2POS-3D: a two-phase optimization strategy for interactive 3D container placement

The placement of irregular three-dimensional components, such as the ones designed for customized packaging, inside a container is a crucial task in the field of CAD-based design. This operation typically involves a number of numerical optimization problems, typically followed by spatial decision process in which designers iteratively, and often manually, evaluate and refine alternative configurations under geometric constraints. This process is often time-consuming, and the final result can be far from optimal. To solve this issue, the present paper proposes 2POS-3D, a two-phase strategy for supporting 3D container placement. In the first phase (called neural stage), a Dynamic Graph Convolutional Neural Network rapidly provides a placement suggestion directly processing point cloud data. This enables real-time visual feedback during design exploration. In the second phase (called evolutionary stage), a Covariance Matrix Adaptation Evolution Strategy optimization procedure refines the initial hypothesis by imposing geometric compatibility and non-penetration constraints. In particular, the neural stage employs a Curvature-Adaptive Normal-Guided Chamfer Distance to emphasize geometrically complex regions during learning. The evolutionary stage implements a computationally efficient Normal-Guided Chamfer variant suitable for real-time refinement. The method is validated against a synthetic dataset of 1000 generated piece–container pairs. The proposed strategy significantly improves over baseline strategies, including pure neural network-based prediction and uninformed evolutionary initialization. In detail, an average Euclidean placement error of 0.06 units and a 96.5% success rate under a 0.2-unit tolerance threshold was in fact reached. The average computation time results in approximately 1.3 s per piece. This is compatible with a possible development in scenarios where rapid placement of parts is required. Finally, additional multi-piece placement experiments demonstrate the possibility of scaling the approach for more complex scenarios.