# A Spring Search Algorithm Applied to Engineering Optimization Problems
## 7 Experimental Results and Discussion
### Algorithms Used for Comparison
Cost** \\ \hline \(SSA\) & 125 & 21.41890 & 10.941113 & 0.515 & 0.515 & 0.4 & 0.7 & 0.3 & 0.02 & 0.6 & 85,067.983 \\ \(EPO\) & 125 & 21.40732

## 9 Conclusions

There are many optimization problems in the different scientific domains that must be solved using the algorithms with each case's necessary characteristics. In this project, a new optimization algorithm called spring search algorithm (SSA) was developed; [PERSON]'s law describes the starting point or basic concept. The search agents of the proposed method are weights that are connected by several springs. The system starts from a transitory situation or state and stabilizes at the equilibrium point, according to the law of the spring. To evaluate the algorithm and purchase it, almost 40 standard objective functions, including unimodal and multimodal functions, in addition to CEC2015, were used to assess the performance of the proposed algorithm in solving optimization problems of a different nature. To review and analyze the algorithm's results, these were compared with eight widely known optimization algorithms: GA, PSO, GSA, TLBO, GWO, GOA, SHO, and EPO. The results in the functions show the superior exploration and exploitation capabilities of SSA compared to other optimization algorithms, for both unimodal and multimodal functions. The same occurs with the simulations using the SSA algorithm and the eight algorithms selected for comparison in the case of CEC2015, which shows the SSA's high aptitude to solve this type of problem to optimize the function. In addition to the work carried out on the almost 40 functions, the SSA algorithm was evaluated in five engineering design optimization problems to evaluate the performance in solving optimization problems in real situations, showing that it is much more competitive than other algorithms. For future work, it is suggested to develop a binary version of the SSA algorithm and apply this algorithm to multi-objective problems. Likewise, extending the concept of [PERSON]'s law to more complex models with more adjustment parameters, which, even though it will reduce simplicity, could generate additional advantages. Conceptualization, M.D., Z.M., R.M.-M., R.A.R.-M., A.D. and J.M.G. ; methodology, M.D. and Z.M. ; software, M.D. ; validation, J.M.G., G.D., R.A.R.-M., R.M.-M., A.D. and O.P.M. ; formal analysis, A.D., O.P.M. ; investigation, M.D. and O.P.M. ; resources, J.M.G. ; data curation, G.D.; writing--original draft preparation, M.D. and Z.M. ; writing--review and editing, O.P.M., R.A.R.-M., R.M.-M., L.P.-A., G.D., and J.M.G. ; visualization, M.D. ; supervision, M.D. and Z.M. ; project administration, M.D. and Z.M. ; funding acquisition, R.A.R.-M. and R.M.-M. All authors have read and agreed to the published version of the manuscript. The current project was funded by Tecnologico de Monterrey and FEMSA Foundation (grant CAMPUSCITY project). The authors declare no conflict of interest. The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Algorithms** & **Best** & **Mean** & **Worst** & **Std. Dev.** & **Median** \\ \hline _SSA_ & 85,067.983 & 85,042.352 & 86,551.599 & 1877.09 & 85,056.095 \\ _EPO_ & 85,054.532 & 85,024.858 & 85,853.876 & 0186.68 & 85,040.241 \\ _SHO_ & 84,807.111 & 84,791.613 & 84,517.923 & 0137.186 & 84,960.147 \\ _GOA_ & 81,691.202 & 50,435.017 & 32,761.546 & 13,962.150 & 42,287.581 \\ _GWO_ & 84,491.266 & 84,353.685 & 84,100.834 & 0392.431 & 84,398.601 \\ _TLBO_ & 83,431.117 & 81,005.232 & 77,992.482 & 1710.777 & 81,035.109 \\ _GSA_ & 82,276.941 & 78,002.107 & 71,043.110 & 3119.904 & 78,398.853 \\ _PSO_ & 82,773.982 & 81,198.753 & 80,687.239 & 1679.367 & 8439.728 \\ _GA_ & 81,569.527 & 80,397.998 & 79,412.779 & 1756.902 & 8347.009 \\ \hline \hline \end{tabular}
\end{table} 
Table 14: Statistical results for Rolling element bearing design problem. ## Abbreviations