Abstract: Wellbore trajectory design is a nonlinear and constrained mathematical optimization problem that is used to build a cost-efficient, safe, and easily reachable trajectory. True measured depth (TMD), torque, and strain energy are used as objective functions to evaluate the wellbore trajectory design in this work. The minimum values of these objective functions enable a trajectory to be drilled with minimum drilling cost and maximum safety. A lot of modifications to the original metaheuristic methods were made during previous applications, which mostly improve the exploration capability of original algorithms keeping exploitation capability unaddressed. To address this issue a new hybridization of cellular automata (CA) technique with grey wolf optimization (GWO) and particle swarm optimization (PSO) algorithms is proposed in this paper which solves these three optimization objectives of drilling through 17 tuning variables. The improvements of the original PSO Algorithm are proposed by updating its exploitation phase with the incorporation of the GWO algorithm and the exploration phase by using a cellular automaton. During the optimization, the operational constraints of a wellbore such as true vertical depth and casings along with the bounds of tuning variables were utilized. Better performances were observed in cases of Pareto optimal front, search capabilities, and diversity of solutions by comparing the proposed method with other standard methods like MOCPSO, MOGWO, and MOPSO. Several parametric tests (IGD, SP, MS) were done to investigate the effect of proposed hybridization. The mean value of IGD was 0.0208 by the proposed method, which is 46.8% better than MOCPSO, 49.78% than MOPSO, and 60.80% better than the MOGWO. The proposed optimization method also had the minimum spacing metric and maximum spread.

中文翻译：

---

基于元胞自动机的多目标混合灰狼优化和粒子群优化算法用于井眼轨迹优化

摘要：井眼轨迹设计是一个非线性和受约束的数学优化问题，用于构建具有成本效益、安全且易于到达的轨迹。在这项工作中，真实测量深度 (TMD)、扭矩和应变能被用作评估井眼轨迹设计的目标函数。这些目标函数的最小值使得能够以最小的钻孔成本和最大的安全性来钻孔。在之前的应用中对原始元启发式方法进行了大量修改，主要是提高了原始算法的探索能力，而未解决开发能力。为了解决这个问题，本文提出了一种新的元胞自动机 (CA) 技术与灰狼优化 (GWO) 和粒子群优化 (PSO) 算法的混合，它解决了钻取 17 个调整变量的这三个优化目标。原始 PSO 算法的改进是通过更新其开发阶段并结合 GWO 算法和使用元胞自动机的探索阶段来提出的。在优化过程中，利用了井眼的操作约束，例如真实垂直深度和套管以及调整变量的界限。通过将所提出的方法与其他标准方法（如 MOCPSO、MOGWO 和 MOPSO）进行比较，在帕累托最优前沿、搜索能力和解决方案多样性的情况下观察到更好的性能。进行了几个参数测试（IGD、SP、MS）以研究提议的杂交的效果。所提方法的IGD平均值为0.0208，比MOCPSO好46.8%，比MOPSO好49.78%，比MOGWO好60.80%。所提出的优化方法还具有最小间距度量和最大扩展。