# Research on Intelligent Optimization of Wellbore Trajectory in Complex Formation
## 1 Introduction  
With the rapid progress of information technology, especially the in-depth development of artificial intelligence, wellbore trajectory prediction technology has achieved a significant breakthrough. These advances are not only reflected in the accuracy of the algorithm model, but also in the substantial increase in computing power, making real-time computing of complex models possible. However, despite the exciting progress in theory, the actual geological exploration and oil and gas drilling operations still face many challenges. The diversity of nature means that each oil field has unique geological characteristics, including the formation structure, the rock physical properties, and underground fluid dynamics. Therefore, even advanced artificial intelligence prediction models need to be customized according to the characteristics of specific projects in order to effectively deal with the uncertainty in actual operation. Despite the progress in optimization models, wellbore trajectory optimization faces significant challenges in complex geological formations. These include abrupt geological changes, unpredictable stress fields, and fluiddynamics variability. These complexities often lead to issues such as trajectory instability, increased drilling costs, and operational risks. Existing methods often struggle to adapt to these dynamic conditions, leaving a research gap in achieving robust, efficient, and accurate optimization. In recent years, the international and domestic academic circles have carried out a lot of research on how to consider the formation characteristics more effectively to optimize the drilling trajectory. Researchers have constructed a variety of optimization models by using the knowledge of geostatistics, geophysics, rock mechanics, and other disciplines, combined with advanced numerical simulation technology and machine learning algorithms. For example, some researchers have developed a multi-objective optimization model that can comprehensively consider multiple factors such as formation pressure, temperature, and rock strength. Other studies have focused on enhancing wellbore stability by improving drilling fluid formulations and BHAs, thereby reducing drilling risks and improving operational efficiency. The genetic algorithm (GA) was proposed by [PERSON], a professor at the University of Michigan [1], and his colleagues in 1975 and was first applied in the field of pattern recognition. Because of its superior performance, it was gradually widely used to solve optimization problems. [PERSON] and [PERSON] [2] et al. (2017) proposed a complex wellbore trajectory optimization method based on adaptive quantum genetic algorithm. Their research is mainly inspired by the negative exponential characteristics of the Fibonacci sequence. The FAQGA is used to optimize the actual measured well depth TMD and complete the parameter optimization in practical engineering to achieve trajectory optimization. Although their research reduces the time complexity, it increases the space complexity. [PERSON] [3] et al. (2023) used multi-objective genetic algorithm and the TOPSIS method to select the best wellbore by combining information such as wellbore length. Their research cases show that the ideal state of this method is close to 60%, and the effect is ideal, especially in the case of deflection. Particle swarm optimization (PSO) is a heuristic search optimization algorithm under the intelligent optimization system. It was proposed by [PERSON] and [PERSON] [4] in 1995. [PERSON] [5] (2004) improved the shortcomings of the particle swarm optimization algorithm, which easily falls into the local minimum point, by adding a penalty function in the study of non-vertical well trace optimization design. [PERSON] and [PERSON] [6] (2014) adjusted the behavior parameters of particle swarm optimization through meta-optimization to speed up the PSO optimization process and applied it to the optimization of deviated wellbore trajectory.