A Conjugate Gradient-Accelerated Constrained Multi-Objective Optimizer for High-Dimensional Problems with Application to Wellbore Trajectory Planning

With declining hydrocarbon reserves, optimizing directional wellbore trajectory planning is crucial for accessing complex reservoirs while managing cost and risk. Multi-segment composite trajectories have been widely used in complex formations, but their high-dimensional nature challenges the efficiency of gradient-free multi-objective optimization methods. This paper proposes a conjugate gradient-assisted multi-objective algorithm to accelerate the optimization process. A dual-population update strategy integrates gradient-based search with constraint satisfaction, while adaptive step size and hybrid search mitigate multi-objective gradient conflicts. Gradients for formation-related objectives are approximated via finite differences. The algorithm is validated on a five-segment Bézier trajectory for an extended-reach horizontal wellbore, demonstrating superior normalized hypervolume, convergence, and diversity compared to gradient-based and evolutionary algorithms. Ablation studies verify the effectiveness of the hybrid strategy. The selected trajectory achieves an optimal balance among wellbore length, curvature, and stability under all constraints. To our knowledge, this is the first application of gradient-based multi-objective optimization to wellbore trajectory planning, offering a promising pathway toward real-time drilling trajectory design with enhanced efficiency and robustness.