# Personalized-Template-Guided Intelligent Evolutionary Algorithm
## 3 Results
### Engineering Problem Experiment
#### 3.4.3 Pressure Vessel Design Problem  
The goal of pressure vessel design is to minimize the manufacturing cost of a pressure vessel (pairing, forming, and welding). Both ends of the pressure vessel are capped with caps, and the head end is capped in a hemispherical shape. The wall thickness \(T_{s}\) of the cylinder part and the wall thickness \(T_{h}\) of the head are integer multiples of 0.625, and the goal is to minimize the manufacturing cost of welded beams under the condition of satisfying constraints. The design of a pressure vessel is shown in Figure 9. For specific definitions, see Equations (31)-(33).  
Definition of the problem:  
\[X=[x_{1},x_{2},x_{3},x_{4}]=[T_{s},T_{h},R,L] \tag{31}\]  
The objective function:  
\[f(x)=0.6224x_{1}x_{3}x_{4}+1.778x_{2}x_{3}^{2}+3.1661x_{1}^{2}x_{4}+19.84x_{1}^ {2}x_{3} \tag{32}\]  
Constraint setting:  
\[\begin{split} g_{1}(x)&=-x_{1}+0.0193x_{3}\leq 0, \\ g_{2}(x)&=-x_{2}+0.00954x_{3}\leq 0,\\ g_{3}(x)&=-\pi x_{3}^{2}x_{4}-\frac{4}{3}\pi x_{3}^ {3}+1296000\leq 0,\\ g_{4}(x)&=x_{4}-240\leq 0,\\ 0&\leq x_{1},x_{2}\leq 100,\quad 10\leq x_{3},x_{4} \leq 200\end{split} \tag{33}\]  
The solution results of PTG and other comparative algorithms are shown in Table 10. The \(L\) value obtained by all the algorithms is 200. After the PTG solution, the optimal solution is \(x_{1}=0\), \(x_{2}=0\), \(x_{3}=40.31961872\), \(x_{4}=200\), and the corresponding value of the objective function is \(753.5014127298541\). It can be seen from the table that PTG has obtained the optimal value compared with other algorithms except MFO and ECO, and the mean square deviation of 30 independent runs is the smallest, and the algor  
\begin{table}
\begin{tabular}{l c c c c c c c} \hline
**Algorithm** & **h** & **l** & **t** & **b** & **Best** & **Mean** & **Std** \\ \hline PTG & \(2.06395\times 10^{-1}\) & \(3.456223\) & \(9.036624\) & \(2.05730\times 10^{-1}\) & \(1.724399\) & \(1.724400\) & \(4.5766\times 10^{-5}\) \\ WOA & \(1.85061\times 10^{-1}\) & \(4.047632\) & \(9.066901\) & \(2.05579\times 10^{-1}\) & \(1.771565\) & \(2.199500\) & \(6.84900\times 10^{-1}\) \\ HHO & \(2.03490\times 10^{-1}\) & \(3.497705\) & \(9.092332\) & \(2.05502\times 10^{-1}\) & \(1.732927\) & \(1.929300\) & \(1.60300\times 10^{-1}\) \\ COA & \(2.10017\times 10^{-1}\) & \(3.304639\) & \(9.249082\) & \(2.10017\times 10^{-1}\) & \(1.778173\) & \(2.524100\) & \(4.29600\times 10^{-1}\) \\ TSA & \(2.07034\times 10^{-1}\) & \(3.430732\) & \(9.089197\) & \(2.05678\times 10^{-1}\) & \(1.731993\) & \(1.741000\) & \(5.70000\times 10^{-3}\) \\ RSA & \(2.48422\times 10^{-1}\) & \(3.132122\) & \(8.357501\) & \(2.47278\times 10^{-1}\) & \(1.918210\) & \(2.287000\) & \(2.84500\times 10^{-1}\) \\ FATA & \(2.06643\times 10^{-1}\) & \(3.450326\) & \(9.039539\) & \(2.05739\times 10^{-1}\) & \(1.724936\) & \(1.726900\) & \(3.30000\times 10^{-3}\) \\ MFO & \(2.06394\times 10^{-1}\) & \(3.456249\) & \(9.036624\) & \(2.05730\times 10^{-1}\) & \(1.724399\) & \(1.779509\) & \(9.0100\times 10^{-2}\) \\ ECO & \(2.04278\times 10^{-1}\) & \(3.502072\) & \(9.036455\) & \(2.05737\times 10^{-1}\) & \(1.726881\) & \(1.886600\) & \(1.61700\times 10^{-1}\) \\ HO & \(2.07432\times 10^{-1}\) & \(3.445703\) & \(9.008467\) & \(2.07018\times 10^{-1}\) & \(1.729205\) & \(1.971400\) & \(2.36400\times 10^{-1}\) \\ \hline \end{tabular}
\end{table}
Table 9: Comparison results of PTG and advanced algorithm in structural design of welded beams.  
Figure 9: Schematic diagram of pressure vessel design problems.  
most stable. The optimal value of PTG is second only to MFO and ECO, and the mean and mean square deviation of 30 independent operations are better than ECO.