# Adaptive Salp Swarm Algorithm for Optimization of Geotechnical Structures
## 8 Conclusions  
The primary objective of this study was to introduce an adaptive version of the salp swarm algorithm (ASSA). Two new equations for the leader- and follower-updating positions were introduced to improve the proposed ASSA's search and discovery abilities. In the standard SSA, the leading salp modifies its position based on a single point, which is the food location. However, due to a lack of knowledge about the real position of the food location, the algorithm may be locked at the local optimum. To overcome this weakness and to improve the exploration ability of the algorithm, in the proposed ASSA, half of the population was considered as leaders, which adjusted their positions not only based on the food location but also based on their previous positions. In addition, instead of the constant value considered in an SSA for follower-position-updating, in the ASSA, a random value was proposed. In addition, at each iteration of the optimization process, the ASSA replaced the worst salp, yielding the highest fitness value with a randomly generated salp. A statistical analysis was carried out in order to make an accurate assessment of the new algorithm's performance. The proposed method was shown to perform admirably in terms of accuracy, stability, and robustness when tested on some well-known unimodal and multimodal test functions. The paper's second goal was to automate a cost-effective design process for spread foundations and retaining walls. A computer program in Matlab was developed to reduce the cost of retaining structures and spread footings. On four case studies of these structures, the proposed method was compared to a classical SSA and some state-of-the-art metaheuristic algorithms. Given the final results, it was demonstrated that the ASSA outperformed the other techniques and should be able to provide better optimal  
\begin{table}
\begin{tabular}{c c c c c} \hline
**Example No.** & **Index** & **ASSA vs. SSA** & **ASSA vs. FA** & **ASSA vs. PSO** \\ \hline \multirow{4}{*}{Ex. 1} & \(p\)-val. & 6.0 \(\times\) 10\({}^{-6}\) & 1.73 \(\times\) 10\({}^{-6}\) & 1.73 \(\times\) 10\({}^{-6}\) \\  & R+ & 453 & 465 & 465 \\  & R\(-\) & 12 & 0.0 & 0.0 \\  & Win & ASSA & ASSA & ASSA \\ \hline \multirow{4}{*}{Ex. 2} & \(p\)-val. & 0.012 & 1.73 \(\times\) 10\({}^{-6}\) & 1.73 \(\times\) 10\({}^{-6}\) \\  & R+ & 354 & 465 & 465 \\  & R\(-\) & 111 & 0.0 & 0.0 \\  & Win & ASSA & ASSA & ASSA \\ \hline \multirow{4}{*}{Ex. 3} & \(p\)-val. & 0.106 & 1.73 \(\times\) 10\({}^{-6}\) & 1.73 \(\times\) 10\({}^{-6}\) \\  & R+ & 311 & 465 & 465 \\  & R\(-\) & 154 & 0.0 & 0.0 \\  & Win & NA & ASSA & ASSA \\ \hline \multirow{4}{*}{Ex. 4} & \(p\)-val. & 1.73 \(\times\) 10\({}^{-6}\) & 1.73 \(\times\) 10\({}^{-6}\) & 1.73 \(\times\) 10\({}^{-6}\) \\  & R+ & 465 & 465 & 465 \\  & R\(-\) & 0.0 & 0.0 & 0.0 \\  & Win & ASSA & ASSA & ASSA \\ \hline \multirow{4}{*}{Ex. 5} & Superior & \multirow{2}{*}{3/0/1} & \multirow{2}{*}{4/0/0} & \multirow{2}{*}{4/0/0} \\  & /Inferior/NA & & & \\ \end{tabular}
\end{table}
Table 20: Results of [PERSON]’s rank sum test for design examples.  
results. The new method concurrently satisfied geotechnical and structural limit states while simultaneously providing a cost-effective design.  
This research received no external funding.  
Not applicable.  
The data that support the findings of this study are available from the corresponding author upon request. This research work abides by the highest standards of ethics, professionalism, and collegiality. All authors have no explicit or implicit conflict of interest of any kind related to this manuscript.