# Non-Vertical Well Trajectory Design Based on Multi-Objective Optimization
## 1 Introduction
proposed a multi-objective cellular automata model combining the grey wolf optimization and particle swarm optimization algorithm for wellbore trajectory optimization. [PERSON] et al. [13] (2023) combined the fast marching method (FMM) with particle swarm optimization (PSO), and discussed the optimization of wellbore trajectory parameters for vertical wells, deviated wells, and horizontal wells. Ant Colony Optimization (ACO) is also a typical heuristic search optimization algorithm. It was first proposed and widely accepted by Italian scholar [PERSON] [14] in the paper 'Ant system: optimization by a colony of conforming agents' in 1996. In order to further improve the iterative efficiency and solution accuracy of the ant colony algorithm, [PERSON] [15] (2011) and [PERSON] [16] (2012) successively improved the ant colony algorithm, and proposed an ant colony hybrid algorithm based on chaos technology and an improved ant colony algorithm based on the adaptive pheromone volatilization factor. Although the research of the two people has improved the iterative efficiency of the ant colony algorithm, it is still unable to solve the huge challenges in wellbore trajectory planning. [PERSON] and [PERSON] [17] (2015) introduced the basic principle and scope of application of the ant colony algorithm in detail in their published articles. In view of this, [PERSON] [18] (2019) proposed a research project on wellbore trajectory planning based on the ant colony algorithm. Firstly, the sum of the squared increment difference of wellbore trajectory coordinates is taken as the objective function, and the azimuth range is taken as the constraint condition. Then, the continuous space is meshed, and finally, the ant colony algorithm is used to solve the problem. Although [PERSON]'s research shows that the ant colony algorithm has a fast convergence speed and good solution accuracy in wellbore trajectory planning, the computational efficiency of the ant colony algorithm will be reduced in the face of more complex construction scenarios. The multi-objective optimization method of the wellbore trajectory is a technical means for the comprehensive optimization of multiple objectives (such as drilling cost, production, geological risk, etc.) faced by wellbore trajectory design in oil drilling engineering. Since there are often conflicts between these objectives, the multi-objective optimization method aims to find a set of Pareto optimal solutions to provide comprehensive support for decision-making. At present, domestic and foreign scholars mainly have used the multi-objective genetic algorithm (MOGA), second-generation non-dominated sorting genetic algorithm (NSGA-II), multi-objective particle swarm optimization (MOPSO), and other intelligent optimization algorithms in dealing with the multi-objective optimization of the wellbore trajectory. [PERSON] et al. (2015) applied the multi-objective genetic algorithm to the two objective functions of wellbore length and torque to optimize the wellbore trajectory with a low risk and low cost ([PERSON] et al. (2014). [PERSON] et al. (2014) used the elite non-dominated sorting genetic algorithm (NSGA-II) to optimize multi-objective drilling in an offshore oilfield with abnormal formation pressure in Louisiana. They considered several optimization objectives, namely drilling depth, drilling time, and drilling cost, and studied dual-objective and three-objective optimization problems, and obtained a set of good non-dominated optimal Pareto frontiers. According to the trade-off results, decision-makers can choose any point from the optimal Pareto boundary or the optimal Pareto surface, and therefore choose the corresponding value of the decision variable for the optimal drilling operation ([PERSON] et al. (2017). [PERSON] et al. (2017) used NSGA-II to optimize the trajectory model of sidetracking horizontal wells with the goal of trajectory length and well profile energy and found that the solution was evenly distributed at the Pareto optimal frontier ([PERSON] et al. (2017). [PERSON] et al.