<p>Designing stable wellbore trajectories in heterogeneous formations remains difficult because geological uncertainty and mechanical constraints interact in non-linear ways. We present an integrated geomechanical–drill string framework that departs from conventional geometry-based or single-physics approaches in three aspects: (i) formation feasibility is encoded through a probability corridor and high-risk mask derived from multi-source logs, enabling uncertainty-aware constraint enforcement; (ii) geomechanical and drill string responses are coupled into a unified objective–constraint structure; and (iii) a hybrid global–local optimization strategy efficiently resolves the resulting non-convex search space. Applied to a shale–sandstone interval in Sichuan–Chongqing, the method consistently avoids unstable zones, suppresses curvature concentration, and maintains compliance with pressure-window and mechanical limits. The results demonstrate a robust and deployment-ready trajectory design paradigm for complex formations.</p>