A multi-plane adaptive-additive algorithm is developed for optimizing computer-generated holograms for the reconstruction of traps in three-dimensional (3D) spaces. This algorithm overcomes the converging stagnation problem of the traditional multi-plane Gerchberg{Saxton algorithm and improves the diffraction efficiency of the holograms effectively. The optimized holograms are applied in a holographic optical tweezers (HOT) platform. Additionally, a computer program is developed and integrated into the HOT platform for the purpose of achieving the interactive control of traps. Experiments demonstrate that the manipulation of micro-particles into the 3D structure with optimized holograms can be carried out effectively on the HOT platform.