## 4 Discussion  
The presented study confirms the application of artificial immune systems in optimization processes. It is suitable to support design selection where natural frequencies are important from a technical requirement perspective. The presented approach demonstrates data management between the AIS and Ansys Workbench based on session and CSV files to exchange information about the design parameters (input data) and measured characteristics (output data). The optimization process is based on a static metamodel. The AIS is not widely implemented in commercial engineering optimization packages compared the to GA. The CAIS variant brings the need to control the additional optimization parameters, which increase the setup complexity and pre-work time. Compared to commercial applications of the genetic algorithm, the AIS gives more beneficial results in terms of the model area and number of fitness function evaluations. Furthermore, the costimulated artificial immune system is more efficient in terms of the number of cases with a similar model area, as presented in Table 7, with the cost of a slightly poorer optimal design configuration.  
Recommendations for further studies include the kinetic energy distribution in the parametric model definition and the incorporation of metamodel updates at each iteration, as well as additional benchmarking and back-to-back comparisons with other bio-inspired algorithms.  
Writing--original draft preparation, R.R.; writing--review and editing, M.S. and S.R. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding. The study was completed with the support of Avio Polska Sp. z o.o. (Grazynskiego 141, 43-300 Bielsko-Biala, Poland), which provided the model, material data, boundary conditions and a shared workstation with an Ansys license.  
Not applicable.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter Name** & **Genetic Algorithm** & **Artificial Immune System** & **Costimulated Artificial Immune** \\  & **(GA)** & **(AIS)** & **System (CAIS)** \\ \hline Casing shell A [in] & 0.110 & 0.099 & 0.098 \\ \hline Casing shell B [in] & 0.165 & 0.142 & 0.150 \\ \hline Casing shell C [in] & 0.111 & 0.120 & 0.120 \\ \hline Forward hook thickness [in] & 0.183 & 0.200 & 0.200 \\ \hline Rear hook thickness [in] & 0.107 & 0.111 & 0.111 \\ \hline Forward hook leaning [\({}^{\circ}\)] & 92.1 & 100.0 & 96.4 \\ \hline Rear hook leaning [\({}^{\circ}\)] & 82.3 & 80.0 & 82.8 \\ \hline Nozzle shell thickness [in] & 0.083 & 0.063 & 0.061 \\ \hline Forward hook position [in] & 0.036 & 0.040 & 0.040 \\ \hline Rear hook position [in] & \(-\)0.048 & \(-\)0.050 & \(-\)0.050 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Design variable comparison: genetic algorithm vs. artificial immune system.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Genetic Algorithm** & **Artificial Immune** & **Costimulated Artificial** \\  & **(GA)** & **System (AIS)** & **Immune System (CAIS)** \\ \hline Number of fitness function evaluations & 1374 & 443 & 380 \\ \hline Model area, in\({}^{2}\) & 19.163 & 19.109 & 19.114 \\ \hline Natural frequency & 125.0 & 125.1 & 125.0 \\ \hline \hline \end{tabular}
\end{table}
Table 7: Algorithm solution comparison: genetic algorithm vs. artificial immune system.  
Data Availability Statement: The data that support the findings of this study are not openly available due to reasons of sensitivity nature of the research.  
Author [PERSON] was employed by the company AvioPolska Sp. z o.o. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.