# Research on Intelligent Optimization of Wellbore Trajectory in Complex Formation
## 5 Results  
### Algorithm Performance Test  
In order to better compare the performance of the improved algorithm, the benchmark test function was defined as follows. For a better understanding of the algorithm testing basis and performance comparison, refer to Table 2 (Benchmark test function definition) and Table 3 (Algorithm function index comparison). In this paper, the performance and stability of the algorithm are effectively improved by introducing the clustering strategy and elite learning strategy into the MOPSO algorithm. In the initialization phase, the empty matrix of elite group, ordinary group, and inferior group is predefined, and three sub-groups are dynamically updated according to the fitness value in each iteration, so as to realize the hierarchical management of particle swarm. The elite learning strategy enhances the diversity of particles and avoids the algorithm falling into the local optimum by adding Gaussian noise to the elite particles. In the main cycle, the elite learning operation is dynamically called to continuously optimize the elite group. These improvements not only increase the ability of the algorithm to solve multi-objective optimization problems, but also enhance the convergence efficiency and result quality, and provide stronger technical support for solving complex optimization problems. The observed improvements in trajectory length and complexity were primarily attributed to the elite learning strategy, which enhanced local exploration capabilities, and \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Test Problem** & **Variable** & **The Goal** & **Constraint Condition Characteristics** \\ \hline Schaffer & 2 & 2 & \(f_{1}(x)=x_{i}^{2}\); \(f_{2}(x)=\left(x_{2}-2\right)^{2}\) \\  & & & \(a\leq x_{i}\leq b\), \(c\leq x_{i}\leq d\) \\  & & & \(f_{1}(x)=\sum\limits_{i=1}^{2}{[-10\exp(-0.2\sqrt{x_{i}^{2}+x_{i+1}^{2}})]}\), \\ Kursawe & 3 & 2 & \(f_{2}(x)=\sum\limits_{i=1}^{3}{[|x_{i}|^{0.8}+5\sin(x_{i}^{3})]}\) \\  & & & \(-5\leq x_{i}\leq 5\), \(i=1,2,3\) \\  & & & \(f_{1}(x)=x_{1}\); \(g(x)=1+\frac{9}{8}\sum\limits_{i=2}^{30}{x_{i}}\) \\ ZDT6 & 30 & 2 & \(f_{2}(x)=g(x)[1-\sqrt{\frac{x_{1}}{g(x)}}-\frac{x_{1}}{g(x)}\sin(10\pi x_{1})]\) \\  & & & \(0\leq x_{i}\leq 1\), \(i=1,2,\cdots,30\) \\  & & & \(f_{2}(x)=g(x)[1-\left(f_{1}(x)/g(x)\right)^{2}]\) \\  & & & \(f_{1}(x)=1-\exp(-4x_{1})\sin^{6}(6\pi x_{1})\) \\ ZDT3 & 10 & 2 & \(g(x)=1+9[\left(\begin{smallmatrix}10\\ \Sigma\\ i=2\end{smallmatrix}\ x_{i}\right)/9]^{0.25}\) \\  & & & \(0\leq x_{i}\leq 1\), \(i=1,2,\cdots,10\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Benchmark test function definition. the clustering strategy, which ensured global solution diversity. These findings suggest that the algorithm effectively balances exploration and exploitation, making it particularly suitable for complex geological formations. To further validate the applicability of the improved MOPSO in complex geological environments, we selected a typical deepwater drilling project for testing. This case involved high-pressure, high-temperature (HPHT) geological conditions, which imposed stricter requirements on the stability of wellbore trajectory optimization. The experimental results demonstrate that, compared to traditional methods, the improved MOPSO achieved significant improvements in trajectory optimization. The optimized wellbore trajectory length was reduced by 5.37%, and trajectory complexity was lowered by 4.76%, further confirming the practical engineering value of the algorithm. Moreover, to ensure the reliability of our experimental results, we performed an analysis of variance (ANOVA) and pairwise \(t\)-tests to assess the statistical significance of performance differences between optimization methods. Table 7 presents the mean values, standard deviations, and \(p\)-values for these comparisons. The statistical results confirm that the improved MOPSO achieved not only superior numerical performance but also statistically significant improvements on the ZDT3 and ZDT6 test functions (\(p<0.05\)).