Multi-objective trajectory planning in the multiple strata drilling process: A bi-directional constrained co-evolutionary optimizer with Pareto front learning

Trajectory planning is essential to ensure the safety and efficiency of the drilling process within varying downhole geological conditions. However, numerous constraints and dispersed objectives make this task challenging, resulting in a broken constrained Pareto front (PF) in the objective space. To address this issue, we present a novel multi-objective optimization algorithm (MOEA), the Bi-directional Constrained Co-evolutionary Optimizer (BCCO), for reducing the friction torque of the drilling string system and maintaining the wellbore stability of the directional drilling process in multiple changeable strata. Inspired by dual-population co evolutionary mechanics, BCCO is thoughtfully developed to enhance complex constraints handling. An ESOINN is introduced to guide the population in exploring the irregular PF and adaptively approximating to it. In addition, a flexible constraint dominance principle is devised to filter out non-inferior infeasible solutions that fully balance feasibility, diversity, and convergence by combining constraint violation, minimum vector angle, and angle-penalized distance. Moreover, we adopt a minimum Manhattan distance (MMD) decision-making method to select the final reference solution for trajectory tracking control. To verify the effectiveness of BCCO, we compared it with seven state-of-the-art constrained MOEAs, four latest published MOEAs used in drilling trajectory planning (DTP) applications, and three ablation MOEAs revised from original BCCO on real-world constrained test instances and four different types of designed standard benchmarks. Extensive testing confirmed adaptability to diverse constrained PFs. BCCO displayed strong convergence and diversity when applied to real-world engineering problems while maintaining feasibility. To evaluate BCCO's DTP performance, we built a wellbore stability model on actual geological formations and empirically tested it with both composite natural curves and third-order Bezier curves in various drilling trajectory scenarios. We established a comprehensive cloud-based DTP test system with the on-site Programmable Logic Controller (PLC) and the workstation via Data Transfer Unit (DTU) communication. Actual DTP cases confirmed the feasibility of BCCO's Pareto solutions, with MMD-selected trajectories ensuring a harmonized drilling process.