# Non-Vertical Well Trajectory Design Based on Multi-Objective Optimization
## 1 Introduction  
In recent years, scholars at home and abroad have conducted a lot of research and exploration on how to better consider the formation information for wellbore trajectory optimization. Using the knowledge of geological statistics, geophysics, rock mechanics, and other disciplines, advanced numerical simulation technology, and machine learning algorithms, a variety of wellbore trajectory optimization models have been proposed. Well trajectory planning and optimization are usually based on the construction requirements of the site to establish the corresponding planning model; then, the optimization algorithm is used to solve optimization problems. In the optimization algorithm, the algorithms for wellbore trajectory planning mainly include the genetic algorithm, particle swarm optimization algorithm, and ant colony algorithm. The genetic algorithm (GA) was proposed by Professor [PERSON] and his colleagues from the University of Michigan in 1975 and was first applied in the field of pattern recognition. Because of its superior performance, it has been widely used to solve optimization problems. [PERSON] et al. (2008) used the genetic algorithm to optimize the length of the horizontal section of a horizontal well [1]. [PERSON] et al. establisheda three-dimensional directional well trajectory based on the vector method and used the genetic algorithm (GA) and linear approximate constraint optimization (COBYLA) combined with geological modeling and logging extraction to optimize the path [2]. [PERSON] and [PERSON] [3] et al. (2017) proposed a complex wellbore trajectory optimization method based on the adaptive quantum genetic algorithm. Their research is mainly inspired by the negative exponential characteristics of the Fibonacci sequence. FAQGA is used to optimize the actual measured well depth TMD, and parameter optimization in practical engineering is completed to realize trajectory optimization. Although their research reduces the time complexity, it increases the space complexity. [PERSON] and [PERSON] (2018) used the quantum genetic algorithm based on the Fibonacci sequence to achieve the optimal convergence speed of the drilling trajectory length [4]. [PERSON] et al. (2023) used the multi-objective genetic algorithm and TOPSIS method to select the best wellbore by combining information such as wellbore length [5]. 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. [PERSON] [6] (2024) combined the independent fast marching model with the genetic algorithm to effectively determine the well location that does not depend on the simulated operation, showing the robustness of its decision-making and accelerating the speed of well location optimization. Particle swarm optimization (PSO) is a heuristic search optimization algorithm under the intelligent optimization system. It was proposed by [PERSON] and [PERSON] [7] in 1995. [PERSON] [8] (2004) improved the shortcomings of the particle swarm optimization algorithm; it is easy to fall into local minima by adding a penalty function in the study of non-vertical well trajectory optimization designs. [PERSON] and [PERSON] [9] (2014) adjusted the behavior parameters of particle swarm optimization through meta-optimization to speed up the PSO process and applied it to the optimization of a deviated wellbore trajectory. [PERSON] et al. [10] (2017) used the particle swarm optimization algorithm to optimize the intelligent prediction method of a wellbore trajectory established by the method based on a support vector product and established the three-dimensional visualization of the wellbore trajectory through the study of computer three-dimensional graphics and visualization. [PERSON] et al. [11] (2019) combined the particle swarm optimization algorithm and analytic hierarchy process to optimize the objective function, taking into account the drilling trajectory length, torque, drilling cost, and target hit accuracy. [PERSON] [12] (2021) et al.