# Personalized-Template-Guided Intelligent Evolutionary Algorithm
## 3 Results
### Engineering Problem Experiment
#### 3.4.4 Reducer Design Issues  
There are seven parameters involved in the design of the reducer, including width \(b\), number of tooth dies \(m\), number of gear teeth \(z\), length of the first shaft between bearings \(l_{1}\), length of the second shaft between bearings \(l_{2}\), diameter of the first shaft \(d_{1}\), and diameter of the second shaft \(d_{2}\). By optimizing the weight of the gear and the axial deformation of the shaft, the weight of the reducer is minimized. The diagram of the problem is shown in Figure 10. For specific definitions, see Equations (34)-(36). Definition of the problem:  
\[X=[x_{1},x_{2},x_{3},x_{4},x_{5},x_{6},x_{7}]=[b,m,p,l_{1},l_{2},d_{1},a_{2}] \tag{34}\]  
The objective function:  
\[ \begin{split} f(x)=& 0.7854x_{1}x_{2}^{2}(3.3333x_{3}^{2 }+14.9334x_{3}-43.0934)-1.508x_{1}(x_{6}^{2}+x_{7}^{2})\\ &+7.4777(x_{6}^{3}+x_{7}^{3})+0.7854(x_{4}x_{6}^{2}+x_{5}x_{7}^{2} )\end{split}  \tag{35}\]  
Constraint setting:  
\[ \begin{split} g_{1}(x)&=\frac{27}{x_{1}x_{2}^{2}x_{3 }}-1\leq 0,\quad g_{2}(x)=\frac{397.5}{x_{1}x_{2}^{2}x_{3}}-1\leq 0,\\ g_{3}(x)&=\frac{1.93x_{4}^{3}}{x_{2}x_{3}x_{6}^{4} }-1\leq 0,\quad g_{4}(x)=\frac{1.93x_{5}^{3}}{x_{2}x_{3}x_{7}^{4}}-1\leq 0,\\ g_{5}(x)&=\frac{1}{110x_{6}^{3}}\sqrt{\left(\frac{ 745x_{4}}{x_{2}x_{3}}\right)^{2}+16.9\times 10^{6}-1}\leq 0,\\ g_{6}(x)&=\frac{1}{85x_{7}^{3}}\sqrt{\left(\frac{ 745x_{5}}{x_{2}x_{3}}\right)^{2}+157.5\times 10^{6}}-1\leq 0,\\ g_{7}(x)&=\frac{x_{2}x_{3}}{40}-1\leq 0,\quad g_{8}(x )=\frac{5x_{2}}{x_{1}}-1\leq 0,\\ g_{9}(x)&=\frac{x_{1}}{12x_{2}}-1\leq 0,\quad g_{10} (x)=\frac{1.5x_{6}+1.9}{x_{4}}-1\leq 0,\quad g_{11}(x)=\frac{1.1x_{7}+1.9}{x_{ 5}}-1\leq 0,\\ 2.6\leq x_{1}&\leq 3.6,\quad 07\leq x_{2} \leq 0.8,\quad 17\leq x_{3}\leq 28,\quad 7.3\leq x_{4}\leq 8.3,\quad 7.3\leq x_{5} \leq 8.3,\\ 2.9\leq x_{6}&\leq 3.9,\quad 5\leq x_{7}\leq 5.5\end{split}  \tag{36}\] \begin{table}
\begin{tabular}{l c c c c c c} \hline \hline
**Algorithm** & \(\mathbf{T_{s}}\) & \(\mathbf{T_{h}}\) & \(\mathbf{R}\) & **Best** & **Mean** & **Std** \\ \hline PTG & 0 & 0 & \(4.031961872\times 10^{1}\) & \(7.535014127298541\times 10^{2}\) & \(7.535014127298540\times 10^{2}\) & \(1.16\times 10^{-13}\) \\ WOA & 0 & 0 & \(4.031961875\times 10^{1}\) & \(7.535014137\times 10^{2}\) & \(8.291512734\times 10^{2}\) & \(2.2867\times 10^{2}\) \\ HHO & 0 & 0 & \(4.031961872\times 10^{1}\) & \(7.535014127\times 10^{2}\) & \(1.107287597\times 10^{3}\) & \(3.5883\times 10^{2}\) \\ COA & 0 & 0 & \(4.032086747\times 10^{1}\) & \(7.535480873\times 10^{2}\) & \(1.442735757\times 10^{3}\) & \(7.6608\times 10^{2}\) \\ TSA & \(3.792\times 10^{-1}\) & \(1.986\times 10^{-1}\) & \(4.031967744\times 10^{1}\) & \(7.535036074\times 10^{2}\) & \(9.015074985\times 10^{2}\) & \(3.0102\times 10^{2}\) \\ RSA & \(6.0034\times 10^{-10}\) & \(4.6716\times 10^{-24}\) & \(4.032531618\times 10^{1}\) & \(7.537143781\times 10^{2}\) & \(7.639325533\times 10^{2}\) & \(1.48806\times 10^{1}\) \\ FATA & 0 & 0 & \(4.031966742\times 10^{1}\) & \(7.535032326\times 10^{2}\) & \(7.535234204\times 10^{2}\) & \(2.03\times 10^{-2}\) \\ MFO & 0 & \(4.031961872\times 10^{1}\) & \(7.535014127298540\times 10^{2}\) & \(7.535014127298539\times 10^{2}\) & \(1.16\times 10^{-13}\) \\ ECO & \(1.5404\times 10^{-7}\) & \(7.76\times 10^{-2}\) & \(4.031961872\times 10^{1}\) & \(7.535014127298540\times 10^{2}\) & \(8.767789495\times 10^{2}\) & \(2.8037\times 10^{2}\) \\ HO & \(2.709\times 10^{-1}\) & 0 & \(4.031961875\times 10^{1}\) & \(7.535014139\times 10^{2}\) & \(8.274684181\times 10^{2}\) & \(2.2569\times 10^{2}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Comparison results of PTG and advanced algorithm in pressure vessel design. The solution results of PTG and other comparative algorithms are shown in Table 11. \(b=3.6\), \(m=0.8\), \(p=28\), \(d_{2}=5\).