## 4 Conclusions  
Using metaheuristic methods and computational numerical modeling, the current work proposed a methodology for the design and optimization of Pelton turbines. The subsequent conclusions can be taken from the results:  
By using the suggested methods, it was possible to obtain an improvement in turbine efficiency of the \"Illuchi N\({}^{\circ}\)2\" power plant of about 2.56%. As a result, the ELEPCO SA company will better utilize its energy resources and generate more revenue. The set of optimal solutions resulting from the implementation of the NSGA-II genetic algorithm tends to converge towards the values of \(\frac{B}{L}=1\), \(\beta_{1}=4^{\circ}\), and \(\beta_{2}=170^{\circ}\). This is in line with the studies conducted by [PERSON] regarding the optimization of Pelton turbines. Using a mesh made up of 1,294,299 elements, a maximum simulation error of 3.59% was obtained in comparison to the operational data. To ascertain the results' independence from the element count, this mesh was previously examined. Furthermore, residual values that were less than \(1\times 10^{-6}\) were noted. This leads to the conclusion that the phenomenon is satisfactorily reproduced by the computational numerical simulation. Further work must be performed involving experimental work and considering other determinant parameters of Pelton turbines, such as the nozzle, spear, and penstock, which play a significant role in overall efficiency. Also, 3D-printed runners must be manufactured as a cost-effective way to test the optimized bucket's geometry. The proposed optimization methodology shows an efficiency improvement across numerical simulation results, which may be reflected on real operating turbines. Conceptualization, G.B. and V.H. ; methodology, G.B. and E.C. ; software, G.B. and S.A.; validation, G.B., V.H. and S.A.; formal analysis, G.B., V.H. and E.C. ; investigation, G.B. ; resources, V.H. and E.C. ; data curation, G.B. and E.C. ; writing--original draft preparation, G.B. ; writing--review and editing, V.H. and E.C. ; visualization, G.B. and S.A.; supervision, V.H. and E.C. ; project administration, V.H. ; funding acquisition, V.H. All authors have read and agreed to the published version of the manuscript. This research was funded by the Escuela Politecnica Nacional through the research project PIS-22-17: \"Study of non-planar additive manufacturing through 3D printing with a modified low-cost printer\" and project PIIF-23-04: \"Thermographic Study of the Influence of Temperature Variations in 3D Printing with Bowden Technology Applied to Automotive Components Printing\". The original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding author. The authors declare that they have no conflicts of interest. \begin{table}
\begin{tabular}{c c} \hline \hline
**Geometry** & **Efficiency \%** \\ \hline Original Geom. & 79.65 \\ Optimized Geom. & 82.21 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Efficiency of the original and optimized geometries. * (3) Installed Global Hydropower Capacity Could Reach 1200 GW in 2022, Report Says. Available online: [[https://www.hydroreview.com/hydro-industry-news/installed-global-hydropower-capacity-could-reach-1200-gw-in-2022-report-says/#gref](https://www.hydroreview.com/hydro-industry-news/installed-global-hydropower-capacity-could-reach-1200-gw-in-2022-report-says/#gref)]([https://www.hydroreview.com/hydro-industry-news/installed-global-hydropower-capacity-could-reach-1200-gw-in-2022-report-says/#gref](https://www.hydroreview.com/hydro-industry-news/installed-global-hydropower-capacity-could-reach-1200-gw-in-2022-report-says/#gref)) (accessed on 26 February 2023). * (4) International Hydropower Association. 2022 Hydropower Status Report. 2022.