# Non-Vertical Well Trajectory Design Based on Multi-Objective Optimization
## 5 Analysis of the Results
### Experimental Results
The final well deviation angle is 88.41\({}^{\circ}\), which is in line with the trajectory characteristics of horizontal wells. The optimization scheme can effectively meet the drilling requirements of horizontal sections, which is conducive to the long-distance contact of target reservoirs and the improvement of productivity potential. To assess the stability of the DR-NSGA-III-MGA algorithm, 30 independent replicate experiments were performed under identical initial conditions. The statistical results reveal the low variability in key performance metrics: the total trajectory length varies within a narrow range around 2161.93 m, with a maximum deviation of 5.27 m across all runs. The build-up rate shows consistent performance, with a maximum fluctuation of 0.15\({}^{\circ}\)/30 m. Coordinates of typical points exhibit small variations, with north, east, and vertical depth values differing by no more than 0.32 m, 0.28 m, and 0.15 m, respectively, across replicates. These results confirm the algorithm's stability, as all metrics show minimal dispersion. Figure 8 shows the visualization of the three-stage wellbore trajectory optimized by DR-NSGA-III-MGA. (a) The 3D trajectory model (start coordinates (0, 0, 0), target coordinates (1203.42, 988.79, 804.46)); (b) north-east horizontal projection (azimuth control error \(\leq\) 0.5\({}^{\circ}\) in horizontal section); (c) north-height projection (build-up rate 4.28\({}^{\circ}\)/30 m with smooth transition); and (d) east-height projection (vertical depth control deviation \(\leq\) 0.2 m). The azimuth angle is controlled within a reasonable range, which indicates that the algorithm is more accurate in the guidance adjustment of the trajectory in the horizontal plane and can be smoothly advanced in accordance with the target direction to avoid the offset risk. The build-up rate is 4.28\({}^{\circ}\)/30 m, which shows a good trajectory curvature control ability. It not only avoids the tool wear caused by excessive build-up, but also helps smooth the transition of the trajectory and ensures wellbore integrity. The length of the stable section is 1167.66 m, which meets the development needs of the long horizontal section. The total length of the trajectory is 2161.93 m, which is relatively reasonable, indicating that the optimization process compresses the drilling path under the premise of ensuring the arrival of the target and controlling the deflection parameters, which is conducive to reducing the construction cycle and drilling cost. The optimization results of key parameters are detailed in Table 2.  
of DR-NSGA-III-MGA algorithm in high-dimensional objective space and provides a rich and reliable decision-making basis for subsequent trajectory scheme screening. Figure 10 reveals the synergy and trade-off relationship between friction, torque, and trajectory complexity. The Pareto solution set is clearly distributed, showing the good search and stratification ability of the algorithm in the multi-objective space. The color mapping further provides the accuracy evaluation dimension, and the drilling path scheme considering both efficiency and accuracy can be selected under different index combinations, which provides reliable support for multi-objective wellbore design. The three-dimensional Pareto frontier in Figure 11 shows the non-inferior distribution relationship among torque, complexity, and accuracy. The results show that some low-torque and medium-complexity solutions can significantly improve the trajectory accuracy while maintaining good trajectory control, representing the potential optimal solution area. On the whole, the distribution of the solution set is continuous and the gradient is clear, which reflects the good search ability and decoupling ability of the optimization algorithm in the multi-objective space. The normalized multi-objective parallel comparison diagram (Figure 12) clearly shows the comprehensive performance characteristics of each non-inferior solution in multi-objective optimization under different objective dimensions.