The shape optimization of complex three-dimensional pipe systems poses a significant challenge in computational mechanics due to the large admissible design space and the strong sensitivity of stress and vibration responses to geometric variations under dynamic operating conditions. Although high-fidelity dynamic simulations can accurately evaluate stress responses and natural frequencies, their high computational cost makes direct simulation-based optimization impractical for large-scale geometry exploration. This study proposes a computational framework that integrates automated geometry generation, high-fidelity simulation–based data construction, neural-network surrogate modeling, and iterative optimization. Pipe geometries are algorithmically generated within a three-dimensional grid-based design space while explicitly satisfying practical design constraints, including curvature limits, minimum straight lengths, collision avoidance, and minimum separation distances between multiple pipes. High-fidelity multibody dynamic simulations are performed offline to evaluate peak dynamic stresses and natural frequencies under operating conditions, thereby constructing a dataset that captures quantitative relationships between pipe geometry, stress response, and modal characteristics. A neural-network surrogate model is trained to directly predict stress and frequency responses from geometric descriptors, and its predictive reliability is established offline using validation data. During the optimization process, the pre-trained surrogate model is used exclusively to evaluate stress safety and resonance-avoidance constraints, without performing repeated high-fidelity simulations. Among feasible designs, high-performing configurations with shorter pipe lengths are selected, and geometric patterns and routing characteristics are represented as probabilistic variables to generate new candidate geometries, progressively contracting the design space. The proposed framework significantly reduces the computational burden associated with repeated high-fidelity analyses while enabling physically consistent and efficient shape optimization. Although demonstrated on a dryer pipe system, the framework is applicable to a wide range of mechanical structures requiring geometry-dependent stress and vibration-constrained optimization.