. Only for fifth node are small differences for thickness in favor of the GA. However, differences in time of optimization (Figure 11) confirm the legitimacy of using the GEGA.  
\begin{table}
\begin{tabular}{c c c c} \hline  & **GA** & **GEGA** & **\(\Delta\) [\%]** \\ \hline Time (s) & 40.30 & 5.67 & 85.94 \\ \hline Medium Mass (kg) & 1.062 & 1.066 & \(-\)0.301 \\ \hline Minimum Mass (kg) & 1.058 & 1.059 & \(-\)0.057 \\ \hline \end{tabular}
\end{table}
Table 2: Comparison of results of optimization of classic GA and GEGA for FEM analysis, where \(\Delta\) is MAE based on GA.  
Figure 11: Mean time of optimization and mean and minimal mass for GE and GEGA: real value (**a**) and relative value (**b**), where GA results are the basis.  
Figure 14: Distribution of thickness (\(h\)) for nodes (\(n\)) for GEGA optimization for ten series.  
Figure 12: Distribution of thickness (\(h\)) for nodes (\(n\)) for GA optimization for ten series.  
Figure 13: Distribution of von Mises stresses (\(\sigma\)) for nodes (\(n\)) for GA optimization for ten series.  
In paper [47], the ANN surrogate model and the GA were presented and time of optimization of the example above problem (Figure 9) was reduced by approximately 40% by the ANN surrogate model. Our new modification reduced the time of optimization by nearly 86%.