## 3 Proposed Method
### Improved SMA
\begin{table}
\begin{tabular}{l c c c c c} \hline \hline \multirow{2}{*}{**Algorithm**} & \multicolumn{5}{c}{**Optimal Values for Variables**} & \multirow{2}{*}{**Optimal Cost**} \\ \cline{2-2} \cline{4-6}  & _Ts_ & _Th_ & \(R\) & \(L\) \\ \hline DQOBLSMA & 0.778246 & 0.384708 & 40.323469 & 199.950065 & 5885.623524 \\ ORISMAL & 0.865273 & 0.427877 & 44.832637 & 145.769573 & 6060.212044 \\ ESMA & 0.974581 & 0.481740 & 50.496415 & 112.689545 & 6417.418230 \\ SMA & 0.814081 & 0.402437 & 42.180339 & 175.629283 & 5949.827184 \\ MEO & 0.850407 & 0.425437 & 44.051816 & 154.133369 & 6046.777664 \\ IADE & 0.788821 & 0.389961 & 40.870447 & 192.471633 & 5904.076066 \\ RWGOV & 0.877511 & 0.432390 & 45.308765 & 140.703767 & 6095.405916 \\ \hline \hline \end{tabular}
\end{table} 
Table 13: Comparison in pressure vessel design. Figure 5: Pressure vessel design problem. **Author Contributions:** Conceptualization, S.D. and Y.Z. ; software, Y.Z. ; validation, S.D. and Q.Z. ; formal analysis, S.D. and Y.Z. ; investigation, S.D. and Y.Z. ; resources, S.D. ; writing--original draft preparation, Y.Z. ; writing--review and editing, S.D. and Y.Z. ; visualization, Y.Z. ; funding acquisition, S.D. All authors have read and agreed to the published version of the manuscript. **Funding:** The authors acknowledge the support of the Key R & D Projects of Zhejiang Province (No. 2022C01236, 2019C01060), the National Natural Science Foundations of China (Grant Nos. 21875271, U20B2021, 21707147, 51372046, 51479037, 91226202, and 91426304), the Entrepreneurship Program of Foshan National Hi-tech Industrial Development Zone, the Major Project of the Ministry of Science and Technology of China (Grant No. 2015 ZX06004-001), Ningbo Natural Science Foundations (Grant Nos. 2014A610006, 2016A610273, and 2019A610106). **Institutional Review Board Statement:** Not applicable. **Informed Consent Statement:** Not applicable. **Data Availability Statement:** Not applicable. **Conflicts of Interest:** The authors declare no conflict of interest. ## References

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