Geometry-aware deep reinforcement learning for real-time integrated scheduling and nesting in additive manufacturing

Additive Manufacturing (AM) is a promising technology for small-volume and customized production. However, the diversity of parts, coupled with batch scheduling and geometric constraints on heterogeneous machines, poses significant challenges for production planning. Unlike most existing studies on AM scheduling that underestimate geometric features, this paper investigates a real-time integrated scheduling and nesting problem with dynamic batch processing and geometric feasibility to minimize the overall makespan across heterogeneous AM machines. We propose GeoPPO, a geometry-aware deep reinforcement learning approach based on Proximal Policy Optimization (PPO). The proposed approach employs dedicated state encoders and specialized decoders within an actor–critic architecture and potential-based reward shaping strategy to produce geometry-aware decisions for part selection, machine assignment, and batch formulation. Computational experiments are conducted on synthetic and real-world instances with representative AM machine configurations and industrial part geometries. The results show that GeoPPO achieves near-optimal makespan on small-scale instances with an average deviation of 5.3% from the best MILP solutions, while reducing computation time from 1200 s to 1-3 s. With increasing problem scale, GeoPPO outperforms MILP on medium-scale instances, whereas MILP becomes computationally intractable for large-scale problems. Across all instances, GeoPPO reduces makespan by 18.1% relative to the best heuristic, and achieves solution quality comparable to the metaheuristic baseline among GA, ALNS, and GWO, while requiring only about 1% of the computational time. Ablation studies and generalization experiments further demonstrate the efficiency and practical applicability of GeoPPO. This research provides an effective and practical solution paradigm for complex scheduling and nesting challenges in AM.