## 5 Conclusions  
In this study, 42,000 parametrical case analyses were conducted to investigate the appropriateness of the use of the HS algorithm for the design of the cantilever retaining walls. The main aim was to evaluate the effects of the change of the design variables on the cost-effective design process. In addition to this, 72 different finite element analyses were performed to check the envisaged design dimensions obtained from optimization results. The results of the analysis show that the most effective factor in the design of cantilever soldier piles is the excavation depth. The application depth of cantilever soldier piles without an additional support structure is limited due to their safety inadequateness. This safety adequateness cannot be obtained with the increase of design dimensions with regard to the envisaged constraints of the solution. It will be an appropriate result to say that 10 m depth can be the upper limit of the excavations, which are supported by cantilever soldier piles. The surrounding soil properties are selected as the most significant factors to designate the design dimensions. The increase of shear strength reduces the necessity to build a retaining structure for resisting lateral earth pressures. In contrast, the decrease of shear strength angle can extend the length and enlarge the diameter of pile in an unforeseen way. The change of unit weight of soil formation is also an important effect but not as much as the change of shear strength. The determination of the coefficient of soil reaction also necessitates a hard process and has an apparent influence on the length of the pile system. Therefore, caution is warranted for the determination or the selection phenomenon of the coefficient of the soil reaction. The application of external load is a problem that can be overcome by the extension of the cantilever soldier pile for the cases applied in the context of this study. Consequently, the integrated evaluation of design variables and results of finite element analyses show that the application of the HS algorithm to cantilever soldier pile retaining walls is an acceptable approach to design cantilever soldier pile retaining wall systems.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{Parameter} & \multicolumn{2}{c}{\(q=0\) kPa} & \multicolumn{2}{c}{\(q=10\) kPa} \\ \cline{2-5}  & \(OR\) & \(PR\) & \(OR\) & \(PR\) \\ \hline _FoS_ & - & 1.15 & - & 1.24 \\ \(M_{max}\) (kNm/m) & 123.74 & 122.99 & 181.43 & 181.4 \\ \(V\) (kN/m) & 34.99 & 44.56 & 45.75 & 50.38 \\ \(z\) (m) & 7.4 & 7.0 & 7.6 & 7.8 \\ \hline \hline \end{tabular}
\end{table}
Table 8: Comparison of optimization results and numerical analysis for 6 m excavation depth.  
**Author Contributions**: [PERSON] and [PERSON] generated the analysis codes. [PERSON], [PERSON], and [PERSON] developed the theory background and formulations of the active control system. The text of the paper was formed by [PERSON] and [PERSON], [PERSON] supervised the research direction. All authors have read and agreed to the published version of the manuscript.  
**Funding**: This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (2020R1A2C1A01011131). This research was also supported by the Energy Cloud R&D Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT (2019M3F2A1073164).  
**Conflicts of Interest**: The authors declare no conflict of interest.